Browsing by Author "Winther, Ole"

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Bayesian inference for spatio-temporal spike-and-slab priors
(2017-12-01) Andersen, Michael Riis; Vehtari, Aki; Winther, Ole; Kai Hansen, Lars
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
In this work, we address the problem of solving a series of underdetermined linear inverse problemblems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the solution in both space and time by imposing a transformed Gaussian process on the spike-and-slab probabilities. An expectation propagation (EP) algorithm for posterior inference under the proposed model is derived. For large scale problems, the standard EP algorithm can be prohibitively slow. We therefore introduce three different approximation schemes to reduce the computational complexity. Finally, we demonstrate the proposed model using numerical experiments based on both synthetic and real data sets.
Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models
(2016-06-01) Vehtari, Aki; Mononen, Tommi; Tolvanen, Ville; Sivula, Tuomas; Winther, Ole
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several Bayesian leave-one-out (LOO) cross-validation approximations that in most cases can be computed with a small additional cost after forming the posterior approximation given the full data. Our main objective is to assess the accuracy of the approximative LOO cross-validation estimators. That is, for each method (Laplace and EP) we compare the approximate fast computation with the exact brute force LOO computation. Secondarily, we evaluate the accuracy of the Laplace and EP approximations themselves against a ground truth established through extensive Markov chain Monte Carlo simulation. Our empirical results show that the approach based upon a Gaussian approximation to the LOO marginal distribution (the so-called cavity distribution) gives the most accurate and reliable results among the fast methods.
Bayesian structure learning for dynamic brain connectivity
(2018-01-01) Andersen, Michael Riis; Winther, Ole; Hansen, Lars Kai; Poldrack, Russell; Koyejo, Oluwasanmi
A4 Artikkeli konferenssijulkaisussa
Human brain activity as measured by fMRI exhibits strong correlations between brain regions which are believed to vary over time. Importantly, dynamic connectivity has been linked to individual differences in physiology, psychology and behavior, and has shown promise as a biomarker for disease. The state of the art in computational neuroimaging is to estimate the brain networks as relatively short sliding window covariance matrices, which leads to high variance estimates, thereby resulting in high overall error. This manuscript proposes a novel Bayesian model for dynamic brain connectivity. Motivated by the underlying neuroscience, the model estimates covariances which vary smoothly over time, with an instantaneous decomposition into a collection of spatially sparse components – resulting in parsimonious and highly interpretable estimates of dynamic brain connectivity. Simulated results are presented to illustrate the performance of the model even when it is mis-specified. For real brain imaging data with unknown ground truth, in addition to qualitative evaluation, we devise a simple classification task which suggests that the estimated brain networks better capture the underlying structure.