Markov Chain Monte Carlo

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(X=true | all other variables) Set X to true with that probability Repeat many times. Frequency with which any variable X is true is it’s posterior probability. Converges to true posterior when frequencies stop changing significantly Time to converge is “mixing time”

Markov Blanket Sampling How to calculate Pr(X=true | all other variables) ? Recall: a variable is independent of all others given it’s Markov Blanket parents children other parents of children So problem becomes calculating Pr(X=true | MB(X)) We solve this sub-problem exactly Fortunately, it is easy to solve

Breathing difficulties Smoking Lung disease Heart disease Breathing difficulties

Breathing difficulties Smoking Lung disease Heart disease Breathing difficulties

Breathing difficulties Smoking Lung disease Heart disease Breathing difficulties

Breathing difficulties Smoking Lung disease Heart disease Breathing difficulties

Breathing difficulties Smoking Lung disease Heart disease Breathing difficulties

Breathing difficulties Smoking Lung disease Heart disease Breathing difficulties

Breathing difficulties Smoking Lung disease Heart disease Breathing difficulties

Breathing difficulties Smoking Lung disease Heart disease Breathing difficulties

Breathing difficulties Smoking Lung disease Heart disease Breathing difficulties Let’s Simulate!

Don Patterson, Dieter Fox, Henry Kautz, Matthai Philipose Expressive, Scalable and Tractable Techniques for Modeling Activities of Daily Living Don Patterson, Dieter Fox, Henry Kautz, Matthai Philipose

Our Model of Activities

Our Model of Activities Linear Temporal Ordering of Sub-Activities

Our Model of Activities Unordered Sequence of Object Touches

Our Model of Activities Each object is required with a probability, P(o) (not shown)

Our Model of Activities Optional Gaussian Timing Constraint

Expressive Scalable Tractable 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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