Probabilistic Reasoning Over Time CSE P 573 Autumn

Probabilistic Reasoning Over Time CSE P 573 Autumn 2004

questions • What is the Markov assumption? • What is difference between filtering and smoothing? • Is finding the most likely sequence of states the same as finding the sequence of most likely states? What algorithm do you use?

questions • Is a Kalman filter appropriate for discrete or for continuous variables? • What kinds of distributions does it handle?

questions • What is the main advantage of an using an HMM (hidden Markov model) over using a DBN (Dynamic Bayesian Network)? • What is the main advantage of using a DBN over an HMM?

questions • What is a "particle" as used in particle filtering algorithms? • • Go on to Ch 15 slides… Go on to Robotics slides…

Track the Robot

Particle Filtering: Core Idea Initialize particles S randomly with weight 1 For each observation yt { For each particle s S { Choose a sample s’ according to P(Xt=s’|Xt-1=s) s = s’ w(s) = P(Yt=yt|Xt=s) * w(s) }}

Particle Filtering: Resampling After every K-th observation is processed: Randomly select (with replacement) a new set of particles S’ according to the distribution {w(s) | s S} S = S’ For all s S { w(s)=1 } Resampling KILLS unlikely particles Resampling DUPLICATES likely particles

Particle Filtering: Computing the Belief State Compute P(Xt=x | y 1, …, yt) as: Sum( w(s) | s S & value(s)=x ) / Sum( w(s) | s S )

Shakey • Shakey Video