---
date: '2024-10-02'
description: observations which are dependent on given Markov process.
id: Hidden Markov model
modified: 2026-06-05 15:08:21 GMT-04:00
tags:
  - seed
  - ml
title: Hidden Markov model
created: '2024-10-02'
published: '2024-10-02'
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slug: thoughts/Hidden-Markov-model
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---
See also [wikipedia](https://en.wikipedia.org/wiki/Hidden_Markov_model)

A Markov model where observations are dependent on a latent [_Markov process_](https://en.wikipedia.org/wiki/Markov_chain) $X$

> \[!abstract\] definition
>
> an HMM has an additional requirement that
> the outcome of $Y$ at time $t = t_0$ must be “influenced” exclusively by the outcome of $X$ at $t = t_0$ and
> that the outcomes of $X$ and $Y$ at $t <t_{0}$ must be <mark>conditionally independent</mark> of
> $Y$ at $t = t_{0}$ given $X$ at time $t = t_{0}$.