arXiv subjects

Alexis Roche

Publications and source records attributed to Alexis Roche.

5 recordsLinked to original sources

arXiv2016

On numerical approximation schemes for expectation propagation

Several numerical approximation strategies for the expectation-propagation algorithm are studied in the context of large-scale learning: the Laplace method, a faster variant of it, Gaussian quadrature, and a deterministic version of variational sampling (i.e., combining quadrature with variational approximation). Experiments in training linear binary classifiers show that the expectation-propagation algorithm converges best using variational sampling, while it also converges well using Laplace-style methods with smooth factors but tends to be unstable with non-differentiable ones. Gaussian quadrature yields unstable behavior or convergence to a sub-optimal solution in most experiments.

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arXiv2015

Composite Bayesian inference

We revisit and generalize the concept of composite likelihood as a method to make a probabilistic inference by aggregation of multiple Bayesian agents, thereby defining a class of predictive models which we call composite Bayesian. This perspective gives insight to choose the weights associated with composite likelihood, either a priori or via learning; in the latter case, they may be tuned so as to minimize prediction cross-entropy, yielding an easy-to-solve convex problem. We argue that composite Bayesian inference is a middle way between generative and discriminative models that trades off between interpretability and prediction performance, both of which are crucial to many artificial intelligence tasks.

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arXiv2013

Approximate inference via variational sampling

A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model by minimizing a strongly consistent empirical approximation to the Kullback-Leibler divergence computed using either deterministic or random sampling. It is shown how variational sampling differs conceptually from both quadrature and importance sampling and established that, in the case of random independence sampling, it may have much faster stochastic convergence than importance sampling under mild conditions. The variational sampling implementation presented in this paper requires a rough initial approximation to the target distribution, which may be found, e.g. using the Laplace method, and is shown to then have the potential to substantially improve over several existing approximate inference techniques to estimate moments of order up to two of nearly-Gaussian distributions, which occur frequently in Bayesian analysis. In particular, an application of variational sampling to Bayesian logistic regression in moderate dimension is presented.

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arXiv2012

EM algorithm and variants: an informal tutorial

The expectation-maximization (EM) algorithm introduced by Dempster et al in 1977 is a very general method to solve maximum likelihood estimation problems. In this informal report, we review the theory behind EM as well as a number of EM variants, suggesting that beyond the current state of the art is an even much wider territory still to be discovered.

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arXiv2010

Selection of a Model of Cerebral Activity for fMRI Group Data Analysis

This thesis is dedicated to the statistical analysis of multi-sub ject fMRI data, with the purpose of identifying bain structures involved in certain cognitive or sensori-motor tasks, in a reproducible way across sub jects. To overcome certain limitations of standard voxel-based testing methods, as implemented in the Statistical Parametric Mapping (SPM) software, we introduce a Bayesian model selection approach to this problem, meaning that the most probable model of cerebral activity given the data is selected from a pre-defined collection of possible models. Based on a parcellation of the brain volume into functionally homogeneous regions, each model corresponds to a partition of the regions into those involved in the task under study and those inactive. This allows to incorporate prior information, and avoids the dependence of the SPM-like approach on an arbitrary threshold, called the cluster- forming threshold, to define active regions. By controlling a Bayesian risk, our approach balances false positive and false negative risk control. Furthermore, it is based on a generative model that accounts for the spatial uncertainty on the localization of individual effects, due to spatial normalization errors. On both simulated and real fMRI datasets, we show that this new paradigm corrects several biases of the SPM-like approach, which either swells or misses the different active regions, depending on the choice of a cluster-forming threshold.

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