NLP – Word Embeddings – ELMo

ELMo (Embeddings from Language Models) is a deep learning approach for representing words as vectors (also called word embeddings). It was developed by researchers at Allen Institute for Artificial Intelligence and introduced in a paper published in 2018.

ELMo represents words as contextualized embeddings, meaning that the embedding for a word can change based on the context in which it is used. For example, the word “bank” could have different embeddings depending on whether it is used to refer to a financial institution or the edge of a river.

ELMo has been shown to improve the performance of a variety of natural language processing tasks, including language translation, question answering, and text classification. It has become a popular approach for representing words in NLP models, and the trained ELMo embeddings are freely available for researchers to use.

How does ELMo differ from Word2Vec or GloVe?

ELMo (Embeddings from Language Models) is a deep learning approach for representing words as vectors (also called word embeddings). It differs from other word embedding approaches, such as Word2Vec and GloVe, in several key ways:

  • Contextualized embeddings: ELMo represents words as contextualized embeddings, meaning that the embedding for a word can change based on the context in which it is used. In contrast, Word2Vec and GloVe represent words as static embeddings, which do not take into account the context in which the word is used.
  • Deep learning approach: ELMo uses a deep learning model, specifically a bidirectional language model, to generate word embeddings. Word2Vec and GloVe, on the other hand, use more traditional machine learning approaches based on a neural network (Word2Vec) and matrix factorization (GloVe).

To generate context-dependent embeddings, ELMo uses a bi-directional Long Short-Term Memory (LSTM) network trained on a specific task (such as language modeling or machine translation). The LSTM processes the input sentence in both directions (left to right and right to left) and generates an embedding for each word based on its context in the sentence.

Overall, ELMo is a newer approach for representing words as vectors that has been shown to improve the performance of a variety of natural language processing tasks. It has become a popular choice for representing words in NLP models.

What is the model for training ELMo word embeddings?

The model used to train ELMo word embeddings is a bidirectional language model, which is a type of neural network that is trained to predict the next word in a sentence given the context of the words that come before and after it. To train the ELMo model, researchers at Allen Institute for Artificial Intelligence used a large dataset of text, such as news articles, books, and websites. The model was trained to predict the next word in a sentence given the context of the words that come before and after it. During training, the model learns to represent words as vectors (also called word embeddings) that capture the meaning of the word in the context of the sentence.

Explain in details the bidirectional language model

A bidirectional language model is a type of neural network that is trained to predict the next word in a sentence given the context of the words that come before and after it. It is called a “bidirectional” model because it takes into account the context of words on both sides of the word being predicted.

To understand how a bidirectional language model works, it is helpful to first understand how a unidirectional language model works. A unidirectional language model is a type of neural network that is trained to predict the next word in a sentence given the context of the words that come before it.

A unidirectional language model can be represented by the following equation:

P(w[t] | w[1], w[2], …, w[t-1]) = f(w[t-1], w[t-2], …, w[1])

This equation says that the probability of a word w[t] at time t (where time is the position of the word in the sentence) is determined by a function f of the words that come before it (w[t-1], w[t-2], …, w[1]). The function f is learned by the model during training.

A bidirectional language model extends this equation by also taking into account the context of the words that come after the word being predicted:

P(w[t] | w[1], w[2], …, w[t-1], w[t+1], w[t+2], …, w[n]) = f(w[t-1], w[t-2], …, w[1], w[t+1], w[t+2], …, w[n])

This equation says that the probability of a word w[t] at time t is determined by a function f of the words that come before it and the words that come after it. The function f is learned by the model during training.

In practice, a bidirectional language model is implemented as a neural network with two layers: a forward layer that processes the input words from left to right (w[1], w[2], …, w[t-1]), and a backward layer that processes the input words from right to left (w[n], w[n-1], …, w[t+1]). The output of these two layers is then combined and used to predict the next word in the sentence (w[t]). The forward and backward layers are typically implemented as recurrent neural networks (RNNs) or long short-term memory (LSTM) networks, which are neural networks that are designed to process sequences of data.

During training, the bidirectional language model is fed a sequence of words and is trained to predict the next word in the sequence. The model uses the output of the forward and backward layers to generate a prediction, and this prediction is compared to the actual next word in the sequence. The model’s weights are then updated to minimize the difference between the prediction and the actual word, and this process is repeated for each word in the training dataset. After training, the bidirectional language model can be used to generate word embeddings by extracting the output of the forward and backward layers for each word in the input sequence.

ELMo model training algorithm

  1. Initialize the word vectors:
  • The word vectors are usually initialized randomly using a Gaussian distribution.
  • Alternatively, you can use pre-trained word vectors such as Word2Vec or GloVe.
  1. Process the input sequence:
  • Input the sequence of words w[1], w[2], ..., w[t-1] into the forward layer and the backward layer.
  • The forward layer processes the words from left to right, and the backward layer processes the words from right to left.
  • Each layer has its own set of weights and biases, which are updated during training.
  1. Compute the output:
  • The output of the forward layer and the backward layer are combined to form the final output o[t].
  • The final output is used to predict the next word w[t].
  1. Compute the loss:
  • The loss is computed as the difference between the predicted word w[t] and the true word w[t].
  • The loss function is usually the cross-entropy loss, which measures the difference between the predicted probability distribution and the true probability distribution.
  1. Update the weights and biases:
  • The weights and biases of the forward and backward layers are updated using gradient descent and backpropagation.
  1. Repeat steps 2-5 for all words in the input sequence.

ELMo generates contextualized word embeddings by combining the hidden states of a bi-directional language model (BLM) in a specific way.

The BLM consists of two layers: a forward layer that processes the input words from left to right, and a backward layer that processes the input words from right to left. The hidden state of the BLM at each position t is a vector h[t] that represents the context of the word at that position.

To generate the contextualized embedding for a word, ELMo concatenates the hidden states from the forward and backward layers and applies a weighted summation. The hidden states are combined using a task-specific weighting of all biLM layers. The weighting is controlled by a set of learned weights γ_task and a bias term s_task. The ELMo embeddings for a word at position k are computed as a weighted sum of the hidden states from all L layers of the biLM:

ELMo_task_k = E(R_k; Θtask) = γ_task_L * h_LM_k,L + γ_task{L-1} * h_LM_k,{L-1} + … + γ_task_0 * h_LM_k,0 + s_task

Here, h_LM_k,j represents the hidden state at position k and layer j of the biLM, and γ_task_j and s_task are the task-specific weights and bias term, respectively. The task-specific weights and bias term are learned during training, and are used to combine the hidden states in a way that is optimal for the downstream task.

Using ELMo for NLP tasks

ELMo can be used to improve the performance of supervised NLP tasks by providing context-dependent word embeddings that capture not only the meaning of the individual words, but also their context in the sentence.

To use a pre-trained bi-directional language model (biLM) for a supervised NLP task, the first step is to run the biLM and record the layer representations for each word in the input sequence. These layer representations capture the context-dependent information about the words in the sentence, and can be used to augment the context-independent token representation of each word.

In most supervised NLP models, the lowest layers are shared across different tasks, and the task-specific information is encoded in the higher layers. This allows ELMo to be added to the model in a consistent and unified manner, by simply concatenating the ELMo embeddings with the context-independent token representation of each word.

The model then combines the ELMo embeddings with the context-independent token representation to form a context-sensitive representation h_k, typically using either bidirectional RNNs, CNNs, or feed-forward networks. The context-sensitive representation h_k is then used as input to the higher layers of the model, which are task-specific and encode the information needed to perform the target NLP task. It can be helpful to add a moderate amount of dropout to ELMo and to regularize the ELMo weights by adding a regularization term to the loss function. This can help to prevent overfitting and improve the generalization ability of the model.

NLP – Word Embeddings – FastText

What is the FastText method for word embeddings?

FastText is a library for efficient learning of word representations and sentence classification. It was developed by Facebook AI Research (FAIR).

FastText represents each word in a document as a bag of character n-grams. For example, the word “apple” would be represented as the following character n-grams: “a”, “ap”, “app”, “appl”, “apple”, “p”, “pp”, “ppl”, “pple”, “p”, “pl”, “ple”, “l”, “le”. This representation has two advantages:

  1. It can handle spelling mistakes and out-of-vocabulary words. For example, the model would still be able to understand the word “apple” even if it was misspelled as “appel” or “aple”.
  2. It can handle words in different languages with the same script (e.g., English and French) without the need for a separate model for each language.

FastText uses a shallow neural network to learn the word representations from this character n-gram representation. It is trained using the skip-gram model with negative sampling, similar to word2vec.

FastText can also be used for sentence classification by averaging the word vectors for the words in the sentence and training a linear classifier on top of the averaged vector. It is particularly useful for languages with a large number of rare words, or in cases where using a word’s subwords (also known as substrings or character n-grams) as features can be helpful.

How are word embeddings trained in FastText?

Word embeddings in FastText can be trained using either the skip-gram model or the continuous bag-of-words (CBOW) model.

In the skip-gram model, the goal is to predict the context words given a target word. For example, given the input sequence “I have a dog”, the goal would be to predict “have” and “a” given the target word “I”, and to predict “I” given the target word “have”. The skip-gram model learns to predict the context words by minimizing the negative log likelihood of the context words given the target word.

In the CBOW model, the goal is to predict the target word given the context words. For example, given the input sequence “I have a dog”, the goal would be to predict “I” given the context words “have” and “a”, and to predict “have” given the context words “I” and “a”. The CBOW model learns to predict the target word by minimizing the negative log likelihood of the target word given the context words.

Both the skip-gram and CBOW models are trained using stochastic gradient descent (SGD) and backpropagation to update the model’s parameters. The model is trained by minimizing the negative log likelihood of the words in the training data, given the model’s parameters.

Explain how FastText represents each word in a document as a bag of character n-grams

To represent a word as a bag of character n-grams, FastText breaks the word down into overlapping substrings (also known as character n-grams). For example, the word “apple” could be represented as the following character 3-grams (trigrams): [“app”, “ppl”, “ple”]. The number of characters in each substring is specified by the user and is typically set to between 3 and 6 characters.

For example, consider the following sentence:

“I have a dog”

If we set the number of characters in each substring to 3, FastText would represent each word in the sentence as follows:

“I”: [“I”] “have”: [“hav”, “ave”] “a”: [“a”] “dog”: [“dog”]

The use of character n-grams allows FastText to learn good vector representations for rare words, as it can use the vector representations of the character n-grams that make up the rare word to compute its own vector representation. This is particularly useful for handling out-of-vocabulary words that may not have a pre-trained vector representation available.

How are vector representations for each word computed from n-gram vectors?

In FastText, the vector representation for each word is computed as the sum of the vector representations of the character n-grams (subwords) that make up the word. For example, consider the following sentence:

“I have a dog”

If we set the number of characters in each substring to 3, FastText would represent each word in the sentence as a bag of character 3-grams (trigrams) as follows:

“I”: [“I”] “have”: [“hav”, “ave”] “a”: [“a”] “dog”: [“dog”]

FastText would then learn a vector representation for each character n-gram and use these vector representations to compute the vector representation for each word. For example, the vector representation for the word “have” would be computed as the sum of the vector representations for the character n-grams [“hav”, “ave”].

Since there can be huge number of unique n-grams, how does FastText deal with the memory requirement?

One of the ways that FastText deals with the large number of unique character n-grams is by using hashing to map the character n-grams to a fixed-size hash table rather than storing them in a dictionary. This allows FastText to store the character n-grams in a compact form, which can save memory.

What is hashing? How are character sequences hashed to integer values?

Hashing is the process of converting a given input (called the ‘key’) into a fixed-size integer value (called the ‘hash value’ or ‘hash code’). The key is typically some sort of string or sequence of characters, but it can also be a number or other data type.

There are many different ways to hash a character sequence, but most algorithms work by taking the input key, performing some mathematical operations on it, and then returning the hash value as an integer. The specific mathematical operations used will depend on the specific hashing algorithm being used.

One simple example of a hashing algorithm is the ‘modulo’ method, which works as follows:

  1. Take the input key and convert it into a numerical value, for example by assigning each character in the key a numerical value based on its ASCII code.
  2. Divide this numerical value by the size of the hash table (the data structure in which the hashed keys will be stored).
  3. The remainder of this division is the hash value for the key.

This method is simple and fast, but it is not very robust and can lead to a high number of collisions (when two different keys produce the same hash value). More sophisticated algorithms are typically used in practice to improve the performance and reliability of hash tables.

How is the Skip-gram with negative sampling applied in FastText?

Skip-gram with negative sampling (SGNS) algorithm is used to learn high-quality word embeddings (i.e., dense, low-dimensional representations of words that capture the meaning and context of the words). The Skip-gram with negative sampling algorithm works by training a predictive model to predict the context words (i.e., the words that appear near a target word in a given text) given the target word. During training, the model is given a sequence of word pairs (a target word and a context word) and tries to predict the context words given the target words.

To train the model, the SGNS algorithm uses a technique called negative sampling, which involves sampling a small number of negative examples (random words that are not the true context words) and using them to train the model along with the positive examples (the true context words). This helps the model to learn the relationship between the target and context words more efficiently by focusing on the most informative examples.

The SGNS algorithm steps are as following:

  • The embedding for a target word (also called the ‘center word’) is calculated by taking the sum of the embeddings for the word itself and the character n-grams that make up the word.
  • The context words are represented by their word embeddings, without adding the character n-grams.
  • Negative samples are selected randomly from the vocabulary during training, with the probability of selecting a word being proportional to the square root of its unigram frequency (i.e., the number of times it appears in the text).
  • The dot product of the embedding for the center word and the embedding for the context word is calculated. We then need to normalize the similarity scores over all of the context words in the vocabulary, so that the probabilities sum to 1 and form a valid probability distribution.
  • Compute the cross-entropy loss between the predicted and true context words. Use an optimization algorithm such as stochastic gradient descent (SGD) to update the embedding vectors in order to minimize this loss. This involves bringing the actual context words closer to the center word (i.e., the target word) and increasing the distance between the center word and the negative samples.

    The cross-entropy loss function can be expressed as:
  • L = – ∑i(y_i log(p(w_i|c)) + (1 – y_i)log(1 – p(w_i|c)))
  • where:
  • L is the cross-entropy loss.
  • y_i is a binary variable indicating whether context word i is a positive example (y_i = 1) or a negative example (y_i = 0).
  • p(w_i|c) is the probability of context word i given the target word c and its embedding.
  • ∑i indicates that the sum is taken over all context words i in the vocabulary.

FastText and hierarchical softmax

FastText can use a technique called hierarchical softmax to reduce the computation time during training. Hierarchical softmax works by organizing the vocabulary into a binary tree, with the word at the root of the tree and its descendant words arranged in a hierarchy according to their probability of occurrence.

During training, the model uses the hierarchical structure of the tree to compute the loss and update the model weights more efficiently. This is done by traversing the tree from the root to the appropriate leaf node for each word, rather than computing the loss and updating the weights for every word in the vocabulary separately.

The standard softmax function has a computational complexity of O(Kd), where K is the number of classes (i.e., the size of the vocabulary) and d is the number of dimensions in the hidden layer of the model. This complexity arises from the need to normalize the probabilities over all potential classes in order to obtain a valid probability distribution. The hierarchical softmax reduces the computational complexity to O(d*log(K)). Huffman coding can be used to construct a binary tree structure for the softmax function, where the lowest frequency classes are placed deeper into the tree and the highest frequency classes are placed near the root of the tree.

In the hierarchical softmax function, a probability is calculated for each path through the Huffman coding tree, based on the product of the output vector v_n_i of each inner node n and the output value of the hidden layer of the model, h. The sigmoid function is then applied to this product to obtain a probability between 0 and 1.

The idea of this method is to represent the output classes (i.e., the words in the vocabulary) as the leaves on the tree and to use a random walk through the tree to assign probabilities to the classes based on the path taken from the root of the tree. The probability of a certain class is then calculated as the product of the probabilities along the path from the root to the leaf node corresponding to the class.

This allows the hierarchical softmax function to compute the probability of each class more efficiently, since it only needs to consider the path through the tree rather than the entire vocabulary. This can significantly reduce the computational complexity of the model, particularly for large vocabularies, making it practical to train word embeddings on very large datasets.

Hierarchical softmax and conditional probabilities

To compute the probability of each context word given the center word and its embedding using the hierarchical softmax function, we first organize the vocabulary into a binary tree, with the words at the nodes of the tree and their descendant words arranged in a hierarchy according to their probability of occurrence.

We then compute the probability of each context word by traversing the tree from the root to the appropriate leaf node for the word. For each inner node n in the tree, we compute the probability of traversing the left or right branch of the tree as follows:

p(left|n) = sigmoid(v_n_i · h) p(right|n) = 1 – p(left|n)

where:

  • v_n_i is the vector representation of inner node n
  • h is the output value of the hidden layer of the model

The probability of a context word w is then computed as the product of the probabilities of the branches along the path from the root to the leaf node corresponding to w.

NLP – Word Embeddings – GloVe

What are word embeddings?

Word embeddings are a type of representation for text data, which allows words with similar meaning to have a similar representation in a neural network model. Word embeddings are trained such that words that are used in similar contexts will have similar vectors in the embedding space. This is useful because it allows the model to generalize better and makes it easier to learn from smaller amounts of data. Word embeddings can be trained using a variety of techniques, such as word2vec and GloVe, and are commonly used as input to deep learning models for natural language processing tasks.

So are they represented as arrays of numbers?

Yes, word embeddings are typically represented as arrays of numbers. The length of the array will depend on the size of the embedding space, which is a parameter that is chosen when the word embeddings are created. For example, if the size of the embedding space is 50, each word will be represented as a vector of length 50, with each element of the vector representing a dimension in the embedding space.

In a neural network model, these word embedding vectors are typically fed into the input layer of the model, and the rest of the layers in the model are then trained to perform some task, such as language translation or sentiment analysis. The model learns to combine the various dimensions of the word embedding vectors in order to make predictions or decisions based on the input data.

How are word embeddings determined?

There are a few different techniques for determining word embeddings, but the most common method is to use a neural network to learn the embeddings from a large dataset of text. The basic idea is to train a neural network to predict a word given the words that come before and after it in a sentence, using the output of the network as the embedding for the input word. The network is trained on a large dataset of text, and the weights of the network are used to determine the embeddings for each word.

There are a few different variations on this basic approach, such as using a different objective function or incorporating additional information into the input to the network. The specific details of how word embeddings are determined will depend on the specific method being used.

What are the specific methods for generating word embeddings?

Word embeddings are a type of representation for natural language processing tasks in which words are represented as numerical vectors in a high-dimensional space. There are several algorithms for generating word embeddings, including:

  1. Word2Vec: This algorithm uses a neural network to learn the vector representations of words. It can be trained using two different techniques: continuous bag-of-words (CBOW) and skip-gram.
  2. GloVe (Global Vectors): This algorithm learns word embeddings by factorizing a matrix of word co-occurrence statistics.
  3. FastText: This is an extension of Word2Vec that learns word embeddings for subwords (character n-grams) in addition to full words. This allows the model to better handle rare and out-of-vocabulary words.
  4. ELMo (Embeddings from Language Models): This algorithm generates word embeddings by training a deep bi-directional language model on a large dataset. The word embeddings are then derived from the hidden state of the language model.
  5. BERT (Bidirectional Encoder Representations from Transformers): This algorithm is a transformer-based language model that generates contextual word embeddings. It has achieved state-of-the-art results on a wide range of natural language processing tasks.

What is the word2vec CBOW model?

The continuous bag-of-words (CBOW) model is one of the two main techniques used to train the Word2Vec algorithm. It predicts a target word based on the context words, which are the words surrounding the target word in a text.

The CBOW model takes a window of context words as input and predicts the target word in the center of the window. The input to the model is a one-hot vector representation of the context words, and the output is a probability distribution over the words in the vocabulary. The model is trained to maximize the probability of predicting the correct target word given the context words.

During training, the model adjusts the weights of the input-to-output connections in order to minimize the prediction error. Once training is complete, the model can be used to generate word embeddings for the words in the vocabulary. These word embeddings capture the semantic relationships between words and can be used for various natural language processing tasks.

What is the word2vec skip-gram model?

The skip-gram model is the other main technique used to train the Word2Vec algorithm. It is the inverse of the continuous bag-of-words (CBOW) model, which predicts a target word based on the context words. In the skip-gram model, the target word is used to predict the context words.

Like the CBOW model, the skip-gram model takes a window of context words as input and predicts the target word in the center of the window. The input to the model is a one-hot vector representation of the target word, and the output is a probability distribution over the words in the vocabulary. The model is trained to maximize the probability of predicting the correct context words given the target word.

During training, the model adjusts the weights of the input-to-output connections in order to minimize the prediction error. Once training is complete, the model can be used to generate word embeddings for the words in the vocabulary. These word embeddings capture the semantic relationships between words and can be used for various natural language processing tasks.

What are the steps for the GloVe algorithm?

GloVe learns word embeddings by factorizing a matrix of word co-occurrence statistics, which can be calculated from a large corpus of text.

The main steps of the GloVe algorithm are as follows:

  1. Calculate the word co-occurrence matrix: Given a large corpus of text, the first step is to calculate the co-occurrence matrix, which is a symmetric matrix X where each element X_ij represents the number of times word i appears in the context of word j. The context of a word can be defined as a window of words around the word, or it can be the entire document.
  2. Initialize the word vectors: The next step is to initialize the word vectors, which are the columns of the matrix W. The word vectors are initialized with random values.
  3. Calculate the pointwise mutual information (PMI) matrix: The PMI matrix is calculated as follows:

PMI_ij = log(X_ij / (X_i * X_j))

where X_i is the sum of all the elements in the ith row of the co-occurrence matrix, and X_j is the sum of all the elements in the jth column of the co-occurrence matrix. The PMI matrix is a measure of the association between words and reflects the strength of the relationship between them.

  1. Factorize the PMI matrix: The PMI matrix is then factorized using singular value decomposition (SVD) or another matrix factorization technique to obtain the word vectors. The word vectors are the columns of the matrix W.
  2. Normalize the word vectors: Finally, the word vectors are normalized to have unit length.

Once the GloVe algorithm has been trained, the word vectors can be used to represent words in a high-dimensional space. The word vectors capture the semantic relationships between words and can be used for various natural language processing tasks.

How is the matrix factorization performed in GloVe? What is the goal?

The goal of matrix factorization in GloVe is to find two matrices, called the word matrix and the context matrix, such that the dot product of these matrices approximates the co-occurrence matrix. The word matrix contains the word vectors for each word in the vocabulary, and the context matrix contains the context vectors for each word in the vocabulary.

To find these matrices, GloVe minimizes the difference between the dot product of the word and context matrices and the co-occurrence matrix using a least-squares optimization method. This results in word vectors that capture the relationships between words in the corpus.

In GloVe, the objective function that is minimized during matrix factorization is the least-squares error between the dot product of the word and context matrices and the co-occurrence matrix. More specifically, the objective function is given by:


How is the objective function minimized?

In each iteration of SGD, a mini-batch of co-occurrence pairs (i, j) is selected from the co-occurrence matrix, and the gradients of the objective function with respect to the parameters are computed for each pair. The parameters are then updated using these gradients and a learning rate, which determines the step size of the updates.

This process is repeated until the objective function has converged to a minimum or a preset number of iterations has been reached. The process of selecting mini-batches and updating the parameters is often referred to as an epoch. SGD is an efficient method for minimizing the objective function in GloVe because it does not require computing the Hessian matrix, which is the matrix of second-order partial derivatives of the objective function.

When should GloVe be used instead of Word2Vec?

GloVe (Global Vectors) and Word2Vec are two widely used methods for learning word vectors from a large corpus of text. Both methods learn vector representations of words that capture the semantics of the words and the relationships between them, and they can be used in various natural language processing tasks, such as language modeling, information retrieval, and machine translation.

GloVe and Word2Vec differ in the way they learn word vectors. GloVe learns word vectors by factorizing a co-occurrence matrix, which is a matrix that contains information about how often words co-occur in a given corpus. Word2Vec, on the other hand, learns word vectors using a shallow neural network with a single hidden layer.

One advantage of GloVe is that it is computationally efficient, as it does not require training a neural network. This makes it well suited for use with large corpora. However, Word2Vec has been shown to perform better on some tasks, such as syntactic analogies and named entity recognition.

How is the co-occurrence matrix reduced to lower dimensions in GloVe?

In GloVe (Global Vectors), the co-occurrence matrix is not directly reduced to lower dimensions. Instead, the co-occurrence matrix is used to learn word vectors, which are then reduced to lower dimensions using dimensionality reduction techniques, such as principal component analysis (PCA) or t-distributed stochastic neighbor embedding (t-SNE).

To learn word vectors from the co-occurrence matrix in GloVe, the matrix is factorized into two matrices, called the word matrix and the context matrix, using a least-squares optimization method. The word matrix contains the word vectors for each word in the vocabulary, and the context matrix contains the context vectors for each word in the vocabulary.

After the word vectors have been learned, they can be reduced to lower dimensions using dimensionality reduction techniques. For example, PCA can be used to project the word vectors onto a lower-dimensional space, while t-SNE can be used to embed the word vectors in a two-dimensional space for visualization.

It is worth noting that reducing the dimensionality of the word vectors may result in some loss of information, as some of the relationships between words may be lost in the lower-dimensional space. Therefore, it is important to consider the trade-off between the dimensionality of the word vectors and their representational power.

Interpreting GloVe from the Ratio of Co-occurrence Probabilities

GloVe uses the ratio of co-occurrence probabilities to learn the word vectors and context vectors. Specifically, it minimizes the difference between the dot product of the word and context vectors and the log of the ratio of co-occurrence probabilities. This allows GloVe to learn word vectors that capture the meanings and relationships between words in the language.

Chatting with GPT – Natural Language Processing

Let’s talk about natural language processing. How does input text data get transformed to numerical vectors?

In natural language processing (NLP), input text data is often transformed into numerical vectors in order to make it more suitable for machine learning algorithms to work with. There are several methods that can be used to transform text data into numerical vectors, including:

  1. One-hot encoding: This is a simple method that converts each word in the text into a unique integer index, and then represents each word as a binary vector, with a “1” in the position corresponding to the index of the word and “0”s in all other positions. One-hot encoding is a common method for converting text data into numerical vectors, but it can result in very large and sparse vectors, which may not be efficient to work with.
  2. Word embeddings: Word embeddings are numerical vectors that represent the meaning of a word in a continuous, low-dimensional space. Word embeddings can be trained on large datasets of text data using techniques such as word2vec or GloVe, and they can capture the contextual relationships between words and the similarity between words. Word embeddings are a popular method for representing text data in NLP, as they can capture the meaning of words in a compact and dense form.
  3. Bag of words: The bag of words model represents text data as a fixed-length vector, with each element in the vector representing the number of times a particular word appears in the text. The bag of words model is a simple and commonly used method for representing text data, but it does not capture the order or context of the words in the text.

There are many other methods for converting text data into numerical vectors, and the specific method that is used may depend on the specific NLP task and the goals of the model. It is important to choose an appropriate method for representing text data in order to effectively capture the meaning and context of the text.

What are word2vec word embeddings? How are they trained?

Word2vec is a method for training word embeddings, which are numerical vectors that represent the meaning of a word in a continuous, low-dimensional space. Word embeddings are a popular method for representing text data in natural language processing (NLP), as they can capture the meaning of words in a compact and dense form and can be used as input to machine learning algorithms.

Word2vec is a type of neural network model that is trained to predict the context of a word given a set of surrounding words, or to predict a target word given a set of context words. During training, the model is presented with a large dataset of text data and learns to predict the context of a word based on the words that appear around it. The learned model can then be used to generate word embeddings by taking the weights of the model’s hidden layer as the word vectors.

There are two main variants of the word2vec model: continuous bag of words (CBOW) and skip-gram. In the CBOW model, the goal is to predict the target word given a set of context words, while in the skip-gram model, the goal is to predict the context words given a target word.

Word2vec word embeddings can be trained on large datasets of text data using techniques such as stochastic gradient descent (SGD) or negative sampling.

Provide the exact steps for the Word2Vec algorithm, include equations.

Word2Vec is a technique for learning vector representations of words, also known as “word embeddings”, in a way that captures the context and meaning of the words. The basic idea behind Word2Vec is to use the context of words in a text corpus to predict a target word, based on a sliding window of surrounding words. The prediction task is accomplished using a shallow neural network with a single hidden layer.

Here are the steps for the Word2Vec algorithm:

  1. Preprocess the text data: This involves cleaning and formatting the text data, such as lowercasing, stemming, and removing stop words.
  2. Tokenize the text: This involves dividing the text into individual words or tokens.
  3. Build a vocabulary: This involves creating a list of all the unique words in the text data and assigning each word a unique index.
  4. Create word-context pairs: For each word in the text, create a word-context pair by considering a window of surrounding words. For example, if the window size is 2, the word-context pairs for the word “cat” in the sentence “The cat sat on the mat” would be (“cat”, “The”), (“cat”, “sat”), (“cat”, “on”), and (“cat”, “the”).
  5. Train the model: Use the word-context pairs to train a shallow neural network with a single hidden layer. The input layer consists of the context words, and the output layer consists of the target word. The hidden layer contains a set of “neurons” that represent the word embeddings.

The training process involves minimizing the error between the predicted output (the target word) and the true output (the context words) using stochastic gradient descent. The error is measured using a loss function, such as the negative log likelihood loss.

Here is the equation for the negative log likelihood loss:

Loss = -log P(w | c)

where w is the target word and c is the context.

  1. Extract the word embeddings: Once the model is trained, the word embeddings can be extracted from the hidden layer of the neural network. These word embeddings can then be used for various natural language processing tasks, such as text classification, machine translation, and information retrieval.

You mentioned that word2vec can be trained using negative sampling. How does that work?

Yes, that’s correct! In addition to the traditional Word2Vec algorithm that uses the negative log likelihood loss function, there is also a variant called “negative sampling” that can be used to train the model. Negative sampling is a simplified training method that can be used to learn word embeddings more efficiently, especially for large text corpora.

Here’s how negative sampling works:

  1. Preprocess and tokenize the text data as described in the previous steps.
  2. Build a vocabulary and create word-context pairs as described in the previous steps.
  3. Train the model: For each word-context pair, randomly sample a number of negative examples (i.e., words that are not the target word). The objective is to maximize the probability of the target word given the context words, while minimizing the probability of the negative examples given the context words.

The training process involves minimizing the following loss function:

Loss = -log(sigmoid(u_w * v_c)) – ∑log(sigmoid(-u_n * v_c))

where u_w and v_c are the embeddings for the target word and the context words, respectively, and u_n is the embedding for a negative example. The sigmoid function is used to squash the output to a value between 0 and 1.

  1. Extract the word embeddings: Once the model is trained, the word embeddings can be extracted from the hidden layer of the neural network as described in the previous steps.

So when word2vec is trained using negative sampling, that means that just the loss function changes, otherwise stochastic gradient descent is still used?

Yes, that’s correct. When training word2vec using negative sampling, the loss function changes, but the underlying training algorithm, stochastic gradient descent (SGD), remains the same.

In word2vec, the goal is to learn a set of word vectors that can predict the surrounding words in a text. Negative sampling is a variant of the word2vec model that uses a different loss function to achieve this goal. Specifically, it uses a simplified version of the traditional word2vec loss function that only considers a small, randomly-selected subset of the negative examples (words that are not the target word) at each training step, rather than considering all of the negative examples. This allows the model to be trained more efficiently, as it doesn’t need to compute the loss for all of the negative examples at each training step.

SGD is still used to optimize the model’s parameters (the word vectors) by updating them in the direction that reduces the loss. The key difference with negative sampling is that the loss function being optimized is different from the traditional word2vec loss function.

But basically word2vec is trained using a pretty simple neural network, with just one hidden layer

Yes, that’s correct. Word2vec is typically implemented as a shallow neural network with just one hidden layer. The input to the network is a one-hot encoded word, and the hidden layer is a dense (fully-connected) layer with a fixed number of units. The output of the hidden layer is passed through a softmax activation function to produce a probability distribution over the vocabulary, which represents the model’s prediction of the probability of each word in the vocabulary given the input word.

You mentioned that there are two variants of word2vec – CBOW and skip-gram, what is the difference between the two?

In the Continuous Bag-of-Words (CBOW) model, the goal is to predict the current word given the surrounding context. For example, given the context “the cat sat on,” the model would try to predict the word “mat.” CBOW uses a sliding window approach to build up the context from the surrounding words.

On the other hand, the Skip-Gram model does the opposite: it tries to predict the surrounding context given a current word. So in the same example, given the word “mat,” the model would try to predict the context “the cat sat on.” Skip-gram works well with small amounts of data and is faster to train than CBOW.

What is the algorithms for the CBOW model?

The CBOW model uses a neural network with a single hidden layer to predict the current word based on the surrounding context. The input to the model is a one-hot encoded vector representing the context words, and the output is a probability distribution over the vocabulary, with the goal of predicting the target word with the highest probability.

The model is trained using the negative sampling loss function, which tries to maximize the probability of the target word given the context and minimize the probability of randomly sampled negative examples (words that are not the target word).

Here’s a summary of the CBOW algorithm:

  1. Initialize the model weights and biases.
  2. Iterate through each training example, which consists of a target word and a context of surrounding words.
  3. Convert the context words and target word to one-hot encoded vectors.
  4. Calculate the hidden layer activations by taking the dot product of the input vector (one-hot encoded context words) and the input weight matrix, and adding the bias.
  5. Apply the activation function (e.g. sigmoid or ReLU) to the hidden layer activations to get the hidden layer output.
  6. Calculate the output layer activations by taking the dot product of the hidden layer output and the output weight matrix, and adding the bias.
  7. Apply the softmax function to the output layer activations to get the predicted probability distribution over the vocabulary.
  8. Calculate the loss using the negative sampling loss function, which compares the predicted probability of the target word to the actual label (1 for the target word, 0 for the negative samples).
  9. Backpropagate the error and update the model weights and biases using gradient descent.
  10. Repeat steps 2-9 until the model has converged (i.e. the loss is minimized).

The CBOW algorithm uses the negative sampling loss function to train the model. The negative sampling loss function is defined as:

Loss = -(log(sigmoid(u_o * v_c)) + ∑ log(sigmoid(-u_i * v_c)))
where:

  • u_o is the output weight vector for the target word.
  • v_c is the input weight vector for the context words.
  • u_i is the output weight vector for a negative sample (a word that is not the target word).

The first term in the loss function maximizes the probability of the target word given the context, while the second term minimizes the probability of the negative samples.

The sigmoid function is applied to the dot product of the weight vectors to squash the output to a value between 0 and 1, which can be interpreted as a probability. The log function is applied to the sigmoid output to make the loss function smoother and easier to optimize.

The negative sampling loss function is used because it is computationally more efficient than the full softmax loss function, which involves calculating the probabilities of all words in the vocabulary.

Why is the dot product used? What does it represent?

In the word2vec algorithm, the dot product of the input and output weight vectors is used to measure the similarity between the context words and the target word. The dot product is a measure of the angle between two vectors, and it is defined as the product of the magnitudes of the vectors and the cosine of the angle between them.

In the case of word2vec, the input and output weight vectors are learned embeddings for the context words and the target word, respectively. These embeddings are learned during training, and they represent the underlying relationships between the words in the vocabulary.

The dot product of the input and output weight vectors is then used to predict the probability of the target word given the context. If the dot product is high, it means that the angle between the vectors is small, indicating that the context and target words are similar. This results in a high probability for the target word. On the other hand, if the dot product is low, it means that the angle between the vectors is large, indicating that the context and target words are dissimilar. This results in a low probability for the target word.

Overall, the dot product is used in the word2vec algorithm as a measure of similarity between the context words and the target word, which is used to predict the probability of the target word given the context.

What is the algorithm for the skip-gram model?

The Skip-Gram model is a neural network that uses a single hidden layer to predict the surrounding context given a current word. The input to the model is a one-hot encoded vector representing the current word, and the output is a probability distribution over the vocabulary, with the goal of predicting the context words with the highest probability.

The Skip-Gram model is trained using the negative sampling loss function, which tries to maximize the probability of the context words given the current word and minimize the probability of randomly sampled negative examples (words that are not in the context).

Here’s a summary of the Skip-Gram algorithm:

  1. Initialize the model weights and biases.
  2. Iterate through each training example, which consists of a current word and a context of surrounding words.
  3. Convert the current word and context words to one-hot encoded vectors.
  4. Calculate the hidden layer activations by taking the dot product of the input vector (one-hot encoded current word) and the input weight matrix, and adding the bias.
  5. Apply the activation function (e.g. sigmoid or ReLU) to the hidden layer activations to get the hidden layer output.
  6. Calculate the output layer activations by taking the dot product of the hidden layer output and the output weight matrix, and adding the bias.
  7. Apply the softmax function to the output layer activations to get the predicted probability distribution over the vocabulary.
  8. Calculate the loss using the negative sampling loss function, which compares the predicted probabilities of the context words to the actual labels (1 for the context words, 0 for the negative samples).
  9. Backpropagate the error and update the model weights and biases using gradient descent.
  10. Repeat steps 2-9 until the model has converged (i.e. the loss is minimized).

The negative sampling loss function used in the Skip-Gram model is defined as:

Loss = -(∑ log(sigmoid(u_c * v_o)) + ∑ log(sigmoid(-u_i * v_o)))

where:

  • u_c is the output weight vector for a context word.
  • v_o is the input weight vector for the current word.
  • u_i is the output weight vector for a negative sample (a word that is not in the context).

The first term in the loss function maximizes the probability of the context words given the current word, while the second term minimizes the probability of the negative samples.

The sigmoid function is applied to the dot product of the weight vectors to squash the output to a value between 0 and 1, which can be interpreted as a probability. The log function is applied to the sigmoid output to make the loss function smoother and easier to optimize.

The negative sampling loss function is used because it is computationally more efficient than the full softmax loss function, which involves calculating the probabilities of all words in the vocabulary.

In which cases is it better to use the CBOW model vs. Skip-Gram for word2vec?

The Continuous Bag-of-Words (CBOW) model and the Skip-Gram model are two approaches for learning vector representations of words, also known as word embeddings, in natural language processing tasks. These models are trained to predict a target word given the context of surrounding words, using a large corpus of text as input.

The main difference between the CBOW and Skip-Gram models is the way in which they define the context of a word. The CBOW model predicts the target word based on the context provided by the surrounding words, while the Skip-Gram model predicts the surrounding context words based on the target word.

In general, the CBOW model is faster to train and performs better on smaller datasets, while the Skip-Gram model is slower to train but can provide better results on larger datasets. The CBOW model is also better at handling rare words, as it takes into account the context provided by multiple surrounding words, while the Skip-Gram model only considers the context provided by a single target word.

In practice, the choice between the CBOW and Skip-Gram models will depend on the specific application and the available resources. If you have a large dataset and the time and computational resources to train a model, the Skip-Gram model may provide better results. If you have a smaller dataset and need to train a model quickly, the CBOW model may be a better choice.

Chatting with GPT – Neural Networks

Chat GPT link

*NOTE: I have manually modified some of the equations produced by ChatGPT, such as adding a t-1 subscript

Hello, please tell me what is ChatGPT?

ChatGPT is a variant of the GPT (Generative Pre-training Transformer) language model that was specifically designed for use in chatbots and conversational AI systems. It is trained on a large dataset of human-human conversations and is able to generate human-like responses to user input. ChatGPT can be used to build chatbots that can hold natural language conversations with users, helping businesses and organizations automate customer service, sales, and other types of interactions.

Like other GPT models, ChatGPT is a transformer-based language model that uses attention mechanisms to process and generate text. It is trained using a combination of supervised learning, in which the model is given labeled examples of conversation, and unsupervised learning, in which the model is trained to predict the next word in a sequence based on the context of the words that come before it. This allows ChatGPT to learn the patterns and structure of human conversation and generate appropriate responses to user input.

I would like to learn more about machine learning, let’s start with the concept of neural networks. Please explain the concept of a neural network.

A neural network is a type of machine learning model that is inspired by the structure and function of the human brain. It is composed of a large number of interconnected “neurons,” which are simple processing units that receive input, transform it, and produce output.

In a neural network, the input data is fed through a series of hidden layers, each of which is made up of a large number of neurons. These hidden layers process the input data using weighted connections between the neurons. The weights of these connections are adjusted during the training process, allowing the neural network to “learn” from the input data.

The output of the neural network is produced by the output layer, which is also made up of a number of neurons. The output layer takes the processed data from the hidden layers and produces the final output of the neural network.

Neural networks can be used for a wide variety of machine learning tasks, including classification, regression, and clustering. They are particularly powerful for tasks that require the processing of large amounts of data or the detection of patterns and relationships in data that are not immediately apparent.

Overall, the concept of a neural network is a key element of machine learning and is used in many different applications and industries.

How does a neural network look in terms of mathematical equations? What is the architecture?

The architecture of a neural network refers to the way that the neurons are organized and connected within the network. A typical neural network consists of an input layer, one or more hidden layers, and an output layer. The input layer receives the raw input data, and the output layer produces the final output of the network. The hidden layers are located between the input and output layers and are responsible for processing the input data and producing intermediate output that is passed on to the output layer.

In terms of mathematical equations, the computation performed by a neural network can be represented by a series of matrix multiplications and element-wise non-linear functions (also called activation functions).

For example, consider a neural network with one hidden layer and an input layer with m inputs and an output layer with n outputs. Let’s say that the input data is represented by a matrix X with dimensions m x N (where N is the number of data points) and the weights between the input layer and the hidden layer are represented by a matrix W1 with dimensions m x p (where p is the number of neurons in the hidden layer). The output of the hidden layer is then given by:

h = f(XW1 + b1)

where f is the activation function and b1 is a bias term.

The weights between the hidden layer and the output layer are represented by a matrix W2 with dimensions p x n, and the final output of the neural network is given by:

y = f(hW2 + b2)

where b2 is a bias term.

This is just a simple example, but it illustrates the basic idea of how a neural network can be represented mathematically. In practice, neural networks can have many more layers and a much larger number of neurons, and the equations can become quite complex. However, the basic idea of using matrix multiplications and non-linear activation functions to transform the input data and produce output remains the same.

What exactly do you mean by activation function? What are some examples of such functions?

An activation function is a mathematical function that is applied to the output of a neuron in a neural network. It determines whether the neuron will “fire” and produce an output, or whether it will remain inactive. Activation functions are a key component of neural networks because they allow the network to learn non-linear relationships in the data.

There are many different activation functions that can be used in neural networks, each with its own properties and characteristics. Some common examples include:

Sigmoid: The sigmoid function is a smooth, S-shaped curve that maps any input value to a value between 0 and 1. It is often used in the output layer of a binary classification neural network because it can produce a probability-like output.

Tanh: The tanh (hyperbolic tangent) function is also a smooth, S-shaped curve, but it maps input values to a range of -1 to 1. It is similar to the sigmoid function, but it allows for negative output values as well.

ReLU (Rectified Linear Unit): The ReLU function is a piecewise linear function that maps negative input values to 0 and positive input values to the same value. It is a simple and efficient activation function that has been widely adopted in many neural network architectures.

Leaky ReLU: The leaky ReLU function is a variant of the ReLU function that allows a small negative slope for negative input values. This can help prevent the “dying ReLU” problem, in which some neurons in the network become inactive and stop producing output.

Softmax: The softmax function is a generalization of the sigmoid function that is often used in the output layer of a neural network for multi-class classification. It maps the input values to a probability distribution over the different classes, such that the sum of the probabilities is 1.

These are just a few examples of the many activation functions that are used in neural networks. The choice of activation function can have a significant impact on the performance of the network, and different activation functions may be better suited for different types of tasks and data.

So how would I choose an activation function then? Would each layer have a different activation function?

The choice of activation function can have a significant impact on the performance of a neural network, and it is an important design decision that can affect the network’s ability to learn from the data and generalize to new examples.

There is no one-size-fits-all activation function that is best for all situations, and it is often necessary to experiment with different activation functions to find the one that works best for a particular task. In general, it can be helpful to consider the properties of the activation function and how they align with the characteristics of the data and the goals of the task.

For example, if you are building a neural network for a binary classification task, you may want to use a sigmoid or a tanh activation function in the output layer, since these functions can produce a probability-like output between 0 and 1. On the other hand, if you are building a neural network for a multi-class classification task, you may want to use a softmax activation function in the output layer, since it can produce a probability distribution over the different classes.

As for the hidden layers of the network, ReLU and its variants (such as Leaky ReLU) are often a good choice, since they are simple and efficient and have been shown to work well in a wide range of tasks. However, other activation functions may also be suitable, depending on the characteristics of the data and the specific goals of the task.

In general, it is possible to use different activation functions in different layers of a neural network, and this can sometimes be helpful to improve the network’s performance. However, it is also important to be mindful of the complexity of the network and to avoid adding unnecessary complexity that could harm the network’s ability to learn effectively.

So once I have my data inputs, my data outputs, and I choose my activation functions, how do I choose the number of layers in my neural network?

The number of layers in a neural network, as well as the number of neurons in each layer, are important design choices that can impact the network’s ability to learn from the data and generalize to new examples. In general, the more layers and neurons a network has, the more capacity it has to learn from the data. However, too many layers and neurons can also make the network more prone to overfitting, which is when the network performs well on the training data but poorly on new, unseen examples.

There is no hard and fast rule for choosing the number of layers and neurons in a neural network, and it is often necessary to experiment with different configurations to find the one that works best for a particular task. However, there are a few guidelines that you can follow to help you make informed decisions:

  • Start with a small number of layers and neurons and gradually increase them until you see improvements in the network’s performance. This can help you avoid the problem of overfitting, since a smaller network is less likely to overfit the data.
  • Consider the complexity of the task and the amount of data you have available. For more complex tasks or larger datasets, you may need a deeper network (i.e., one with more layers) to learn effectively. On the other hand, for simpler tasks or smaller datasets, a shallower network may be sufficient.
  • Experiment with different architectures and compare the performance of the different models. This can help you identify the best-performing configuration for your task.

Ultimately, the choice of the number of layers and neurons in a neural network is a trade-off between model capacity and generalization. You want to choose a configuration that has enough capacity to learn from the data, but not so much that it overfits the data. Finding the right balance can require some experimentation and trial and error, but with the right approach, you can build a neural network that performs well on your task.

Once I will choose the number of layers, the number of neurons in each layers, the activation functions, how do I train the model then? How will the weights be calculated?

To train a neural network, you need to adjust the weights of the connections between the neurons in such a way that the output of the network is as close as possible to the desired output for a given set of inputs. The process of adjusting the weights to minimize the difference between the predicted output and the desired output is known as optimization.

There are several optimization algorithms that can be used to train a neural network, each with its own pros and cons. Some common optimization algorithms include:

  • Stochastic Gradient Descent (SGD): SGD is a simple and widely-used optimization algorithm that involves updating the weights of the network based on the gradient of the loss function with respect to the weights. The loss function is a measure of how well the network is doing at predicting the desired output given the input data, and the gradient is a vector that points in the direction of the steepest increase in the loss function. SGD involves repeatedly updating the weights in the opposite direction of the gradient, in an attempt to minimize the loss function and improve the performance of the network.
  • Adam (Adaptive Moment Estimation): Adam is a variant of SGD that uses an adaptive learning rate, which means that the step size for updating the weights is adjusted based on the past gradient information. Adam tends to be more efficient and require fewer hyperparameter tuning compared to SGD.
  • Mini-batch gradient descent: Mini-batch gradient descent is a variant of SGD that involves dividing the training data into small batches and updating the weights based on the average of the gradients of the loss function for each batch. This can be more efficient than SGD, especially for large datasets, since it allows the network to learn from the data more quickly.
  • RProp (Resilient Backpropagation): RProp is a variant of SGD that uses a heuristic approach to adjust the learning rate for each weight individually, based on the past gradient information. It is generally faster and more efficient than SGD, and it is often used in large-scale neural network training.

Please explain stochastic gradient descent further, include equations

Stochastic Gradient Descent (SGD) is a widely-used optimization algorithm for training neural networks and other machine learning models. It involves updating the weights of the model based on the gradient of the loss function with respect to the weights. The loss function is a measure of how well the model is doing at predicting the desired output given the input data, and the gradient is a vector that points in the direction of the steepest increase in the loss function.

SGD works by iteratively updating the weights of the model in the opposite direction of the gradient, in an attempt to minimize the loss function and improve the performance of the model. The update rule for SGD can be expressed as follows:

w = w – alpha * gradient

where w is the weight of the model, alpha is the learning rate (a hyperparameter that controls the step size for updating the weights), and gradient is the gradient of the loss function with respect to the weight.

The learning rate is an important hyperparameter in SGD, and it determines the step size for updating the weights. A larger learning rate can lead to faster convergence, but it can also make the optimization process more unstable. On the other hand, a smaller learning rate can lead to slower convergence, but it can also make the optimization process more stable.

SGD can be implemented in a number of ways, and it is often used in conjunction with other techniques, such as mini-batch gradient descent or momentum, to improve the efficiency and stability of the optimization process.

You also mentioned ADAM – Adaptive Moment Estimation, how does this algorithm differ from SGD? Please provide equations.

Adam (Adaptive Moment Estimation) is a variant of Stochastic Gradient Descent (SGD) that uses an adaptive learning rate, which means that the step size for updating the weights is adjusted based on the past gradient information. Adam is a popular optimization algorithm that is often used to train neural networks and other machine learning models.

One of the key differences between Adam and SGD is that Adam uses an exponentially weighted average of the past gradients to scale the learning rate, rather than a fixed learning rate as in SGD. This allows Adam to automatically adjust the learning rate based on the characteristics of the data and the optimization process, which can lead to faster convergence and better performance.

The update rule for Adam can be expressed as follows:

m = beta1 * m_t-1 + (1 – beta1) * gradient

v = beta2 * v_t-1 + (1 – beta2) * gradient^2

w = w_t-1 – alpha * m / (sqrt(v) + epsilon)

where w is the weight of the model, alpha is the learning rate (a hyperparameter that controls the step size for updating the weights), m and v are the exponentially weighted averages of the past gradients and squared gradients, respectively, beta1 and beta2 are hyperparameters that control the decay rate of the moving averages, and epsilon is a small value that is used to prevent division by zero.

Adam uses two moving averages, one for the gradients and one for the squared gradients, which allows it to incorporate both the mean and the variance of the past gradients into the learning rate. This can help to stabilize the optimization process and prevent oscillations or divergences.

You also listed RProp (Resilient Backpropagation) as an optimization algorithms, please explain RProp with equations.

Resilient backpropagation (RProp) is an optimization algorithm used in artificial neural networks for training supervised learning models. It is an extension of the backpropagation algorithm that aims to improve the convergence speed of the training process by adapting the learning rate for each weight in the network during training.

Like backpropagation, RProp uses the gradient of the loss function to update the weights of the network. The gradient is calculated using the chain rule and the weights are updated using the following equation:

weight(t+1) = weight(t) – learning_rate * gradient(t)

In backpropagation, the learning rate is a fixed hyperparameter that is set before training. In RProp, the learning rate is not fixed and is instead adapted for each weight based on the sign of the gradient. In RProp, the learning rate for each weight in the network is updated individually, based on the sign of the gradient of the loss function with respect to that weight. This means that the learning rate for each weight is updated individually based on the convergence of that weight, rather than being updated based on the convergence of all weights in the network. This can improve the convergence speed of the training process, as the learning rate can be adjusted according to the convergence of each weight.

The learning rate is updated using the following equation:

learning_rate(i)_t+1 = learning_rate(i)_t – step_size(i)_t-1 * sng (dE_t-1 / dw(i)_t-1 )

I have also often heard the AdaGrad optimizer mentioned, please explain that to me

In AdaGrad, the learning rate is not fixed and is instead adapted for each weight based on the history of the gradients of the loss function with respect to that weight. Specifically, the learning rate is adjusted based on the sum of the squares of the gradients of the loss function with respect to the weight.

The learning rate for each weight is updated using the following equation:

learning_rate(t+1) = learning_rate(t) / sqrt(sum(gradient(t)^2))

where sum(gradient(t)^2) is the sum of the squares of the gradients of the loss function with respect to the weight up to time t.

This means that the learning rate for each weight is inversely proportional to the sum of the squares of the gradients of the loss function with respect to that weight. This has the effect of decreasing the learning rate for weights that have had large gradients in the past, and increasing the learning rate for weights that have had small gradients in the past.

I have also heard of gradient boosting, explain that

Gradient boosting is a machine learning technique for building predictive models by creating an ensemble of weak learners and combining their predictions to create a stronger, more accurate model. The general idea of gradient boosting is to train a sequence of weak learners (e.g. decision trees) in a stage-wise manner, with each subsequent learner trying to correct the errors made by the previous learner. At each stage, the gradient boosting algorithm fits a new weak learner to the residual errors made by the previous learner. The residual errors are the difference between the true values and the predicted values of the target variable.

In gradient boosting, weights are assigned to the incorrectly classified samples in order to give more importance to the samples that are difficult to classify. This helps the weak learners in the ensemble to focus more on the samples that are most likely to improve the overall performance of the model.

The steps of the gradient boosting algorithm can be summarized in the following equations:

  1. Initialize the ensemble with a single weak learner, such as a decision tree, and make predictions using this learner:

prediction(1) = weak_learner_prediction(1)

  1. Calculate the residual errors between the true values and the predicted values of the target variable:

residual_error(t) = true_value(t) – prediction(t)

  1. Train a new weak learner to predict the residual errors from the previous step:

weak_learner_prediction(t+1) = train(weak_learner, residual_error(t))

  1. Update the predictions of the ensemble by adding the predictions of the new weak learner to the previous predictions:

prediction(t+1) = prediction(t) + weak_learner_prediction(t+1)

  • Repeat steps 2-4 until the desired number of weak learners has been trained.

What is AdaBoost and what are the steps of the algorithm? Include equations.

AdaBoost works by weighting the observations in the training set and adjusting the weight of each observation at each iteration of the algorithm based on the performance of the previous models. The idea behind AdaBoost is to train a sequence of weak learners in an iterative manner, with each learner trying to correct the mistakes of the previous learner. The final model is a weighted average of all the weak models.

Here are the steps of the AdaBoost algorithm:

  1. Initialize the weights of the observations in the training set:
    • At the beginning, all the observations in the training set are given the same weight.
  2. Train a weak learner:
    • Train a weak learner (e.g., a decision tree) on the training set using the current weights of the observations (My note: sample with replacement).
  3. Calculate the error of the weak learner:
    • Calculate the error (my note: total error) on the training set using the following equation:error = sum(weights[i] * I[prediction[i] != y[i]])
    where I is the indicator function that returns 1 if the prediction is incorrect and 0 if the prediction is correct, weights is the array of weights for the observations, prediction is the array of predictions made by the weak learner, and y is the array of true labels for the observations.
  4. Calculate the weight of the weak learner:
    • Calculate the weight of the weak learner using the following equation :
      alpha = 0.5 * log((1 – total error) / total error)
  5. Adjust the weights of the observations:
    • Adjust the weights of the observations using the following equation:
      weights[i+1] = weights[i] * exp(-alpha * I[prediction[i] == y[i]])
  6. Normalize the weights:
    • Normalize the weights so that they sum up to 1.
  7. Repeat steps 2-6:
    • Repeat steps 2-6 a predetermined number of times or until the error of the model becomes small enough.
  8. Return the final model:
    • Return the final model as a weighted average of all the weak models.

My note:

Short note on exp(-alpha * I[prediction[i] == y[i]]) i.e. for misclassification

When the performance is relatively large the last stump did a good job in classifying the records now the new sample weight will be much larger than the old one. When the performance is relatively low the last stump did not do a good job in classifying the records now the new sample weight will only be little larger than the old one.

No misclassification: When the performance is relatively large the last stump did a good job in classifying the records now the new sample weight will be very small than the old one. When the performance is relatively small the last stump did not do a good job in classifying the records now the new sample weight will only be little smaller than the old one.

What is the difference between gradient boosting algorithm and adaptive boosting?

Gradient boosting and adaptive boosting are both ensemble learning algorithms that can be used to improve the performance of a weak learner (a model that performs only slightly better than random guessing) by combining the predictions of multiple weak learners.

The main difference between gradient boosting and adaptive boosting is the way in which the weak learners are trained and combined.

In gradient boosting, the weak learners are trained sequentially, with each learner trying to correct the mistakes of the previous learner. In adaptive boosting (also known as AdaBoost), the weak learners are also trained sequentially, but the training process is different. Each weak learner is trained on a different subset of the training data, and the weights of the training examples are adjusted after each learner is trained to give more weight to the examples that were misclassified. The final prediction is made by combining the predictions of all of the learners using a weighted sum, where the weight of each learner is determined by its accuracy on the training data.

Off-topic, using NLP to summarize Russian propaganda articles on the invasion of Ukraine

I have a pretty simple article summarizer in python that I use for my blog. It’s not machine learning, it’s pretty basic – collecting N articles based on a search query, cleaning up the text, tokenizing, removing stop words. Then word frequencies are calculated and each sentence is scored based on those frequencies. Top N sentences are selected for the summary.

I usually use it to summarize articles on some specific supplements, but today for fun I decided to try a different search query. My query was “путин россия украина спецоперация”. I think that even though this summarizer is pretty simple, the summary turned out to be pretty meaningful. It gives a pretty good overview of what sort of info you would get if you were reading Russian news. I selected the top 15 sentences for the summary.

Что касается слов президента о спецоперации на Донбассе, то они показывают, что наши военнослужащие снова спасают мир от коричневой чумы нацизма, и все поставленные задачи, вне всякого сомнения, будут выполнены. Верховный главнокомандующий еще раз подтвердил, спецоперация на Украине будет доведена до своего логического завершения по тем задачам, которые он озвучил 24 февраля, в день начала СВО», — сказал полковник. И президент в своей речи указал на союзников из Европы, Азии, Африки и Латинской Америки, которые не прогибаются перед так называемым гегемоном, выбирают суверенный путь развития и хотят коллективно решать вопросы безопасности и сформировать многополярный мир.

Украинские издания утверждают, что СНБО одобрил санкции против патриарха Кирилла, а также Сергея Кириенко, Евгения Пригожина, Романа Абрамовича, Олега Дерипаски, Михаила Фридмана, Виктора Медведчука, а также Виктора Януковича. Наш долг перед памятью миллионов жертв Второй мировой войны — жестко реагировать на попытки фальсификации истории, противодействовать распространению любых форм неонацизма, русофобии и расизма», — призвал президент. Все указывает на то, что временной, человеческий, материальный, дипломатический ресурс «спецоперации» близится к исчерпанию, и Путин делает решительный шаг, чтобы закончить как можно скорее, зафиксировав прибыли и убытки. “Наша задача, наша миссия, солдат, ополченцев Донбасса – эту войну прекратить, защитить людей и, конечно, защитить саму Россию”, – подчеркнул Путин.

Выступление Путина демонстрирует готовность Вооруженных сил России довести специальную военную операцию на Украине до победного конца, пояснил URA.RU военный эксперт, ветеран разведки, полковник Анатолий Матвийчук. Война, развязанная Западом и киевской хунтой, будет закончена», — заключил Красов. Российское высокоточное оружие опережает иностранные аналоги на годы и десятилетия, при этом значительно превосходит их по тактико-техническим характеристикам, а оборонная промышленность лежит в основе суверенитета России, отметил президент.

Говоря о шагах со стороны Запада, ранее председатель комиссии Госдумы по расследованию фактов вмешательства иностранных государств во внутренние дела России Василий Пискарев заявлял о том, что зарубежные НКО насаждают радикальные идеологии в российском обществе, сообщает РАПСИ. «Сперва коллективный Запад изощрялся доказать, что якобы „разорвал в клочья“ российскую экономику, теперь там думают, что изолировали нашу страну от всего остального мира. Вооруженные силы России надежно защищают свою страну и несут свободу другим народам, заявил Путин, открывая работу форума «Армия-2022» и Армейских международных игр — 2022. «У России в запасе есть несколько военных вариантов, и для США и их союзников по НАТО эти сценарии — серьезный повод для беспокойства», — пишет журнал. Несмотря на то, что Запад был воодушевлен последними «успехами» ВСУ, генерал США Марк Милли призвал опасаться непредсказуемости России.

Yerba Mate (Ilex Paraguariensis) articles summary using NLP

The following summary was created using a google search for specific phrases and then performing natural language processing steps for sentence scoring. Yerba mate is an evergreen tree/shrub that grows in subtropical regions of South America. The leaves of the plant are used to make tea. Yerba mate tea contains caffeine and theobromine, which are known to affect the mood. I was interested in summarizing the existing articles in regards to research on this plant in psychiatry.

The first search phrase used was “yerba mate psychiatry depression research evidence“, and the number of collected articles for this phrase was 18. The text from all articles was combined, and relative word frequencies were calculated (after removing stop-words). These relative frequencies were then used to score each sentence. Sentence length distribution was checked, and the 90th percentile of 30 words was chosen to select sentences below the maximum length. Below are the 10 highest scoring sentences that summarize the text from the 18 articles.

We can infer from the summary that studies have been performed using the yerba mate extract on rats and tasks for chosen as proxies for the rats’ depression and anxiety levels. There are no mentions of human studies in the summary. Also the chosen sentences indicate that based on these studies, yerba mate has potential antidepressant activity, and it may improve memory as well. The results of the anxiety study were not mentioned and it’s not clear whether there were any side effects from yerba mate. These results are in line with descriptions of personal experiences of reddit users that I have reviewed, as many report better mood and improved focus after drinking yerba mate tea. Some users do report increased anxiety correlated with yerba mate consumption.

View abstract. J Agric.Food Chem. Vitamin C Levels Cerebral vitamin C (ascorbic acid (AA)) levels were determined as described by Jacques-Silva et al. Conclusion: In conclusion, the present study showed that Ilex paraguariensis presents an important effect on reducing immobility time on forced swimming test which could suggest an antidepressant-like effect of this extract. Despite previous some studies show the antidepressant-like activity of flavonoids [31, 32] which are present in the extract of I. paraguariensis, any study has evaluated the possible antidepressant-like activity of it. The presence of nine antioxidants compounds was investigated, namely, gallic acid, chlorogenic acid, caffeic acid, catechin, quercetin, rutin, kaempferol, caffeine, and theobromine. Abstract In this study, we investigated the possible antidepressant-like effect of I. paraguariensis in rats. Another study showed that an infusion of I. paraguariensis can improve the memory of rats treated with haloperidol and this effect was related to an indirect modulation of oxidative stress . In addition to flavonoids as quercetin and rutin and phenolic compounds as chlorogenic and caffeic acids, yerba mate is also rich in caffeine and saponins . After four weeks, behavioral analysis of locomotor activity and anxiety was evaluated in animals receiving water (n = 11) or I. paraguariensis (n = 9). In the same way, we evaluated if the presence of stimulants compounds like caffeine and theobromine in the extract of I. paraguariensis could cause anxiety. In the present study, we evaluated the possible antidepressant-like effect of I. paraguariensis by using forced swimming test (FST) in rats. Forced Swimming Test This experiment was performed using the FST according to the method previously published by Porsolt et al. In this context, Yerba mate (Ilex paraguariensis) is a beverage commonly consumed in South America especially in Argentina, Brazil, Uruguay, and Paraguay. I. paraguariensis reduced the immobility time on forced swimming test without significant changes in locomotor activity in the open field test.

I also tried several other search phrases, such as “yerba mate mood anxiety evidence” and “yerba mate side effects evidence“. In total of 17 articles were collected for the first query and 19 articles for the second query. The summaries are presented below. There was nothing in the summary directly discussing mood or anxiety, but there are mentions of neuroprotective effects and antioxidant effects. We can also learn that a cup of yerba mate tea has similar caffeine content as a cup of coffee, and that drinking yerba mate is not recommended while pregnant or breastfeeding. As in the previous summary, no human trials were mentioned, so it seems that all the summarized studies were performed on rats. The side effects query summary mentions the risk of transferring the caffeine from the tea to the fetus when pregnant, as well as a link to cancer for those who drink both alcohol and yerba mate. It also mentions and anxiety is a side effect of the tea.

Query 1:
View abstract. J Agric.Food Chem. On the other hand, studies conducted on an animal model showed chemopreventive effects of both pure mate saponin fraction and Yerba Mate tea in chemically induced colitis in rats. Yerba Mate Nutrition Facts The following nutrition information is provided by the USDA for one cup (12g) of a branded yerba mate beverage (Mate Revolution) that lists just organic yerba mate as an ingredient. Researchers found that steeping yerba mate (such as in yerba mate tea) may increase the level of absorption. Yerba mate beverages are not recommended for children and women who are pregnant or breastfeeding. Chlorogenic acid and theobromine tested individually also had neuroprotective effects, but slightly weaker than Yerba Mate extract as a whole, but stronger than known neuroprotective compounds, such as caffeine [ 83 ]. The caffeine content in a cup (about 150 mL) of Yerba Mate tea is comparable to that in a cup of coffee and is about 80 mg [ 1 , 11 , 20 ]. In aqueous and alcoholic extracts from green and roasted Yerba Mate, the presence of chlorogenic acid (caffeoylquinic acid), caffeic acid, quinic acid, dicaffeoylquinic acid, and feruloylquinic acid was confirmed. After consumption of Yerba Mate tea, antioxidant compounds are absorbed and appear in the circulating plasma where they exert antioxidant effects [ 55 ]. According to the cited studies, Yerba Mate tea consumption attenuates oxidative stress in patients with type 2 diabetes, which may prevent its complications.

Query 2:
View abstract. J Agric.Food Chem. Because yerba mate has a high concentration of caffeine, drinking mate tea while pregnant can increase the risk of transferring caffeine to the fetus. J Ethnopharmacol. South Med J 1988;81:1092-4.. View abstract. J Am Coll Nutr 2000;19:591-600.. View abstract. Am J Med 2005;118:998-1003.. View abstract. J Psychosom Res 2003;54:191-8.. View abstract. Yerba mate consumed by those who drink alcohol is linked to a higher risk of developing cancer. Anxiety and nervousness are a side effect of excessive yerba mate tea consumption.

NLP: Summarizing l-theanine articles

In this post I will describe my use of NLP (Natural language processing, not neuro-linguistic programming. Natural language processing is cool, while neuro-linguistic programming is some pseudoscience stuff) in the application of summarizing articles from the internet. Specifically, I chose the topic of l-theanine and psychiatry, as previously I have already summarized the Nootropics subreddit discussions on l-theanine. The next step, therefore, is to summarize existing articles on this topic.

Summarizing experience with green tea from the Nootropics subreddit

The first step was to perform an automated Google search for a specific term. I chose the term “l-theanine psychiatry” and set the number of unique urls to be 15. Some of the resulting urls are listed below:

Can L-Theanine Help Treat Symptoms of Bipolar Disorder?

Effects of L-Theanine Administration on Stress-Related Symptoms and Cognitive Functions in Healthy Adults: A Randomized Controlled Trial

L-theanine

How does the tea L-theanine buffer stress and anxiety

It can be seen that the article titles are quite relevant to our topic. The next step is formatting the text and summarizing the information.

The idea behind the summarization technique is calculating word frequencies for each word in the combined text of all articles (after stop words removal), and then selecting words in the top 10% of frequencies. These words will be the ones used in scoring each sentence. More frequent words will be given more importance, as they are deemed more relevant to the chosen topic, therefore sentences containing those words will receive higher scores. This is not a machine learning approach, but a basic frequency count method. In total, 148 words were used for sentence scoring. Some of the most frequent words (from all articles combined) are listed below:

Theanine, administration, effects, placebo, weeks, study, four, sleep, scores, cognitive, may, stress, function, fluency, studies, related, symptoms, participants, bacs, anxiety

BACS was one of the top frequent words, it stands for the Brief Assessment of Cognition in Schizophrenia. Once each sentence was scores, 15 highest scoring sentences were selected in order to create a summary. The summary of the articles is presented below. From the summary we can infer that l-theanine was studied for its effects on cognition, anxiety, and stress. Some studies had positive results, indicating that l-theanine performed significantly better than placebo in regards to positive cognitive effects such as improved verbal fluency and executive function. Studies also noted significant improvements in stress reduction with the use of l-theanine. Other studies did not find any significant differences between l-theanine and placebo.


Second, only about 20% of symptoms (the PSQI subscales) and cognitive functions (the BACS verbal fluency, especially letter fluency and executive function) scores showed significant changes after L- theanine administration compared to the placebo administration, suggesting that the effects are not large on daily function of the participants.

Although psychotropic effects were observed in the current study, four weeks L-theanine administration had no significant effect on cortisol or immunoglobulin A levels in the saliva or serum, which was inconsistent with previous studies reporting that salivary cortisol [34] and immunoglobulin A [33] levels were reduced after acute L-theanine administration.

Considering the comparison to the placebo administration, the current study suggests that the score for the BACS verbal fluency, especially letter fluency, but not the Trail Making Test, Stroop test, or other BACS parameters, significantly changes in response to the 4 weeks effects of L-theanine.

The BACS verbal fluency, especially letter fluency (p = 0.001), and executive function scores were significantly increased after L-theanine administration (p = 0.001 and 0.031, respectively; ), while the Trail Making Test A and B scores were significantly improved after placebo administration (p = 0.042 and 0.038, respectively).

When score reductions in the stress-related symptoms were compared between L-theanine and placebo administrations, changes in the PSQI sleep latency, sleep disturbance, and use of sleep medication subscales were significantly greater (p = 0.0499, 0.046, and 0.047, respectively), while those in the SDS and PSQI scores showed a non-statistically significant trend towards greater improvement (p = 0.084 and 0.073, respectively), during the L-theanine period compared to placebo.

Stratified analyses revealed that scores for verbal fluency (p = 0.002), especially letter fluency (p = 0.002), increased after L-theanine administration, compared to the placebo administration, in individuals who were sub-grouped into the lower half by the median split based on the mean pretreatment scores.

Discussion In this placebo-controlled study, stress-related symptoms assessed with SDS, STAI-T, and PSQI scores decreased, while BACS verbal fluency and executive function scores improved following four weeks L-theanine administration.

The present study aimed to examine the effects of four weeks L-theanine administration (200 mg/day, four weeks) in a healthy population, i.e., individuals without any major psychiatric disorder.

The PSQI subscale scores for sleep latency, sleep disturbance, and use of sleep medication reduced after L-theanine administration, compared to the placebo administration (all p < 0.05).

The effects on stress-related symptoms were broad among the symptom indices presented in the study, although a comparison to the placebo administration somewhat limits the efficacy of L-theanine administration for some sleep disturbance measurements.

For cognitive functions, BACS verbal fluency and executive function scores improved after four weeks L-theanine administration.

PMID: 31623400 This randomized, placebo-controlled, crossover, and double-blind trial aimed to examine the possible effects of four weeks L-theanine administration on stress-related symptoms and cognitive functions in healthy adults.

The anti-stress effects of L-theanine (200 mg/day) have been observed following once- [ 33 , 34 ] and twice daily [ 35 ] administration, while its attention-improving effects have been observed in response to treatment of 100 mg/day on four separate days [ 36 ] and 200 mg/day single administration [ 37 ], which was further supported by decreased responses in functional magnetic resonance imaging [ 38 ].

These results suggest that four weeks L-theanine administration has positive effects on stress-related symptoms and cognitive function in a healthy population.

Summarizing experience with green tea from the Nootropics subreddit

We can’t all get our own labs with grad assistants and grants in order to conduct research, but that doesn’t mean there aren’t other ways to obtain data. Some might say that only studies with randomized trials with test and control groups matter, but I believe that subreddits can provide supplemental information. We should look at the data with a grain of salt, but a lot of people do describe sincerely their experiences with nootropics on reddit. Users also often link studies and scientific articles in the forums.

Not all nootropics are covered by randomized studies and rarely do psychiatrists collect data on experiences with nootropics. For these reasons people mostly discuss their experiences with nootopics and supplements online, in forums such as subreddits and Facebook groups. For example, there have not been many studies on lithium orotate, but probably thousands of people are taking it at the moment. There are very few published papers on this supplement, so how could one find out about possible benefits and side effects? Personally I had a good experience with very small doses of lithium orotate helping to reduce intrusive thoughts and reviving memories from the past. Where does information about my experience exist? Only in the Nootropics and depressionregimens subreddits. No psychiatrist or doctor was ever interested in my experience with microdosing lithium, but that doesn’t mean that this information could not be useful to someone else.

There are multiple Facebook groups specifically dedicated to topics such as treatment resistant depression, PMDD, borderline personality disorder, etc. There are a lot of discussions of supplements in those groups, but unfortunately I don’t know how to obtain data from Facebook. The good thing about reddit is that Reddit offers a free API that allows you to download data from subreddits, so you can get the titles of posts, text, and comments, up to about 1000 posts per subreddit per day. Thank you, Reddit! This is really great!

For this exercise, I decided to use natural language processing to summarize text from the Nootropics subreddit, filtering for posts about green tea. I used the subreddit to filter for posts which contained keywords from the following list: green tea, theanine, ltheanine, matcha, l-theanine, and l theanine. Matcha is a type of green tea powder, therefore still green tea, and l-theanine is a water soluble amino acid found in green tea. In total there were 730 posts in my dataset, with the post created dates ranging from September 2011 to January 2022.

Examples of post titles:

  • L Theanine cured my ( social) anxiety. I’m blown away. I’m usually socially awkward but I MASTERED a job interview.
  • Comprehensive List of GABAA Receptor Anxiolytics That Potentially Produce no Tolerance or Dependence.
  • Green tea supplement ruins man’s liver
  • Neurochemical and behavioral effects of green tea (Camellia sinensis): A model study Increased serotonin and dopamine metabolism
  • Why do 1-2 cups of green tea seem to anecdotally calm so many people down in this subreddit, even though there are only trace amounts of theanine in a cup?

Once the data was collected, the title and body were combined for each post and text processing was performed. Processing included removing accented characters, expanding common contractions, removing newlines, tabs, and special characters. Python’s spellchecker library was used in order to correct spelling errors.

The first summary method used was word frequencies and sentence scoring. All posts were combined together into one document, and the frequency of each word was calculated. In total there were 10,677 unique words/terms, but not each term was meaningful, and some appeared only several times. For this reason, only the top 5% most frequent words were selected in order to be used for sentence scoring. I also assigned higher scores to words green, tea, theanine, ltheanine, and matcha, in order to capture more posts that are more likely to focus on green tea.

The combined text was separated into individual sentences, and sentences were then scored by adding up the scores of each word in the sentences. As mentioned above, the top 5% most frequent words had scores assigned above 0, with the score being equal to the frequency. The remaining words were assigned a score of 0. Some of the most frequent words included anxiety, effects, ltheanine, day, good, sleep, caffeine, depression, tea, help, work, brain, and life.

Here are the resulting top ten sentences. Some resulting sentences were quite long, so I am pasting the sentence parts most relevant to green tea.

L-Theanine: Glutamate inhibitor * Increases glycine by 17.2% for one week * Increases -1-waves within 30-45m orally * At certain dosages, can increase GABA by 19.8% * Antagonizes AMPA and Kainate * [ * Partial co-agonist for NMDA, though significantly less potent than endogenous ligands * Blocks glutamate transporters(and therefore reuptake of glutamate and glutamine) * Not sedative in regular doses but promotes relaxation * Only those who have high baseline anxiety benefit from relaxation * Nontoxic and noncarcinogenic in very high doses (4g/kg).

L-Theanine + Taurine * Anti-excitatory and sedative * Highly bioavailable and consistent * L-Theanine + Taurine + Agmatine * Anti-excitatory and sedative * Highly bioavailable and consistent * Potentiates GABAergic and can suppress NMDA better than theanine * Anti-tolerance building * L-Theanine + Rosmarinic Acid * Both are anti-glutaminergic * Potent GABAA agonist comparable to benzos * Low total formula dose * 400mg L-Theanine + 150mg RA (1875mg Rosemary extract) * Taurine + Ashwagandha * GABAA potentiation of Taurine * NMDA suppression * L-Theanine + Taurine + Ashwagandha * GABAA potentiation of Taurine * Total glutamate suppression * Taurine + Magnolia * GABAA potentiated at benzo site plus influx of GABA in body * Apigenin + Magnolia * GABAA 1 agonist plus PAM * Both very potent * Chinese Skullcap + Magnolia * GABAA 2 + 3 agonist plus PAM * Chinese Skullcap + Apigenin + Magnolia * GABAA 1 + 2 + 3 agonist plus PAM EDIT: Added GABA-T and GAD explanations EDIT 2: Found new and more accurate evidence claiming that L-Theanine is actually an NMDA partial co-agonist, not an antagonist. This backs up sources that claim to see Ca2+ activity increase and become suppressed with NMDA antagonists. It also backs up sources finding L-Theanine to be an NMDA antagonist.

HELPED SOMEWHAT, OR NOT TOO SURE Cyamemazine (anxiety), alimemazine (sleep), magnesium L-threonate and glycinate (sleep), white noise (anxiety), SuperBetter app, vitamin D3, reading about Young schemas, ginkgo biloba (energy, focus), melatonin (sleep), chamomile (sleep), verbena (sleep), lavender (sleep), ALCAR, taurine, NAC, cannabis (sleep), gratitude journal, music (anxiety), coleus forskohlii (weight loss), CLA (from safflower, weight loss), metformin (weight loss, triggered an hypoglycemia the first time I tried it), green tea, risperidone (anxiety, cravings, irritability), L-methylfolate. DID NOT SEEM TO HELP Inositol, chromium picolinate, zinc, CoQ10, apple cider vinegar, meratrim (sphaeranthus indicus + garcinia mangostana), hydroxyzine, tiapride, binaural beats.
L-theanine :** Pretty good anxiolytic, and helps a bit with focus, especially when combined with coffee. Not too sedative.
 **CBD :** When L-theanine or skullcap is not quiet enough, can add some extra anxiolysis, but nothing spectacular either, and not enough on its own.

Medication and supplement augmentation suggestions. My diagnosis is Major Depression/Generalized Anxiety. Possibly on the light end of the Borderline spectrum. I also have Restless Leg Syndrome hence some of the meds. High Cholesterol and stage 2 hypertension. Current regimen is: Bupropion 100mg Lithium Carbonate 300mg (1 in morning, 2 before bed) Gabapentin 300mg (3 times a day) Pramipexole 1mg (at bedtime) Turmeric/bioperine 2000mg x2 Omega 3 Fish Oil 3,600mg x2 Vitamin D3 5,000IU x2 Vitamin C 500mg Multivitamin L-Theanine 200mg Kratom caps (4-6 size 00 about 3 times a week with at least a day between) Tianeptine 25mg (Monday, Wednesday, Friday only) Phenibut (1 size 00 Tuesday/Thursday only).

l-Theanine, Cannabis, Glutamate/GABA and Anxiety: Could this be a potential cure for Cannabis Induced Paranoia and Anxiety? Just a thought – But could Glutamate be responsible for the anxiety and paranoia commonly felt from cannabis? This is just under informed speculation, but THC has been found to increase striatal glutamate in the brain. ( L-Theanine has been found to “block” glutamate signaling in the brain. See here; >L-theanine relieves anxiety in large part because it bears a close resemblance to the brain-signaling chemical glutamate. L-theanine produces the opposite effect in the brain. >While glutamate is the brains most important excitatory neurotransmitter, L-theanine binds to the same brain cell receptors and blocks them to glutamates effects. This action produces inhibitory effects.1,2 That inhibition to brain overactivity has a calming, relaxing effect in which anxiety fades.3 > I have always noticed that when I take L-Theanine, it helps me get higher from cannabis, all while blocking any paranoia and anxiety that I get from it. Cannabis is the only drug I have found that is potentiated by L-Theanine. With other substances, I have noticed that L-Theanine blocks a lot of the pleasurable effects, while reducing anxiety (Namely when taken with stimulants, but also with Phenibut) Since Cannabis increases glutamate in the brain, and Glutamate is associated with anxiety, and L-Theanine essentially blocks it, could L-Theanine be a good anxiety and paranoia cure for weed? Will somebody with more knowledge on this subject help me out here?

How much trouble am I in when I show this to my PsyD? Venturing outside my personal echo chamber to solicit general opinions on my supplement regime. Cognizant that I am doing it wrong, but I will really feel that I am doing it wrong when I start getting grumpy. Please don’t hate me. L-Theanine 200mg L-Carnosine 1000mg Reishi Extract 2000mg Cats Claw 1000mg Alpha-lipoic acid 500mg Ashwagandha 250mg Synapsa Bacopa Monnieri 640mg N-acetyl l-cysteine 1200mg Palmitoylethnolamide 800mg Maitake mushroom extract 3000mg Chaga 3600mg Polygala Tenuifolia 200mg Lions mane 4200mg Acetyl l-carnitine 500mg Sarcosine 2000mg Wulinshen 1000mg.

Caffeine + L-Theanine. Like the beginners guide says, Id recommend this stack for anyone looking to wet their feet with nootropics. The 1 (Caffeine):2 (L-Theanine) ratio works well for me, but in order for me to really feel the L-Theanine I need to take it on a empty stomach. My favorite dosage is 200mg Caffeine and 400mg of L-Theanine immediately before writing. It helps me to be very relaxed, not filter my thoughts, and achieve a flow state. This stack combined with music from MajesticCasual or TheSoundYouNeed YouTube channels is pretty amazing for writing. BTW, for some people 400mg of L-Theanine is too much and may make you drowsy (though not for me). L-Theanine helps reduce anxiety, but I try to make sure I meditate instead of relying on L-Theanine. I save it for when I am writing.

Please give Dosage Guidance: Kava Kava – 700 MG Capsules (This I just ordered to try, not take daily, I have never tried Kava before) – Maybe 1x a day Sulbutiamine Capsules/Tablets 200 MG – 2 Capsules once a day (400 MG 1x a Day) Uridine Monophosphate Capsules 250mg – (500-750 MG 1x a Day) Agmatine Sulfate 250mg Capsules – Maybe start with 2 Capsules 1x a day? Agmatine Sulfate 1000mg Capsules – Only for going up on higher doses. L-Theanine 200 MG – 1x a Day Mens Daily Multimineral Multivitamin Supplement – 1x a Day Vitamin D3 5,000 IU – 1x a day Vitamin B Complex – 1x a day Magnesium Glycinate 400 MG – 1x a Day Omega 3 Fish Oil 4,080mg – EPA 1200mg + DHA 900mg Capsules – 1x a Day Kratom – 4 grams – 3x a day Ashwaghanda – KSM-66, 300mg, 2x a day. Ashwagandha – Sensoril 125mg Do not know dosage? Youtheory Sleep Powder Advanced, 6 Ounce Bottle – It has full doses of a few calming amino acids and some melatonin. TLDR: I want to quit my antidepressants, and purchased a bunch of Supplements to start taking while weaning off my meds, please give me help/tips on this journey, as well as check out the list and let me know if you recommend other supplements to try, or any tips on how to take these.

L-theanine has done wonders for me sleep, anxiety and productivity. With L-t I have had much better sleep due to increased relaxation and reduces anxiety. This has lead to much better and longer sleep, making me really productive at work. It is also helping a lot with anxiety from coffee, it is all but gone now. I just get the nice energy boost and focus boost with no anxiety effect. I usually take 1 or 2 pills of 225mg depending on how i feel. If I feel chill enough, I will only have 1 at night. If I feel the anxiety and neck tightness coming on from coffee I will take another one then.

Supplementation guide to stimulants. As I have some extensive experience with ADHD medication and stims (ADHD-PI diagnosed myself), over the years through research and trial and error I have built a list of supplements that works for mitigating side effects and minimizing comedown while enhancing their intended effects. I read a post about this a couple years ago and wanted to add my own twist to it in hopes of promoting harm reduction. The supplement + stim dosages here given are intended to be used for studying/productivity purposes, although this will still work if you are taking more than the therapeutic amount. If you have any inputs, advice or additions to the list I am happy to add them. Stimulants used for the purposes of studying SHOULD NOT be taken everyday to avoid dopaminergic downregulation. Three times a week at most is recommended to allow the body to regain homeostasis. Stimulants that these supplements can work for include: * Amphetamines (Adderall, Dexamphetamine, Methamphetamine) * Methylphenidates and Analogues (Focalin, Concerta/Ritalin, ethylphenidate, Isopropylphenidate) * Caffeine (Coffee, Tea, Caffeine Pills) (To a certain degree) * Eugeroics (Modafinil, Adrafinil, Armodafinil) (To a certain degree).
*L-Theanine (200mg/1-3x)\\***  (Reduces euphoria/ Reduces Jitters / Lowers Anxiety / Relaxation) (Anecdotal : Amazing supplement if you are an anxiety sensitive person, smooths out the experience) >[Effects of L-theanine on stress related symptoms and cognitive functions in healthy adults].

I think that given then simple method that was used to select these top sentences, the results can be viewed as pretty successful. No neural networks were applied here, only word frequencies were used to generate sentence scores, but by reading the results we can actually learn a lot about green tea as a nootropic. My first observation would be that people mostly talk about l-theanine and not green tea. This makes sense, since the nootropics subreddit is mostly about discussions on supplements in pill form. Another observation is that people try l-theanine hoping to reduce anxiety and improve sleep. Information was provided stating that l-theanine could be reducing anxiety by inhibiting glutamate, an excitatory neurotransmitter. One user mentioned that l-theanine helps them with THC induced paranoia and proposed that THC increases glutamate in the brain and l-theanine in turn decreases anxiety by reducing available glutamate. Other users also mention l-theanine helping them with the anxiety and jitteriness after drinking coffee. In terms of side-effects that were mentioned, sedation and drowsiness were some of them.

In conclusion, I was able to extract a pretty good summary of green tea/l-theanine by using a pretty simple word frequency method. Given that now I have this code, I can just change the supplement keywords and create a similar summary for any other supplement. It’s definitely much faster than scrolling through the subreddit, looking for relevant posts.

Reddit Depression Regimens cont’d

Previous posts on the topic of scraping reddit data from the depressionregiments subreddit:

Reddit Depression Regimens – Topic Modeling

Reddit Depression Regimens – Topic Modeling cont’d

Next we will create some plots with javascript. For example, it would be interesting to see how often specific psychotropic medications and supplements are mentioned in the text data.
Below is a chart with frequencies of the most common antidepressant medications. The counts were performed by combining the frequencies of the brand name and the chemical name (for example Wellbutrin count is wellbutrin (54) + bupropion (27) = 81).

The data was generated using python and exported as a .csv file, with columns ‘term’ and ‘freq’.

HTML part:

<html>
<head>
  https://cdn.plot.ly/plotly-2.0.0.min.js
  https://d3js.org/d3.v5.min.js
  https://cdn.jsdelivr.net/npm/chart.js@2.9.3
  http://script1.js
</head>
<body onload="draw()">
chart 1
<div id="jsdiv" style="border:solid 1px red"></div>
chart 2
<canvas id="chart"></canvas>
</body>

JS part:

function makeChart(meds) {
  // meds is an array of objects where each object is something like

  var hist_labels = meds.map(function(d) {
    return d.term;
  });
  var hist_counts = meds.map(function(d) {
    return +d.freq;
  });

  arrayOfObj = hist_labels.map(function(d, i) {
      return {
        label: d,
        data: hist_counts[i] || 0
      };
    });
  sortedArrayOfObj = arrayOfObj.sort(function(a, b) {
      return b.data - a.data;
    });

   newArrayLabel = [];
   newArrayData = [];
   sortedArrayOfObj.forEach(function(d){
      newArrayLabel.push(d.label);
      newArrayData.push(d.data);
    });


  var chart = new Chart('chart', {
    type: "horizontalBar",
    options: {
      maintainAspectRatio: false,
      legend: {
        display: false
      }
    },
    data: {
      labels: newArrayLabel,
      datasets: [
        {
          data: newArrayData,
          backgroundColor: "#33AEEF"
        }]
    },
    options: {
      scales: {
        yAxes: [{
          scaleLabel: {
            display: true,
            labelString: 'med name'
          }
        }],
        xAxes: [{
            scaleLabel: {
                display: true,
                labelString: 'freq'
            }
        }],
      },
      legend: {
          display: false
      },
      title: {
          display: true,
          text: 'Frequencies of common antidepressants'
        }
    }    
  });
}

// Request data using D3
d3
  .csv("med_list_counts_df.csv")
  .then(makeChart);

We can generate charts with other medication/supplement lists using the same code. Below is a plot with frequencies of common antipsychotics. As you can see, antipsychotics are not mentioned that frequently as antidepressants, and a lot of names in the input list were not mentioned at all (such as haldol or thorazine), and therefore they do not show up in the chart.

Other medications and common supplements mentioned: