The Gaussian Variational Approximation of Stochastic Differential Equations

Posted in Science on August 22, 2008


The Gaussian Variational Approximation of Stochastic Differential Equations

Lecture slides:

  • Gaussian Process Approximations to<br>Stochastic Differential Equatio
  • Overview
  • The Variational Method in Bayesian Modeling
  • Gauss-Var: The finite D case
  • Gaussian variational densities
  • Graph
  • GPs with factorising likelihood
  • Graph
  • The infinite case: Stochastic differential equations
  • Goal: Predict latent path & uncertainty
  • The prior measure
  • Taking the limit & Fancy notation
  • The posterior measure
  • Variational approximation
  • Markovian posterior
  • The Kullback Leibler (KL) divergence
  • The KL divergence cont’d7
  • Consistency
  • Lagrange function
  • The full solution
  • Variational Equations
  • Smoothing algorithm
  • Graph
  • Ornstein-Uhlenbeck process
  • Motion in double-well potential
  • Graph
  • ODEs for Lagrange multipliers
  • Variational result and comparison to MCMC
  • A Hamiltonian approach for the ’potential’ case
  • The 1 - D case
  • Data and surface terms
  • Ornstein - Uhlenbeck Process
  • Graph
  • Effective potential
  • Graph
  • Future work

Author: Manfred Opper, University Of Southampton

Watch Video

Tags: Science, Lectures, Computer Science, Machine Learning, VideoLectures.Net, Gaussian Processes