Hidden Markov Model

This project is a demonstration of how to use Hidden Markov Models (HMMs) to predict the probability of a given word transitioning to the next word in a sentence. The code is written in Python and uses the hmmlearn library.

Getting Started

To get started with this project, you will need to install the hmmlearn library. You can do this by running the following command: pip install --force-reinstall hmmlearn==0.2.6 Once you have installed the hmmlearn library, you can run the code in a Jupyter notebook or in a Python environment of your choice.

POS Tagging

For this first part of the project, we will use a dataset of sentences and their corresponding POS tags. The dataset is available on Kaggle at the following link: https://www.kaggle.com/code/trunganhdinh/hidden-markov-model-for-pos-tagging/data?select=NER+dataset.csv

The code consists of several parts:

1. Preprocessing the data
2. Computing the transition probability matrix, emission matrix etc.
3. Defining a Hidden Markov Model
4. Calculating the log likelihood of a given sentence

We first preprocess the data by removing the stop words and converting the words to lowercase. We then split the sentences into individual words and store them in a list. We also store the corresponding POS tags in a list.

To create a transition probability matrix, we take a set of sentences and splits them into individual words. We then creates a count matrix that stores the frequency of transitions between words. The count matrix is normalized to get the transition probability matrix.

To define a Hidden Markov Model, we uses the hmmlearn library.

We define the number of hidden states and observable states, and trains the model using the Baum-Welch algorithm. To calculate the log likelihood of a given sentence, we converts a list of words to a list of word ids. Then by iterating through the list of word ids, we calculate the log likelihood of each transition based on the word transition matrix.

Toy Example

The code also includes a toy example that demonstrates how to use Hidden Markov Models. In the example we give, we have 5 hidden states ('happy', 'sad', 'angry', 'calm' and 'disgusted') that relate to the emotions. The observable states are the facial expressions ('smiling', 'frowning', 'grimacing', 'crying' and "neutral").

In this toy example we use the baum_welch algorithm to train the model. The baum_welch algorithm is an iterative algorithm that uses the forward-backward algorithm to calculate the probability of a given sequence of observations. Then we use the viterbi algorithm to calculate the most likely sequence of hidden states that generated a sequence of observations from the transition and emission matrix that we calculated using the baum_welch algorithm. The start probability is defined as follow :

n_hidden_states = len(hidden_emotions)
startprob = np.ones(n_hidden_states) / n_hidden_states