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The Gaussian Variational Approximation of Stochastic Differential Equations
Published on Feb 25, 20077508 Views
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Chapter list
Gaussian Process Approximations to<br>Stochastic Differential Equatio00:03
Overview00:58
The Variational Method in Bayesian Modeling01:52
Gauss-Var: The finite D case05:44
Gaussian variational densities06:40
Graph08:03
GPs with factorising likelihood08:57
Graph10:15
The infinite case: Stochastic differential equations11:12
Goal: Predict latent path & uncertainty12:36
The prior measure14:03
Taking the limit & Fancy notation15:46
The posterior measure17:55
Variational approximation18:46
Markovian posterior20:42
The Kullback Leibler (KL) divergence23:40
The KL divergence cont’d726:00
Consistency26:40
Lagrange function28:17
The full solution29:26
Variational Equations30:22
Smoothing algorithm30:39
Graph31:35
Ornstein-Uhlenbeck process32:23
Motion in double-well potential33:38
Graph34:32
ODEs for Lagrange multipliers35:05
Variational result and comparison to MCMC35:11
A Hamiltonian approach for the ’potential’ case38:21
The 1 - D case39:38
Data and surface terms40:38
Ornstein - Uhlenbeck Process41:04
Graph42:02
Effective potential42:27
Graph42:31
Future work43:36