keywords: Hidden Markov Model, window size / receptive field, bayesian statistics, information theory

Abstract:

Consider an input which has the structure of a Hidden Markov Model (HMM).
The values of each of the hidden variables probabilistically depends only on
the values of the neighboring ones, and these are accessible only through
noisy channels.
In the case of a finite HMM, using belief propagations algorithms, we
calculated analytically in simple cases the probability of correct
detection of a given hidden variable as a function of the size of the HMM.
Using information theory, one thus defines a window size / receptive field
of the HMM, which corresponds to the set of observations which are
relevant to the detection of the given hidden variable.