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We propose a novel alternative approach to our previous work (Ben Hammouda et al., 2023) to improve the efficiency of Monte Carlo (MC) estimators for rare event probabilities for stochastic reaction networks (SRNs). In the same spirit of…
This article presents new methodology for sample-based Bayesian inference when data are partitioned and communication between the parts is expensive, as arises by necessity in the context of "big data" or by choice in order to take…
The computational complexity of MCMC methods for the exploration of complex probability measures is a challenging and important problem. A challenge of particular importance arises in Bayesian inverse problems where the target distribution…
We propose a new method for simplification of Gaussian process (GP) models by projecting the information contained in the full encompassing model and selecting a reduced number of variables based on their predictive relevance. Our results…
In this work, a fully nonparametric geostatistical approach to estimate threshold exceeding probabilities is proposed. To estimate the large-scale variability (spatial trend) of the process, the nonparametric local linear regression…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…
In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response,…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…
We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the…
Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…
Importance sampling of target probability distributions belonging to a given convex class is considered. Motivated by previous results, the cost of importance sampling is quantified using the relative entropy of the target with respect to…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
We consider the problem of computationally-efficient prediction from high dimensional and highly correlated predictors in challenging settings where accurate variable selection is effectively impossible. Direct application of penalization…
Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…
Bayesian inversions followed by estimations of rare event probabilities are often needed to analyse groundwater hazards. Instead of focusing on the posterior distribution of model parameters, the main interest lies then in the distribution…
Covariance estimation for high-dimensional datasets is a fundamental problem in modern day statistics with numerous applications. In these high dimensional datasets, the number of variables p is typically larger than the sample size n. A…
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…
We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e.…
The global minimum-variance portfolio is a typical choice for investors because of its simplicity and broad applicability. Although it requires only one input, namely the covariance matrix of asset returns, estimating the optimal solution…