Related papers: Optimal Particle-based Approximation of Discrete D…
When sampling multi-modal probability distributions, correctly estimating the relative probability of each mode, even when the modes have been discovered and locally sampled, remains challenging. We test a simple reweighting scheme designed…
We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete--time state--space Markov model. The algorithm employs two layers of particle filters to approximate the…
Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. In this paper, we propose to approximate the log-likelihood…
Motivated by the computation of the non-parametric maximum likelihood estimator (NPMLE) and the Bayesian posterior in statistics, this paper explores the problem of convex optimization over the space of all probability distributions. We…
We study the maximum likelihood estimator of density of $n$ independent observations, under the assumption that it is well approximated by a mixture with a large number of components. The main focus is on statistical properties with respect…
We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity. This problem is equivalent to…
We consider the distributed version of the Multiple Knapsack Problem (MKP), where $m$ items are to be distributed amongst $n$ processors, each with a knapsack. We propose different distributed approximation algorithms with a tradeoff…
Markov chain Monte Carlo (MCMC) methods are simulated by local exploration of complex statistical distributions, and while bypassing the cumbersome requirement of a specific analytical expression for the target, this stochastic exploration…
We propose a novel projection-based particle method for solving the McKean-Vlasov stochastic differential equations. Our approach is based on a projection-type estimation of the marginal density of the solution in each time step. The…
In this paper, we present a method for reducing a regular, discrete-time Markov chain (DTMC) to another DTMC with a given, typically much smaller number of states. The cost of reduction is defined as the Kullback-Leibler divergence rate…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
We present a reduced-dimension, ballistic deposition, Monte Carlo particle packing algorithm and discuss its application to the analysis of the microstructure of hard-sphere systems with broad particle size distributions. We extend our…
Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where…
We explore whether splitting and killing methods can improve the accuracy of Markov chain Monte Carlo (MCMC) estimates of rare event probabilities, and we make three contributions. First, we prove that "weighted ensemble" is the only…
Diffusion alignment adapts pretrained diffusion models to sample from reward-tilted distributions along the denoising trajectory. This process naturally admits a Sequential Monte Carlo (SMC) interpretation, where the denoising model acts as…
Binary optimization has a wide range of applications in combinatorial optimization problems such as MaxCut, MIMO detection, and MaxSAT. However, these problems are typically NP-hard due to the binary constraints. We develop a novel…
Particle filters are a widely used Monte Carlo based data assimilation technique that estimates the probability distribution of a system's state conditioned on observations through a collection of weights and particles. A known problem for…
Twisted particle filters are a class of sequential Monte Carlo methods recently introduced by Whiteley and Lee to improve the efficiency of marginal likelihood estimation in state-space models. The purpose of this article is to extend the…
In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for…
Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantization. Formally, we seek a weighted mixture of Dirac measures…