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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Maximum-entropy Markov model ： ウィキペディア英語版 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. ==Model== Suppose we have a sequence of observations $O\_1,\; \backslash dots,\; O\_n$ that we seek to tag with the labels $S\_1,\; \backslash dots,\; S\_n$that maximize the conditional probability $P(S\_1,\; \backslash dots,\; S\_n\; |\; O\_1,\; \backslash dots,\; O\_n)$. 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: :$P(S\_1,\; \backslash dots,\; S\_n\; |\; O\_1,\; \backslash dots,\; O\_n)\; =\; \backslash prod\_^nP(S\_|S\_,O\_t).$ Each of these transition probabilities come from the same general distribution $P(s|s\text{'},o)$. For each possible label value of the previous label $s\text{'}$, the probability of a certain label $s$ is modeled in the same way as a maximum entropy classifier: :$P(s|s\text{'},o)\; =\; P\_(s|o)\; =\; \backslash frac\backslash exp\backslash left(\backslash sum\_a\backslash lambda\_af\_a(o,s)\backslash right).$ Here, the $f\_a(o,s)$ are real-valued or categorical feature-functions, and $Z(o,s\text{'})$ is a normalization term ensuring that the distribution sums to one. This form for the distribution corresponds to the maximum entropy probability distribution satisfying the constraint that the empirical expectation for the feature is equal to the expectation given the model: :$\backslash operatorname\_e\backslash left()\; =\; \backslash operatorname\_p\backslash left()\; \backslash quad\; \backslash text\; a\; .$ The parameters $\backslash lambda\_a$ can be estimated using generalized iterative scaling. Furthermore, a variant of the Baum–Welch algorithm, which is used for training HMMs, can be used to estimate parameters when training data has incomplete or missing labels.〔 The optimal state sequence $S\_1,\; \backslash dots,\; S\_n$ can be found using a very similar Viterbi algorithm to the one used for HMMs. The dynamic program uses the forward probability: :$\backslash alpha\_(s)\; =\; \backslash sum\_\; \backslash alpha\_t(s\text{'})\; P\_(s|o\_).$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maximum-entropy Markov model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.