Machine Learning Summer School (MLSS), Cambridge 2009

Particle Filters

author: Simon Godsill, University of Cambridge
published: Nov. 2, 2009, recorded: September 2009, views: 8868

Slides

Slides
0:00	Sequential Monte Carlo Methods
1:19	Overview
3:23	In many applications
5:04	When the system is linear
5:12	Contents
8:53	Bayes' Theorem and inference
10:12	Monte Carlo Methods -1
11:21	Monte Carlo Methods -2
11:47	In cases -1
12:09	In cases -2
12:58	In cases -3
14:36	Alternatively -1
15:25	Alternatively -2
16:23	Alternatively -3
16:56	There are numerous versions of Monte Cralo samplers -1
17:20	There are numerous versions of Monte Cralo samplers -2
17:58	Important trick -1
18:03	Important trick -2
18:11	Important trick -3
18:26	state space models, filtering and smoothing
19:16	Note -1
19:56	Note -2
20:52	Note -3
22:13	Summarise as a "state space" or "dynamical" model -1
22:30	Summarise as a "state space" or "dynamical" model -2
23:50	Picture -1
24:15	Example: linear AR model observed in noise
25:31	Form state vector as:
26:11	Picture -2
26:17	Form state vector as:
26:20	Picture -2
26:46	Picture -3
27:01	Alternatively, in terms of state evolution and observation densities -1
27:31	Alternatively, in terms of state evolution and observation densities -2
28:08	Example: Non-linear model
29:23	Estimation tasks
29:56	Specifically: -1
30:30	Specifically: -2
30:42	Specifically: -3
30:50	Picture -4
31:05	Filtering -1
32:30	Filtering -2
33:27	The sequential scheme is as follows:
34:07	Linear Gaussian models
35:21	We can write this equivalenly as: -1
36:03	We can write this equivalenly as: -2
36:21	We first require -2
36:27	Filtering -2
36:47	We first require -2
36:53	We first require -3
37:11	Now from 11 we have -1
37:26	Now from 11 we have -2
37:56	Now from 11 we have -3
38:34	The correction step -1
38:36	Now from 11 we have -3
38:58	The correction step -1
39:19	The correction step -2
39:47	where -1
39:52	where -2
40:01	Hence the whole kalman filtering recursion can be summarised as: -1
40:18	Things you can do with a Kalman filter
41:47	Likelihood evaluation -1
42:39	Likelihood evaluation -2
43:11	Likelihood evaluation -3
43:45	Likelihood evaluation -4
44:58	Numerical methods
45:53	The extended Kalman filter
46:14	Perform a 1st order Taylor expansion
46:59	Monte Carlo Filtering -1
47:46	Example: Non-linear model
49:03	Monte Carlo Filtering -1
49:48	Monte Carlo Filtering -2
50:53	Monte Carlo Filtering -3
51:28	Monte Carlo Filtering -4
52:01	Monte Carlo Filtering -5
52:14	Monte Carlo Filtering -6
52:32	Resampling -1
53:04	Monte Carlo Filtering -6
53:23	Resampling -1
56:03	Resampling -2
56:22	Resampling -3
56:43	Monte Carlo Filtering -5
56:57	Resampling -3
56:59	Sequential Monte Carlo -1
57:27	Sequential Monte Carlo -2
58:04	Sequential Monte Carlo -3
59:04	Sequential Monte Carlo -4
59:46	Sequential Monte Carlo -5
59:55	Sequential Monte Carlo -4
60:30	Sequential Monte Carlo -5
60:54	Sequential Monte Carlo -6
61:40	Sequential Monte Carlo -4
62:07	Sequential Monte Carlo -5
62:11	Sequential Monte Carlo -4
62:16	Sequential Monte Carlo -5
62:19	Sequential Monte Carlo -6
62:25	Sequential Monte Carlo -7
62:28	Three steps -1
62:58	Three steps -2
63:11	Three steps -3
63:24	Three steps -4
63:29	Step 0 -1
64:18	Step 0 -2
64:41	Step 0 -3
65:16	Step 2
66:03	Three steps -1
66:10	Step 2
66:46	Options -1
67:21	Options -2
67:44	A basic algorithm
68:22	Example: standard nonlinear model
69:24	Picture -5
76:31	General Sequential Impportance Sampling
76:54	A basic algorithm
78:43	The importance function -1
79:15	The importance function -2
79:56	Repeated application -1
80:06	Conclusions

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