# Markov models

## Summary

Markov models are a kind of probabilistic model often used in language modeling. The observations are assumed to follow a Markov chain, where each observation is independent of all past observations given the previous one.

## Context

This concept has the prerequisites:

- Markov chains (Markov models are based on Markov chains.)
- matrix multiplication (Markov models can be conveniently represented using transition matrices.)
- conditional distributions (Markov models are defined in terms of the transition distribution, which is a conditional distribution.)
- conditional independence (Markov models can be defined in terms of a conditional independence property.)

## Core resources (we're sorry, we haven't finished tracking down resources for this concept yet)

## Supplemental resources (the following are optional, but you may find them useful)

## -Paid-

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 13.1, pages 607-610

Additional dependencies:

- d-separation

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Sections 17.2-17.2.2.1, pages 589-593

## See also

- N-gram language models are a commonly used application of Markov models, where the goal is to model the distribution over text.
- Hidden Markov models are a widely used class of probabilistic models where the data are explained in terms of a latent Markov chain.
- Brownian motion is a kind of continuous Markov model.