隐Markov模型.pptVIP

Media Computing CS@BIT * 第四讲 隐Markov模型 北京理工大学计算机系 2003.11 Markov过程与Markov链 Markov过程：具有无后效性的随机过程。即tm时刻所处状态的概率只和tm-1时刻的状态有关，而与tm-1时刻之前的状态无关。比如布朗运动，柏松过程。 Markov链：时间离散，状态离散的马尔可夫（Markov）过程。 转移概率：akl=P(πi=l|πi-1=k) 初始概率 Markov链的参数 Sunny Rain Cloudy State transition matrix : The probability of the weather given the previous days weather. Initial Distribution : Defining the probability of the system being in each of the states at time 0. States : Three states - sunny, cloudy, rainy. Markov链的例子 Each urn contain colored balls and there are 4 distinct colors. Choose an urn according to some random procedure, get a ball from the urn, and record (observe) its color. The ball is replaced. Select a new urn and repeat the above procedure. Colors of selected balls are observed but sequence of choosing urns is hidden. Urn-and-Ball Model Hidden Markov Models-HMM(1) 一个双重随机过程，两个组成部分： ● Markov链：描述状态的转移。 用转移概率 描述 ● 一般随机过程：描述状态与观察序列间的关 系用输出概率 描述 Circles indicate states Arrows indicate probabilistic dependencies between states Green circles are hidden states Dependent only on the previous state “The past is independent of the future given the present.” Purple nodes are observed states Dependent only on their corresponding hidden state HMM (2) N : {s1…sN } are the values for the hidden states M : {o1…oM } are the values for the observations P = {pi} are the initial state probabilities A = {aij} are the state transition probabilities B = {bik} are the observation state probabilities {N, M, P, A, B} A B A A A B B S S S O O O S O S O HMM (3) An HMM, λ, is a 5-tuple consisting of N the number of states M the number of possible observations {?1, ?2, .. ?N} The starting state probabilities P(q0 = Si) = ?i a11 a22 … a1N a21 a22 … a2N : : : aN1 aN2 … aNN b1(1) b1(2) … b1(M) b2(1) b2(2) … b2(M) : : : bN(1) bN(2) … bN(M) The state transition probabilities P(qt+1=Sj | qt=Si)=aij The observation proba