SP11 cs188 lecture 18 -- HMMs I 6PP

SP11 cs188 lecture 18 -- HMMs I 6PP - Announcements CS 188:...

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1 CS 188: Artificial Intelligence Spring 2011 Lecture 18: HMMs and Particle Filtering 4/4/2011 Pieter Abbeel --- UC Berkeley Many slides over this course adapted from Dan Klein, Stuart Russell, Andrew Moore Announcements § W4 out, due next week Monday § P4 out, due next week 2 Announcements § Course contest § Fun! (And extra credit.) § Regular tournaments § Instructions posted soon! 3 Outline § Markov Models ( = a particular Bayes net) § Hidden Markov Models (HMMs) § Representation ( = another particular Bayes net) § Inference § Forward algorithm ( = variable elimination) § Particle filtering ( = likelihood weighting with some tweaks) § Why do we study them? § Widespread use for reasoning over time or space § Concept: Stationary distribution 5 Reasoning over Time § Often, we want to reason about a sequence of observations § Speech recognition § Robot localization § User attention § Medical monitoring § Need to introduce time into our models § Basic approach: hidden Markov models (HMMs) § More general: dynamic Bayes ` nets 6 Markov Models § A Markov model is a chain-structured BN § Each node is identically distributed (stationarity) § Value of X at a given time is called the state § As a BN: § Parameters: called transition probabilities or dynamics, specify how the state evolves over time (also, initial probs) X 2 X 1 X 3 X 4
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2 Conditional Independence § Basic conditional independence: § Past and future independent of the present § Each time step only depends on the previous § This is called the (first order) Markov property § Note that the chain is just a (growing) BN § We can always use generic BN reasoning on it if we truncate the chain at a fixed length X 2 X 1 X 3 X 4 8 Example: Markov Chain § Weather: § States: X = {rain, sun} § Transitions: § Initial distribution: 1.0 sun § What ` s the probability distribution after one step? rain sun 0.9 0.9 0.1 0.1 This are two new representations of a CPT, not BNs! 9 sun rain sun rain 0.1 0.9 0.9 0.1 Query: P(X t ) § Question: probability of being in state x at time t? § Slow answer: § Enumerate all sequences of length t which end in s § Add up their probabilities § = join on X 1 through X t-1 followed by sum over X 1 through X t-1 10 Mini-Forward Algorithm § Question: What ` s P(X) on some day t? § An instance of variable elimination! (In order X 1 , X 2 , ) sun rain sun rain sun rain sun rain Forward simulation 11 Example § From initial observation of sun § From initial observation of rain P( X 1 ) P( X 2 ) P( X 3 ) P( X ) P( X 1 ) P( X 2 ) P( X 3 ) P( X ) 12 Stationary Distributions § If we simulate the chain long enough: § What happens?
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This note was uploaded on 08/26/2011 for the course CS 188 taught by Professor Staff during the Spring '08 term at University of California, Berkeley.

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SP11 cs188 lecture 18 -- HMMs I 6PP - Announcements CS 188:...

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