Related papers: Large deviations principle for the Adaptive Multil…
Population dynamics provides a numerical tool allowing for the study of rare events by means of simulating a large number of copies of the system, supplemented with a selection rule that favours the rare trajectories of interest. The…
High-dimensional classification has become an increasingly important problem. In this paper we propose a "Multivariate Adaptive Stochastic Search" (MASS) approach which first reduces the dimension of the data space and then applies a…
In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…
Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate…
We consider the problem of reconstructing rank-one matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the Alternating…
Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive,…
A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…
Adaptive simulated annealing (ASA) is a global optimization algorithm based on an associated proof that the parameter space can be sampled much more efficiently than by using other previous simulated annealing algorithms. The author's ASA…
The probability of rare and extreme events is an important quantity for design purposes. However, computing the probability of rare events can be expensive because only a few events, if any, can be observed. To this end, it is necessary to…
In this paper, we consider an importance sampling problem for a certain rare-event simulations involving the behavior of a diffusion process pertaining to a chain of distributed systems with random perturbations. We also assume that the…
This paper presents an advancement to an approach for model-independent surrogate-based optimization with adaptive batch sampling, known as Adaptive Model Refinement (AMR). While the original AMR method provides unique decisions with…
We present the AMPS algorithm, a finite element solution method that combines principal submatrix updates and Schur complement techniques, well-suited for interactive simulations of deformation and cutting of finite element meshes. Our…
In this paper we address the problem of performing Bayesian inference for the parameters of a nonlinear multi-output model and the covariance matrix of the different output signals. We propose an adaptive importance sampling (AIS) scheme…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
In this work, we consider the numerical estimation of the probability for a stochastic process to hit a set B before reaching another set A. This event is assumed to be rare. We consider reactive trajectories of the stochastic Allen-Cahn…
The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows one to treat a molecular system with different levels of resolution depending on the location of the molecules. The construction of a Hamiltonian based on the this idea…
Alternating Direction Method of Multipliers (ADMM) is a popular method for solving large-scale Machine Learning problems. Stochastic ADMM was proposed to reduce the per iteration computational complexity, which is more suitable for big data…
Birth-death processes form a natural class where ideas and results on large deviations can be tested. In this paper, we derive a large deviation principle under the assumption that the rate of a jump down (death) is growing asymptotically…
Importance sampling (IS) is a Monte Carlo methodology that allows for approximation of a target distribution using weighted samples generated from another proposal distribution. Adaptive importance sampling (AIS) implements an iterative…
In the fields of statistics, machine learning, image science, and related areas, there is an increasing demand for decentralized collection or storage of large-scale datasets, as well as distributed solution methods. To tackle this…