Maximum entropy Markov model

In machine learning, a maximum-entropy Markov model (MEMM), or conditional Markov model (CMM), is a graphical model for sequence labeling that combines features of hidden Markov models (HMMs) and maximum entropy (MaxEnt) models. An MEMM is a discriminative model that extends a standard maximum entropy classifier by assuming that the unknown values to be learnt are connected in a Markov chain rather than being conditionally independent of each other. MEMMs find applications in natural language processing, specifically in part-of-speech tagging and information extraction.

Suppose we have a sequence of observations ${\displaystyle O_{1},\dots ,O_{n}}$ that we seek to tag with the labels ${\displaystyle S_{1},\dots ,S_{n}}$that maximize the conditional probability ${\displaystyle P(S_{1},\dots ,S_{n}|O_{1},\dots ,O_{n})}$. In a MEMM, this probability is factored into Markov transition probabilities, where the probability of transitioning to a particular label depends only on the observation at that position and the previous position's label:

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