8 research outputs found
Expectation propagation for continuous time stochastic processes
We consider the inverse problem of reconstructing the posterior measure over
the trajec- tories of a diffusion process from discrete time observations and
continuous time constraints. We cast the problem in a Bayesian framework and
derive approximations to the posterior distributions of single time marginals
using variational approximate inference. We then show how the approximation can
be extended to a wide class of discrete-state Markov jump pro- cesses by making
use of the chemical Langevin equation. Our empirical results show that the
proposed method is computationally efficient and provides good approximations
for these classes of inverse problems
Fermions and Loops on Graphs. I. Loop Calculus for Determinant
This paper is the first in the series devoted to evaluation of the partition
function in statistical models on graphs with loops in terms of the
Berezin/fermion integrals. The paper focuses on a representation of the
determinant of a square matrix in terms of a finite series, where each term
corresponds to a loop on the graph. The representation is based on a fermion
version of the Loop Calculus, previously introduced by the authors for
graphical models with finite alphabets. Our construction contains two levels.
First, we represent the determinant in terms of an integral over anti-commuting
Grassman variables, with some reparametrization/gauge freedom hidden in the
formulation. Second, we show that a special choice of the gauge, called BP
(Bethe-Peierls or Belief Propagation) gauge, yields the desired loop
representation. The set of gauge-fixing BP conditions is equivalent to the
Gaussian BP equations, discussed in the past as efficient (linear scaling)
heuristics for estimating the covariance of a sparse positive matrix.Comment: 11 pages, 1 figure; misprints correcte
Improving posterior marginal approximations in latent Gaussian models
Contains fulltext :
84349.pdf (preprint version ) (Open Access)AISTATS 2010 : Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistic
Properties of bethe free energies and message passing in gaussian models
Contains fulltext :
92234.pdf (publisher's version ) (Open Access
Efficient Bayesian multivariate fMRI analysis using a sparsifying spatio-temporal prior
Contains fulltext :
84236.pdf (Publisher’s version ) (Closed access)Bayesian logistic regression with a multivariate Laplace prior is introduced as a multivariate approach to the analysis of neuroimaging data. It is shown that, by rewriting the multivariate Laplace distribution as a scale mixture, we can incorporate spatio-temporal constraints which lead to smooth importance maps that facilitate subsequent interpretation. The posterior of interest is computed using an approximate inference method called expectation propagation and becomes feasible due to fast inversion of a sparse precision matrix. We illustrate the performance of the method on an fMRI dataset acquired while subjects were shown handwritten digits. The obtained models perform competitively in terms of predictive performance and give rise to interpretable importance maps. Estimation of the posterior of interest is shown to be feasible even for very large models with thousands of variables