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Artifacts from Combining Hidden Markov Models

By Rune B. Lyngsø

Abstract

Hidden Markov models (HMMs) have found wide spread use in bioinformatics. In short, an HMM consists of a set of states; each state has a probability distribution over what state to move to next when being in this state (often an HMM is drawn as a directed graph with nodes representing states and edges showing transitions from one state to another with non-zero probability, cf. e.g. Figure 1) and a probability distribution over what symbol is emitted whenever the state is visited (unless the state is silent, in which case no symbol is emitted when the state is visited). In bioinformatics and other areas where we are mainly interested in finite strings, HMMs will usually be equipped with a start state and an end state. One can now think of an HMM as a string generating stochastic machine that starts in the start state; as long as the current state is Figure 1: The transition structure of two simple HMMs with four and five states, respectively, are shown to the left and at the bottom. The transition structure of an HMM ‘combining ’ them is shown above and to the right, with states to which it is not possible to get from the combined starts state or from which it is not possible to get to the combined end state faded. Blue states are start states and red states are end states

Year: 2011
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