Introduction to Hidden Markov Models
نویسنده
چکیده
A. Definition A hidden Markov model is a tool for representing probability distributions over sequences of observations [1]. In this model, an observation Xt at time t is produced by a stochastic process, but the state Zt of this process cannot be directly observed, i.e. it is hidden [2]. This hidden process is assumed to satisfy the Markov property, where state Zt at time t depends only on the previous state, Zt−1 at time t−1. This is, in fact, called the first-order Markov model. The nthorder Markov model depends on the n previous states. Fig. 1 shows a Bayesian network representing the first-order HMM, where the hidden states are shaded in gray. We should note that even though we talk about “time” to indicate that observations occur at discrete “time steps”, “time” could also refer to locations within a sequence [3]. The joint distribution of a sequence of states and observations for the first-order HMM can be written as,
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تاریخ انتشار 2015