# Exploration of Statistical Language Models

Last Updated on July 25, 2023 by Editorial Team

**Author(s): Anay Dongre**

Originally published on Towards AI.

A Statistical Language Model is a powerful tool used in Natural Language Processing that aims to predict the likelihood of a sequence of words in a given language. In simple terms, it is like having a language genie who can predict the next word you are going to use in a sentence. This model takes into account the probability of the sequence of words based on their occurrence in a corpus of language data. By analyzing a large amount of text data, the model can learn the patterns of how words are used in a language and predict the most likely next word based on those patterns.

## Introduction

Language is the primary mode of communication for humans, and it is the foundation for human expression and interaction. As such, natural language processing (NLP) has emerged as a crucial area of research and development. Statistical Language Models (SLMs) are one of the key techniques in NLP that allow computers to understand and generate natural language. SLMs are based on the idea that language is not a random collection of words but rather a system of rules and patterns. By applying statistical techniques to these patterns, SLMs can learn and predict the probability of certain words and phrases in a given context. This ability to predict the likelihood of different language patterns is what makes SLMs a powerful tool in language processing.

## Background

The development of SLM can be traced back to the 1940s, when the concept of information theory was introduced by Claude Shannon. In the 1950s, the first SLM was proposed by Claude Shannon and Warren Weaver. Since then, SLM has evolved significantly, with advancements in machine learning and natural language processing (NLP).

## Idea behind SLMs

The main idea behind statistical language modeling is to use mathematical and statistical methods to model the probability distribution of sequences of words in natural language. The goal is to create a model that can generate a sentence or a text that is similar to what a human would produce. The model takes into account the relationships between words and the probability of certain word sequences, based on a given training set of texts.

Statistical language modeling is based on the assumption that the probability of a word appearing in a sentence depends on the words that came before it. For example, the probability of the word βcatβ appearing in a sentence is higher if the preceding word is βtheβ rather than βa.β This relationship can be captured using a probabilistic model, which assigns a probability to every possible sequence of words in a language.

The model is trained on a large corpus of texts, which can be either general or specific to a particular domain or application. The goal is to learn the statistical patterns that are characteristic of the language or domain, such as the frequency of certain words or the probability of certain word combinations. The resulting model can then be used to generate new text or to analyze and classify existing text.

## Types of SLMs

There are mainly two types of Statistical Language Models: n-gram models and neural network-based models.

**n-gram Models:**The n-gram models are based on the probability of occurrence of a word given the previous n-1 words. The probability is calculated using the maximum likelihood estimation method. The most commonly used n-gram models are bigram, trigram, and 4-gram models. The bigram model calculates the probability of a word given the previous word, while the trigram model calculates the probability of a word given the previous two words. The 4-gram model calculates the probability of a word given the previous three words.

The formula for the n-gram model can be written as:P(w_nU+007Cw_1,w_2,w_3,β¦,w_n-1) = P(w_nU+007Cw_n-1,w_n-2,β¦,w_n-N+1)

Where: P(w_nU+007Cw_1,w_2,w_3,β¦,w_n-1) is the probability of word w_n given the previous words w_1,w_2,w_3,β¦,w_n-1 P(w_nU+007Cw_n-1,w_n-2,β¦,w_n-N+1) is the probability of word w_n given the previous n-1 words w_n-1,w_n-2,β¦,w_n-N+1

**Neural Network-based Models:**The neural network-based models are based on deep learning techniques and use artificial neural networks to model the probability of the next word in a sequence. The most commonly used neural network-based language models are Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, and Transformers.

RNNs process a sequence of inputs and use the output of the previous step as input for the next step. LSTM networks are a special type of RNN that can retain information over a longer period of time. Transformers are a newer type of neural network-based model that are designed to process input sequences in parallel.

The formula for the neural network-based language model can be written as: P(w_nU+007Cw_1,w_2,w_3,β¦,w_n-1) = f(w_n-1,h_n)

Where: P(w_nU+007Cw_1,w_2,w_3,β¦,w_n-1) is the probability of word w_n given the previous words w_1,w_2,w_3,β¦,w_n-1 f is a function that takes the output of the previous step (w_n-1) and the hidden state of the model (h_n) and outputs the probability of the next word (w_n).

Implementation of Bi-gram Model

`import torch`

import torch.nn as nn

import torch.optim as optim

# Define the training data

corpus = ['this is a sentence', 'another sentence here', 'and yet another sentence']

# Create a vocabulary of all unique words in the corpus

vocab = set()

for sentence in corpus:

for word in sentence.split():

vocab.add(word)

# Assign an index to each word in the vocabulary

word_to_ix = {word: i for i, word in enumerate(vocab)}

# Define the model architecture

class BigramLanguageModel(nn.Module):

def __init__(self, vocab_size, embedding_dim, hidden_dim):

super(BigramLanguageModel, self).__init__()

self.embedding = nn.Embedding(vocab_size, embedding_dim)

self.linear1 = nn.Linear(embedding_dim, hidden_dim)

self.linear2 = nn.Linear(hidden_dim, vocab_size)

def forward(self, inputs):

embeds = self.embedding(inputs)

hidden = self.linear1(embeds)

output = self.linear2(hidden)

return output

# Set hyperparameters

EMBEDDING_DIM = 10

HIDDEN_DIM = 10

LEARNING_RATE = 0.1

NUM_EPOCHS = 100

# Instantiate the model

model = BigramLanguageModel(len(vocab), EMBEDDING_DIM, HIDDEN_DIM)

# Define the loss function and optimizer

loss_function = nn.CrossEntropyLoss()

optimizer = optim.SGD(model.parameters(), lr=LEARNING_RATE)

# Train the model

for epoch in range(NUM_EPOCHS):

total_loss = 0

for sentence in corpus:

# Split the sentence into bigrams

bigrams = [(sentence.split()[i], sentence.split()[i+1]) for i in range(len(sentence.split())-1)]

for bigram in bigrams:

# Convert the bigram to PyTorch tensor format

input = torch.tensor([word_to_ix[bigram[0]]], dtype=torch.long)

target = torch.tensor([word_to_ix[bigram[1]]], dtype=torch.long)

# Zero the gradients, forward pass, compute loss, backward pass, and update parameters

optimizer.zero_grad()

output = model(input)

loss = loss_function(output, target)

loss.backward()

optimizer.step()

total_loss += loss.item()

if epoch % 10 == 0:

print('Epoch {}: Loss = {:.2f}'.format(epoch, total_loss))

*It takes in a corpus of sentences, creates a vocabulary of unique words in the corpus, and assigns an index to each word in the vocabulary. It then defines a neural network with an embedding layer, a linear layer, and an output layer, and trains the network using the bigrams in each sentence. The code uses stochastic gradient descent as the optimizer and cross-entropy loss as the loss function. Finally, the code prints the total loss at each epoch to track the progress of the training.*

## Applications of SLMβs

Statistical Language Models (SLMs) have a wide range of applications in natural language processing (NLP) and computational linguistics. Some of the most common applications of SLMs include:

**Text generation:**SLMs are used to generate coherent and meaningful text sequences by predicting the probability distribution of words in a given context. Text generation applications of SLMs include chatbots, dialogue systems, and automatic text summarization.**Information retrieval:**SLMs are used in information retrieval systems to rank the relevance of documents based on the probability distribution of words in a given query. By modeling the probability distribution of words in both the query and the documents, SLMs can help in retrieving relevant documents based on the similarity of their probability distributions.**Machine translation:**SLMs are widely used in machine translation systems to predict the probability distribution of words in a source language and generate the corresponding translation in a target language. By modeling the probability distribution of words in both the source and target languages, SLMs can help in accurately translating text from one language to another.**Speech recognition:**SLMs can be used to develop language models for automatic speech recognition systems. By modeling the probability distribution of words in a spoken sentence, SLMs can help in accurately recognizing and transcribing spoken words into text.

## Conclusion

As the field of NLP continues to evolve and grow, it is clear that Statistical Language Models will remain a fundamental tool for understanding and processing language. With the help of SLMs, we can continue to push the boundaries of what is possible in language technology and create even more innovative and powerful applications.

## References

- Manning, C. D., & SchΓΌtze, H. (1999). Foundations of statistical natural language processing. MIT press.
- Bengio, Y., Ducharme, R., Vincent, P., & Jauvin, C. (2003). A neural probabilistic language model. Journal of machine learning research, 3(Feb), 1137β1155.
- Chen, S., & Goodman, J. (1999). An empirical study of smoothing techniques for language modeling. Computer speech & language, 13(4), 359β394.
- Jurafsky, D., & Martin, J. H. (2020). Speech and Language Processing. Pearson.

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Published via Towards AI