Hidden Markov Models

This repository contains the code for a Hidden Markov Model (HMM) built from scratch (using Numpy). The code addresses the three fundamental tasks of HMMs: likelihood, decoding, and learning.

Project structure

This project is organised as follows.

.
├── Hidden Markov Model.ipynb           # notebook to display HMM features
├── hmm.py                              # script containing the core HMM class
└── README.md

Usage

The HiddenMarkovModel class is defined in hmm.py. To instantiate it, simply define the state space, the observation space, and initialized model parameters (transition probabilities, emission probabilities, and initial probabilities).

Below is an example model instantiated using the HiddenMarkovModel class. The hidden states are the weather outdoors (hot, cold), and the observations are the number of ice creams eaten by a certain individual (1, 2, 3).

from hmm import HiddenMarkovModel

states = ["hot", "cold"]  # weather
observations = [1, 2, 3]  # number of ice creams eaten
initial_probs = [0.8, 0.2]
transition_probs = [[0.6, 0.4], [0.5, 0.5]]
emission_probs = [[0.2, 0.4, 0.4], [0.5, 0.4, 0.1]]

model = HiddenMarkovModel(states, observations, transition_probs,
                          emission_probs, initial_probs)

Once instantiated, the three HMM tasks can be addressed using three simple function calls.

observation_sequence = [1, 2, 3, 2, 2, 1, 2]

# task 1 : likelihood (compute likelihood of an observation sequence)
prob = model.likelihood(observation_sequence)

# task 2 : decoding (find the most likely hidden state sequence for an observation sequence)
path, prob = model.decode(observation_sequence)

# task 3 : learning (learn HMM parameters given an observation sequence)
model.learn(observation_sequence, iterations=1)

Acknowledgements

• Hidden Markov Models by Daniel Jurafsky & James H. Martin
• YouTube playlist on HMMs by Prof. Donald J. Patterson