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We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the plane. We identify a large class of lattices, or more generally…
This paper studies the performative prediction problem which optimizes a stochastic loss function with data distribution that depends on the decision variable. We consider a setting where the agent(s) provides samples adapted to the…
We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to have a feasible…
The aim of this paper is to study, in the infinite dimensional framework, the existence and uniqueness for the solution of the following multivalued generalized backward stochastic differential equation, considered on a random, possibly…
We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are…
We analyze the statistical complexity vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period {\tau}. It is shown that if the Bandt and Pompe procedure is used to assign a probability distribution…
The error threshold transition in a stochastic (i.e. finite population) version of the quasispecies model of molecular evolution is studied using finite-size scaling. For the single-sharp-peak replication landscape, the deterministic model…
Spatial birth and death processes are obtained as solutions of a system of stochastic equations. The processes are required to be locally finite, but may involve an infinite population over the full (noncompact) type space. Conditions are…
Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower…
Motivated by certain problems of statistical physics we consider a stationary stochastic process in which deterministic evolution is interrupted at random times by upward jumps of a fixed size. If the evolution consists of linear decay, the…
The focus of this work is on spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models, soft-thresholded Gaussian processes and develop the efficient posterior computation algorithms.…
We study the long time behavior of isentropic compressible Euler equations with linear damping driven by a white-in-time noise, on a one-dimensional torus. We prove the existence of a statistically stationary solution in the class of weak…
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate…
This article describes a novel approach to chance-constrained programming based on the sample average approximation (SAA) method. Recent work focuses on heuristic approximations to the SAA problem and we introduce a novel approach which…
In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…
From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly…
The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…
With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of…