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CS188 Discussion Note Week 10: Hidden Markov Model By Nuttapong Chentanez Goal: Want to reason about a sequence of observation - Speech recognition, Robot localization, Medical monitoring, Human motion synthesis - An HMM is - Initial Distribution: P(X1) - Transition: P(X|X-1) - Emissions: P(E|X) - Independences: 1. future depend only on present 2. Observation depend only on current state Example Markov model - A chain-structured BN - Each node has the same CPT (stationarity) - Value of node is called state - Need P(X1) and P(Xa|Xa-1) - Future and past are independent given present Mini-forward algorithm - What is a probability of being state x at time t? - Brute force, - Better way, cache the value Say, P(R0) = <0.5, 0.5> Filtering/monitoring – computing belief state -Given current belief state, how to update with evidence Example P(R2 | U1, U2) - From initial observation of sun - The longer we simulate, the more the uncertainty accumulates. - For most chain, will end up with a stationary distribution regardless of initial distribution - Therefore, can use Markov Chain to predict for a short time Hidden Markov Model(HMM) -Markov Chain not so useful in practice, because there is no observation -HMM is a Markov Chain with observed output (effects) at each time step Viterbi Algorithm - What is the most likely state sequence given observations? - Could brute-force but slow Example - Observation [true, true, false, true, true]