1 Chapter 15 Probabilistic Reasoning over Time

2 Outline Time and UncertaintyTime and Uncertainty Inference: Filtering, Prediction, SmoothingInference: Filtering, Prediction, Smoothing Hidden Markov modelsHidden Markov models Brief Introduction to Kalman FiltersBrief Introduction to Kalman Filters Dynamic Bayesian networksDynamic Bayesian networks Particle FilteringParticle Filtering

3 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

4 Markov processes (Markov chains)

5 Example

6 Inference tasks t

7 Filtering

8 Filtering example RtP(Ut) t0.9 f0.2 R t-1 P(R t ) t0.7 f0.3

9 Filtering example R t-1 P(R t ) t0.7 f0.3 RtP(Ut) t0.9 f0.2

10 Smoothing

11 Smoothing example R t-1 P(R t ) t0.7 f0.3 RtP(Ut) t0.9 f0.2

12 Most likely explanation

13 Viterbi example

14 Hidden Markov models

15 Country dance algorithm

16 Country dance algorithm

17 Country dance algorithm

18 Country dance algorithm

19 Kalman Filters

20 Updating Gaussian distributions

21 Simple 1-D example

22 General Kalman update

23 2-D tracking example: Filtering

24 2-D tracking example: smoothing

25 Where it breaks

26

27 Dynamic Bayesian networks

28 DBNs vs. HMMs

29 DBNs vs Kalman Filters

30 Exact inference in DBNs

31 Likelihood weighting for DBNs

32 Particle Filtering

33 Particle Filtering contd.

34 Particle ltering performance

35 Chapter 15, Sections 1-5 Summary