Related papers: Optimal Particle-based Approximation of Discrete D…
In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…
Point multipole expansions are widely used to gain physical insight into complex distributions of charges and to reduce the cost of computing interactions between such distributions. However, practical applications that typically retain…
In a complete bipartite graph with vertex sets of cardinalities $n$ and $m$, assign random weights from exponential distribution with mean 1, independently to each edge. We show that, as $n\rightarrow\infty$, with $m = \lceil…
Switching state-space models (SSSM) are a very popular class of time series models that have found many applications in statistics, econometrics and advanced signal processing. Bayesian inference for these models typically relies on Markov…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
This paper is concerned with the optimal approximation of a given multivariate Dirac mixture, i.e., a density comprising weighted Dirac distributions on a continuous domain, by an equally weighted Dirac mixture with a reduced number of…
Reinforcement learning demonstrated immense success in modelling complex physics-driven systems, providing end-to-end trainable solutions by interacting with a simulated or real environment, maximizing a scalar reward signal. In this work,…
We propose a sampling-based framework for finite-horizon trajectory and policy optimization under differentiable dynamics by casting controller design as inference. Specifically, we minimize a KL-regularized expected trajectory cost, which…
Sequential Monte Carlo (SMC), also known as particle filters, has been widely accepted as a powerful computational tool for making inference with dynamical systems. A key step in SMC is resampling, which plays the role of steering the…
It is well known in many settings that reversible Langevin diffusions in confining potentials converge to equilibrium exponentially fast. Adding irreversible perturbations to the drift of a Langevin diffusion that maintain the same…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
We consider the numerical approximation of acoustic wave propagation problems by mixed BDM(k+1)-P(k) finite elements on unstructured meshes. Optimal convergence of the discrete velocity and super-convergence of the pressure by one order are…
Markov Chain Monte Carlo (MCMC) techniques are now widely used for cosmological parameter estimation. Chains are generated to sample the posterior probability distribution obtained following the Bayesian approach. An important issue is how…
We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin…
Approximate inference in high-dimensional, discrete probabilistic models is a central problem in computational statistics and machine learning. This paper describes discrete particle variational inference (DPVI), a new approach that…
Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…
We introduce a mini-batch stochastic variance-reduced algorithm to solve finite-sum scale invariant problems which cover several examples in machine learning and statistics such as principal component analysis (PCA) and estimation of…