ashutosh saxena lecture 14 - cornell university...ashutosh saxena lecture 14 lecture slides also...
TRANSCRIPT
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Hidden Markov Models
CS4758: Robot Learning
Ashutosh SaxenaAshutosh Saxena
Lecture 14
Lecture slides also taken from Eric
Sudderth and Andrew Moore.
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Target Tracking
Radar-based tracking
of multiple targets
Visual tracking of
articulated objects(L. Sigal et. al., 2006)
• Estimate motion of targets in 3D world from indirect, potentially noisy measurements
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Robot Navigation: SLAMSimultaneous Localization and Mapping
CAD
LandmarkSLAM
(E. Nebot,Victoria Park)
CADMap
EstimatedMap
• As robot moves, estimate its pose & world geometry
(S. Thrun,San Jose Tech Museum)
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Financial Forecasting
• Predict future market behavior from historical data, news reports, expert opinions, …
http://www.steadfastinvestor.com/
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Outline
Introduction to Temporal Processes
� Markov chains
� Hidden Markov models
Discrete-State HMMs
� Inference: Filtering, smoothing, Viterbi, classification� Inference: Filtering, smoothing, Viterbi, classification
� Learning: EM algorithm
Continuous-State HMMs
� Linear state space models: Kalman filters
� Nonlinear dynamical systems: Particle filters
Applications and Extensions
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Example
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Outline
Introduction to Temporal Processes
� Markov chains
� Hidden Markov models
Discrete-State HMMs
� Inference: Filtering, smoothing, Viterbi, classification� Inference: Filtering, smoothing, Viterbi, classification
� Learning: EM algorithm
Continuous-State HMMs
� Linear state space models: Kalman filters
� Nonlinear dynamical systems: Particle filters
Applications and Extensions
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Discrete HMMs: Observations
Discrete Observations
Continuous Observations
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Linear State Space Models
• States & observations jointly Gaussian:� All marginals & conditionals Gaussian
� Linear transformations remain Gaussian
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Simple Linear DynamicsBrownian Motion Constant Velocity
Time Time