arXiv subjects

Amandine Schreck

Publications and source records attributed to Amandine Schreck.

3 recordsLinked to original sources

arXiv2016

Convergence of Markovian Stochastic Approximation with discontinuous dynamics

This paper is devoted to the convergence analysis of stochastic approximation algorithms of the form $θ\_{n+1} = θ\_n + γ\_{n+1} H\_{θ\_n}(X\_{n+1})$ where $\{θ\_nn, n \geq 0\}$ is a $R^d$-valued sequence, $\{γ, n \geq 0\}$ is a deterministic step-size sequence and $\{X\_n, n \geq 0\}$ is a controlled Markov chain. We study the convergence under weak assumptions on smoothness-in-$θ$ of the function $θ\mapsto H\_θ(x)$. It is usually assumed that this function is continuous for any $x$; in this work, we relax this condition. Our results are illustrated by considering stochastic approximation algorithms for (adaptive) quantile estimation and a penalized version of the vector quantization.

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arXiv2015

A shrinkage-thresholding Metropolis adjusted Langevin algorithm for Bayesian variable selection

This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin (MALA) step to propose local moves associated with a shrinkage-thresholding step allowing to propose new models. The geometric ergodicity of this new trans-dimensional Markov Chain Monte Carlo sampler is established. An extensive numerical experiment, on simulated and real data, is presented to illustrate the performance of the proposed algorithm in comparison with some more classical trans-dimensional algorithms.

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arXiv2013

Adaptive Equi-Energy Sampler : Convergence and Illustration

Markov chain Monte Carlo (MCMC) methods allow to sample a distribution known up to a multiplicative constant. Classical MCMC samplers are known to have very poor mixing properties when sampling multimodal distributions. The Equi-Energy sampler is an interacting MCMC sampler proposed by Kou, Zhou and Wong in 2006 to sample difficult multimodal distributions. This algorithm runs several chains at different temperatures in parallel, and allow lower-tempered chains to jump to a state from a higher-tempered chain having an energy 'close' to that of the current state. A major drawback of this algorithm is that it depends on many design parameters and thus, requires a significant effort to tune these parameters. In this paper, we introduce an Adaptive Equi-Energy (AEE) sampler which automates the choice of the selection mecanism when jumping onto a state of the higher-temperature chain. We prove the ergodicity and a strong law of large numbers for AEE, and for the original Equi-Energy sampler as well. Finally, we apply our algorithm to motif sampling in DNA sequences.

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