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State transitions in a hidden Markov model (example) ''x'' — hidden states ''y'' — observable outputs ''a'' — transition probabilities ''b'' — output probabilities]] A hidden Markov model ('''HMM''') is a Statistical Model in which the system being modeled is assumed to be a Markov Process with unknown parameters, and the challenge is to determine the hidden parameters from the Observable parameters. The extracted model parameters can then be used to perform further analysis, for example for Pattern Recognition applications. A HMM can be considered as the simplest Dynamic Bayesian Network . In a regular Markov model, the state is directly visible to the observer, and therefore the state transition probabilities are the only parameters. In a ''hidden'' Markov model, the state is not directly visible, but variables influenced by the state are visible. Each state has a probability distribution over the possible output tokens. Therefore the sequence of tokens generated by an HMM gives some information about the sequence of states. Hidden Markov models are especially known for their application in Temporal pattern recognition such as speech, handwriting, gesture recognition, musical score following and Bioinformatics . ARCHITECTURE OF A HIDDEN MARKOV MODEL The diagram below shows the general architecture of an HMM. Each oval shape represents a random variable that can adopt a number of values. The random variable is the value of the hidden variable at time . The random variable is the value of the observed variable at time . The arrows in the diagram (often called a trellis diagram) denote conditional dependencies. From the diagram, it is clear that the value of the hidden variable (at time ) ''only'' depends on the value of the hidden variable (at time ). This is called the Markov Property . Similarly, the value of the observed variable only depends on the value of the hidden variable (both at time ). PROBABILITY OF AN OBSERVED SEQUENCE The probability of observing a sequence of length is given by : where the sum runs over all possible hidden node sequences Although it is straight-forward to compute by matrix multiplication of (submatricies of) the transition matrix, doing so for many real-life problems requires potentialy (very) large amounts of compute storage and compute time. There exist a variety of algorithms that, while not providing exact results, do provide reasonably good results, with considerably less demand on storage and compute time. These include the s, a well-designed application of the Viterbi algorithm will provide results within a fraction of a Decibel of the exact results; a fraction of a decibel is "good enough" in this context. USING HIDDEN MARKOV MODELS There are three Canonical problems associated with HMM:
A concrete example ''This example is further elaborated in the Viterbi Algorithm page.'' Applications of hidden Markov models
HISTORY Hidden Markov Models were first described in a series of statistical papers by Leonard E. Baum and other authors in the second half of the 1960s . One of the first applications of HMMs was Speech Recognition , starting in the mid- 1970s .Rabiner, p. 258 In the second half of the 1980s , HMMs began to be applied to the analysis of biological sequences, in particular DNA . Since then, they have become ubiquitous in the field of Bioinformatics .Durbin et al. SEE ALSO
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