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We explore two complementary modifications of the hybridization-expansion continuous-time Monte Carlo method, aiming at large multi-orbital quantum impurity problems. One idea is to compute the imaginary-time propagation using a matrix…
This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…
Maximum likelihood (ML) estimation using Newton's method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the log-likelihood and its gradient and Hessian. We estimate the gradient and…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
An algorithm is proposed for the segmentation of image into multiple levels using mean and standard deviation in the wavelet domain. The procedure provides for variable size segmentation with bigger block size around the mean, and having…
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…
The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…
Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and…
Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic…
Optimization-based samplers such as randomize-then-optimize (RTO) [2] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
We study the class of state-space models and perform maximum likelihood estimation for the model parameters. We consider a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function with the…
We propose a new algorithm for approximating the non-asymptotic second moment of the marginal likelihood estimate, or normalizing constant, provided by a particle filter. The computational cost of the new method is $O(M)$ per time step,…
We present an original simulation-based method to estimate likelihood ratios efficiently for general state-space models. Our method relies on a novel use of the conditional Sequential Monte Carlo (cSMC) algorithm introduced in…
This article addresses the problem of efficient Bayesian inference in dynamic systems using particle methods and makes a number of contributions. First, we develop a correlated pseudo-marginal (CPM) approach for Bayesian inference in state…
We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…
We present a mathematical framework for constructing and analyzing parallel algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in…
We consider stochastic approximation with block-coordinate stepsizes and propose adaptive stepsize rules that aim to minimize the expected distance from the next iterate to an (unknown) target point. These stepsize rules employ online…
A new approach to inference in state space models is proposed, based on approximate Bayesian computation (ABC). ABC avoids evaluation of the likelihood function by matching observed summary statistics with statistics computed from data…