Kim, Kwonill 2012.07.17

1. Ch8. Approximate inference in switching LDSs using Gaussian mixturesD. BarberBayesian Time Series Models, edited by Barber, Cemgil and Chiappa Kim, Kwonill 2012.07.17

2. Overview • Switching LDS • Intractable exact inference • Exponentially increasing gaussian mixtures • Collapsing gaussian mixtures

3. One system, but different phases

4. Switching LDS • HMM + LDS • Jump Markov Model,

5. Exact Inference is Intractable!! • Stgaussian components!!

6. Problems • Discrete + Continuous • Exponential # of gaussian mixtures • Relation to other methods • Gaussian mixture, not a single gaussian per a switch state

7. Gaussian Sum Filtering Collapsing • For filtering: continuous Gaussian Weight discrete ∝

8. Expectation Correction • For smoothing

9. Demo: Traffic Flow by Traffic Light If sa=1, a→d : a→b = 0.75 : 0.25 If sa=2, a→d If sa=3, a→b If sb=1, b→d : b→c = 0.5 : 0.5 If sa=2, b→c Flow-in to a Flow-out from d

10. Comparison of Smoothing Techniques PF: Particle Filter RBPF: Rao-Blackwellised PF EP: Expectation Propagation GSFS: Gaussian Sum Filtering w/ single Gaussian KimS: Kim’s Smoother w/ GSFS ECS: Expectation Correction w/ single Gaussian GSFM: GSF w/ 4 Gaussians KimM: Kim’s Smoother w/ GSFM ECM: Expectation Correction w/ 4 Gaussians Gibbs: Gibbs Sampling

11. Summary