Hidden Markov Model

A hidden Markov model is a Markov Chain with a single discrete state variable $X_t$ with domain $\set{1,...,S}$ and a single, discrete evidence variable.

The Transition Model

is a single $S\times S$ matrix.

The Sensor Model
$P(e_t\mid X_t=i)$ is an $S$-vector.

The idea is that we can now formulate Markov Inference as matrix calculations (which can be sped up by optimized algorithms).

To make this work we create a diagonal sensor matrix from the Sensor Model vector.

Filtering

Smoothing

Zustandsraum
Emissionen

Sensor Model
Anfangsverteilung

Beispiel Veranschaulichung