1. Markov Chain Monte Carlo

2. 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”

3. 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

4. Breathing difficulties
Smoking
Lung disease
Heart disease
Breathing difficulties

5. Breathing difficulties
Smoking
Lung disease
Heart disease
Breathing difficulties

6. Breathing difficulties
Smoking
Lung disease
Heart disease
Breathing difficulties

7. Breathing difficulties
Smoking
Lung disease
Heart disease
Breathing difficulties

8. Breathing difficulties
Smoking
Lung disease
Heart disease
Breathing difficulties

9. Breathing difficulties
Smoking
Lung disease
Heart disease
Breathing difficulties

10. Breathing difficulties
Smoking
Lung disease
Heart disease
Breathing difficulties

11. Breathing difficulties
Smoking
Lung disease
Heart disease
Breathing difficulties

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

13. 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

14. Our Model of Activities

15. Our Model of Activities
Linear Temporal Ordering of Sub-Activities

16. Our Model of Activities
Unordered Sequence of Object Touches

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

18. Our Model of Activities
Optional Gaussian Timing Constraint

19. 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)

20. Short Demo
Long Demo