Related papers: A Multi-Step Richardson-Romberg Extrapolation Meth…
For the nonparametric regression models with covariates contaminated with normal measurement errors, this paper proposes an extrapolation algorithm to estimate the nonparametric regression functions. By applying the conditional expectation…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
This paper addresses the complexity reduction of stochastic homogenisation of a class of random materials for a stationary diffusion equation. A cost-efficient approximation of the correctors is built using a method designed to exploit…
The aim of this work is to provide fast and accurate approximation schemes for the Monte Carlo pricing of derivatives in LIBOR market models. Standard methods can be applied to solve the stochastic differential equations of the successive…
In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…
Subsampling is a popular approach to alleviating the computational burden for analyzing massive datasets. Recent efforts have been devoted to various statistical models without explicit regularization. In this paper, we develop an efficient…
We present a way to include non local potentials in the standard Diffusion Monte Carlo method without using the locality approximation. We define a stochastic projection based on a fixed node effective Hamiltonian, whose lowest energy is an…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
Reliability-based design optimization (RBDO) provides a rational and sound framework for finding the optimal design while taking uncertainties into ac-count. The main issue in implementing RBDO methods, particularly stochastic simu-lation…
We show how to extend a recently proposed multi-level Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the…
Motivated by the goal of improving the efficiency of small sample design, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modelling and…
We introduce forward-backward stochastic differential equations, highlighting the connection between solutions of these and solutions of partial differential equations, related by the Feynman-Kac theorem. We review the technique of…