Related papers: Homotopy Sampling, with an Application to Particle…

We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…

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,…

In recent work (arXiv:1006.3100v1), we have presented a novel approach for improving particle filters for multi-target tracking. The suggested approach was based on drift homotopy for stochastic differential equations. Drift homotopy was…

Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…

Data science relies on pipelines that are organized in the form of interdependent computational steps. Each step consists of various candidate algorithms that maybe used for performing a particular function. Each algorithm consists of…

Partially observable Markov decision processes (POMDPs) are a general mathematical model for sequential decision-making in stochastic environments under state uncertainty. POMDPs are often solved \textit{online}, which enables the algorithm…

Particle filtering is a Bayesian inference method and a fundamental tool in state estimation for dynamic systems, but its effectiveness is often limited by the constraints of the initial prior distribution, a phenomenon we define as the…

Sampling from unnormalized target distributions is a fundamental yet challenging task in machine learning and statistics. Existing sampling algorithms typically require many iterative steps to produce high-quality samples, leading to high…

Particle Marginal Metropolis-Hastings (PMMH) is a general approach to Bayesian inference when the likelihood is intractable, but can be estimated unbiasedly. Our article develops an efficient PMMH method that scales up better to higher…

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distributions. For models that…

The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian…

Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…

Conformal inference is a statistical method used to construct prediction sets for point predictors, providing reliable uncertainty quantification with probability guarantees. This method utilizes historical labeled data to estimate the…

Particle filters provide Monte Carlo approximations of intractable quantities such as point-wise evaluations of the likelihood in state space models. In many scenarios, the interest lies in the comparison of these quantities as some…

Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows…

In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and…

Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…

Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…

Homotopy approaches to Bayesian inference have found widespread use especially if the Kullback-Leibler divergence between the prior and the posterior distribution is large. Here we extend one of these homotopy approach to include an…

The extraction of nonstationary signals from blind and semi-blind multivariate observations is a recurrent problem. Numerous algorithms have been developed for this problem, which are based on the exact or approximate joint diagonalization…