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CS221: HMM and Particle Filters

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CS 221: Artificial Intelligence Lecture 5: Hidden Markov Models and Temporal Filtering Sebastian Thrun and Peter Norvig Slide credit: Dan Klein, Michael Pfeiffer
Class-On-A-Slide X 5 X 2 E 1 X 1 X 3 X 4 E 2 E 3 E 4 E 5
Example: Minerva
Example: Robot Localization
Example: Groundhog
Example: Groundhog
Example: Groundhog
Overview ,[object Object],[object Object],[object Object],[object Object]
Reasoning over Time ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Markov Models ,[object Object],[object Object],[object Object],[object Object],[object Object],X 2 X 1 X 3 X 4
Conditional Independence ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],X 2 X 1 X 3 X 4
Example: Markov Chain ,[object Object],[object Object],[object Object],[object Object],[object Object],rain sun 0.9 0.9 0.1 0.1 This is a CPT, not a BN!
Mini-Forward Algorithm ,[object Object],[object Object],sun rain sun rain sun rain sun rain Forward simulation
Example ,[object Object],[object Object],P( X 1 ) P( X 2 ) P( X 3 ) P( X  ) P( X 1 ) P( X 2 ) P( X 3 ) P( X  )
Stationary Distributions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example: Web Link Analysis ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Overview ,[object Object],[object Object],[object Object],[object Object]
Hidden Markov Models ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],X 5 X 2 E 1 X 1 X 3 X 4 E 2 E 3 E 4 E 5
Example: Robot Localization ,[object Object],[object Object],[object Object],1 0 Prob Example from Michael Pfeiffer
Example: Robot Localization ,[object Object],1 0 Prob
Example: Robot Localization ,[object Object],1 0 Prob
Example: Robot Localization ,[object Object],1 0 Prob
Example: Robot Localization ,[object Object],1 0 Prob
Example: Robot Localization ,[object Object],1 0 Prob
Hidden Markov Model ,[object Object],[object Object],[object Object],[object Object],[object Object],X 5 X 2 E 1 X 1 X 3 X 4 E 2 E 3 E 4 E 5
Inference in HMMs (Filtering) E 1 X 1 X 2 X 1
Example ,[object Object],[object Object],[object Object],[object Object]
Example HMM
Example: HMMs in Robotics
Overview ,[object Object],[object Object],[object Object],[object Object]
Example: Robot Localization
Particle Filtering ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],0.0 0.1 0.0 0.0 0.0 0.2 0.0 0.2 0.5
Representation: Particles ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Particles: (3,3) (2,3) (3,3) (3,2) (3,3) (3,2) (2,1) (3,3) (3,3) (2,1)
Particle Filtering: Elapse Time ,[object Object],[object Object],[object Object],[object Object],[object Object]
Particle Filtering: Observe ,[object Object],[object Object],[object Object],[object Object],[object Object]
Particle Filtering: Resample ,[object Object],[object Object],[object Object],[object Object],Old Particles: (3,3) w=0.1 (2,1) w=0.9 (2,1) w=0.9 (3,1) w=0.4 (3,2) w=0.3 (2,2) w=0.4 (1,1) w=0.4 (3,1) w=0.4 (2,1) w=0.9 (3,2) w=0.3 New Particles: (2,1) w=1 (2,1) w=1 (2,1) w=1 (3,2) w=1 (2,2) w=1 (2,1) w=1 (1,1) w=1 (3,1) w=1 (2,1) w=1 (1,1) w=1
Particle Filters
Sensor Information: Importance Sampling
Robot Motion
Sensor Information: Importance Sampling
Robot Motion
Particle Filter Algorithm ,[object Object],[object Object],[object Object]
Particle Filter Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Overview ,[object Object],[object Object],[object Object],[object Object]
Other uses of HMM ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Real HMM Examples ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
HMM Application Domain: Speech ,[object Object],s p ee ch l a b Graphs from Simon Arnfield ’s web tutorial on speech, Sheffield: http://www.psyc.leeds.ac.uk/research/cogn/speech/tutorial/ “ l” to “a” transition:
Time for Questions
Learning Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Learning: Basic Idea ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Let’s first learn a Markov Chain ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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