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Dynamical Systems, Stochastic Processes and Bayesian Inference

The Gaussian Variational Approximation of Stochastic Differential Equations

author:Manfred Opper, University of Southampton
published: Feb. 25, 2007, recorded: December 2006, views: 351

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Slides

Slides
0:03	Gaussian Process Approximations to Stochastic Differential Equatio
0:58	Overview
1:52	The Variational Method in Bayesian Modeling
5:44	Gauss-Var: The finite D case
6:40	Gaussian variational densities
8:03	Graph
8:57	GPs with factorising likelihood
10:15	Graph
11:12	The infinite case: Stochastic differential equations
12:36	Goal: Predict latent path & uncertainty
14:03	The prior measure
15:46	Taking the limit & Fancy notation
17:55	The posterior measure
18:46	Variational approximation
20:42	Markovian posterior
23:40	The Kullback Leibler (KL) divergence
26:00	The KL divergence cont’d7
26:40	Consistency
28:17	Lagrange function
29:26	The full solution
30:22	Variational Equations
30:39	Smoothing algorithm
31:35	Graph
32:23	Ornstein-Uhlenbeck process
33:38	Motion in double-well potential
34:32	Graph
35:05	ODEs for Lagrange multipliers
35:11	Variational result and comparison to MCMC
38:21	A Hamiltonian approach for the ’potential’ case
39:38	The 1 - D case
40:38	Data and surface terms
41:04	Ornstein - Uhlenbeck Process
42:02	Graph
42:27	Effective potential
42:31	Graph
43:36	Future work

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