CS221: HMM and Particle Filters

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

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]

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

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]

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

Sensor Information: Importance Sampling

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]

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:

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]

CS221: HMM and Particle Filters

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CS221: HMM and Particle Filters