Measures on Hidden Markov Models

Notes on Hidden Markov Models

A Markov model, or Markov chain, can be viewed as a stochastic finite state automaton in which each transition is labeled with a probability in such a way that the set of transitions from a given state have their probability labels adding up to 1. If in addition each state is labeled with an observable symbol, the probability of a string of symbols [x1, x2, ..., xn] (abbreviated as x1,n) is the...

Tutorial on Hidden Markov Models

Notes on Hidden Markov Models

The model A hidden Markov model is characterized by a set of M states, by an initial probability distribution for the first state, by a transition probability matrix linking successive states, and by a state-dependent probability distribution on the outputs. We represent the state at time t as a multinomial random variable qt, with components q t, for i = 1, . . . ,M . Thus q t is equal to one ...

Characterizing sequence knowledge using online measures and hidden Markov models.

What knowledge do subjects acquire in sequence-learning experiments? How can they express that knowledge? In two sequence-learning experiments, we studied the acquisition of knowledge of complex probabilistic sequences. Using a novel experimental paradigm, we were able to compare reaction time and generation measures of sequence knowledge online. Hidden Markov models were introduced as a novel ...

Metrics and Similarity Measures for Hidden Markov Models

Hidden Markov models were introduced in the beginning of the 1970's as a tool in speech recognition. During the last decade they have been found useful in addressing problems in computational biology such as characterising sequence families, gene finding, structure prediction and phylogenetic analysis. In this paper we propose several measures between hidden Markov models. We give an efficient ...