Chapter 15 Probabilistic Reasoning over Time

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Chapter 15 Probabilistic Reasoning over Time
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Outline

• Time and Uncertainty
• Inference Filtering, Prediction, Smoothing
• Hidden Markov models
• Brief Introduction to Kalman Filters
• Dynamic Bayesian networks
• Particle Filtering

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Time and uncertainty

• The world changes we need to track and predict
  it
• Diabetes management vs vehicle diagnosis
• Basic idea copy state and evidence variables for
  each time step

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Markov processes (Markov chains)
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Example
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Inference tasks
t
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Filtering
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Filtering example
Rt P(Ut)
t 0.9
f 0.2
Rt-1 P(Rt)
t 0.7
f 0.3
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Filtering example
Rt P(Ut)
t 0.9
f 0.2
Rt-1 P(Rt)
t 0.7
f 0.3
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Smoothing
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Smoothing example
Rt-1 P(Rt)
t 0.7
f 0.3
Rt P(Ut)
t 0.9
f 0.2
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Most likely explanation
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Viterbi example
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Hidden Markov models
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Country dance algorithm
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Country dance algorithm
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Country dance algorithm
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Country dance algorithm
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Kalman Filters
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Updating Gaussian distributions
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Simple 1-D example
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General Kalman update
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2-D tracking example Filtering
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2-D tracking example smoothing
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Where it breaks
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Dynamic Bayesian networks
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DBNs vs. HMMs
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DBNs vs Kalman Filters
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Exact inference in DBNs
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Likelihood weighting for DBNs
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Particle Filtering
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Particle Filtering contd.
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Particle ltering performance
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Chapter 15, Sections 1-5 Summary