Markov Chain Monte Carlo

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Markov Chain Monte Carlo
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MCMC with Gibbs Sampling

• Fix the values of observed variables
• Set the values of all non-observed variables
  randomly
• Perform a random walk through the space of
  complete variable assignments. On each move
• Pick a variable X
• Calculate Pr(Xtrue all other variables)
• Set X to true with that probability
• Repeat many times. Frequency with which any
  variable X is true is its posterior probability.
• Converges to true posterior when frequencies stop
  changing significantly
• Time to converge is mixing time

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Markov Blanket Sampling

• How to calculate Pr(Xtrue all other variables)
  ?
• Recall a variable is independent of all others
  given its Markov Blanket
• parents
• children
• other parents of children
• So problem becomes calculating Pr(Xtrue MB(X))
• We solve this sub-problem exactly
• Fortunately, it is easy to solve

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Smoking
Lungdisease
Heartdisease
Breathingdifficulties
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Smoking
Lungdisease
Heartdisease
Breathingdifficulties
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Smoking
Lungdisease
Heartdisease
Breathingdifficulties
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Smoking
Lungdisease
Heartdisease
Breathingdifficulties
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Smoking
Lungdisease
Heartdisease
Breathingdifficulties
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Smoking
Lungdisease
Heartdisease
Breathingdifficulties
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Smoking
Lungdisease
Heartdisease
Breathingdifficulties
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Smoking
Lungdisease
Heartdisease
Breathingdifficulties
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Smoking
Lungdisease
Heartdisease
Breathingdifficulties
Lets Simulate!
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Expressive, Scalable and Tractable Techniques for
Modeling Activities of Daily Living

• Don Patterson, Dieter Fox, Henry Kautz, Matthai
  Philipose

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Our Model of Activities
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Our Model of Activities
Linear Temporal Ordering of Sub-Activities
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Our Model of Activities
Unordered Sequence of Object Touches
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Our Model of Activities
Each object is required with a probability,
P(o) (not shown)
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Our Model of Activities
Optional Gaussian Timing Constraint
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• Expressive
• General and intuitive way to specify activities
• Scalable
• We mine these models from the web
• Tractable
• We convert models to Dynamic Bayesian Networks
• We reason in real-time using stochastic
  Monte-Carlo techniques (particle filters)

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Short Demo
Long Demo