Related papers: A connection between Tempering and Entropic Mirror…

Many practical samplers rely on time-dependent drifts -- often induced by annealing or tempering schedules -- to improve exploration and stability. This motivates a unified non-asymptotic analysis of the corresponding Langevin diffusions…

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…

Attention mechanisms have revolutionized several domains of artificial intelligence, such as natural language processing and computer vision, by enabling models to selectively focus on relevant parts of the input data. While recent work has…

Gerber and Chopin (2015) recently introduced Sequential quasi-Monte Carlo (SQMC) algorithms as an efficient way to perform filtering in state-space models. The basic idea is to replace random variables with low-discrepancy point sets, so as…

In this short note, we give the convergence analysis of the policy in the recent famous policy mirror descent (PMD). We mainly consider the unregularized setting following [11] with generalized Bregman divergence. The difference is that we…

Sequential Monte Carlo (SMC), or particle filtering, is a popular class of methods for sampling from an intractable target distribution using a sequence of simpler intermediate distributions. Like other importance sampling-based methods,…

Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack…

We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors…

This work proposes an adaptive sequential Monte Carlo sampling algorithm to solve Bayesian inverse problems in scenarios where likelihood evaluations are costly but can be approximated using a surrogate model built from previous evaluations…

Score-matching generative models have proven successful at sampling from complex high-dimensional data distributions. In many applications, this distribution is believed to concentrate on a much lower $d$-dimensional manifold embedded into…

SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. Gerber and Chopin (2015) introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives:…

We consider the problem of upper bounding the expected log-likelihood sub-optimality of the maximum likelihood estimate (MLE), or a conjugate maximum a posteriori (MAP) for an exponential family, in a non-asymptotic way. Surprisingly, we…

This paper provides a unified perspective for the Kullback-Leibler (KL)-divergence and the integral probability metrics (IPMs) from the perspective of maximum likelihood density-ratio estimation (DRE). Both the KL-divergence and the IPMs…

Nonnegative matrix factorization (NMF) is a standard linear dimensionality reduction technique for nonnegative data sets. In order to measure the discrepancy between the input data and the low-rank approximation, the Kullback-Leibler (KL)…

Estimating the Kullback--Leibler (KL) divergence between language models has many applications, e.g., reinforcement learning from human feedback (RLHF), interpretability, and knowledge distillation. However, computing the exact KL…

This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm's iterates under the…

Auxiliary variable methods such as the Parallel Tempering and the cluster Monte Carlo methods generate samples that follow a target distribution by using proposal and auxiliary distributions. In sampling from complex distributions, these…

We consider the problem of sampling from a probability distribution $\pi$. It is well known that this can be written as an optimisation problem over the space of probability distribution in which we aim to minimise the Kullback--Leibler…

Distributed optimization often requires finding the minimum of a global objective function written as a sum of local functions. A group of agents work collectively to minimize the global function. We study a continuous-time decentralized…

The reverse Monte Carlo (RMC) method is widely used in structural modelling and analysis of experimental data. More recently, RMC has been applied to the calculation of equilibrium thermodynamic properties and dynamic problems. These…