Related papers: A Langevin-like Sampler for Discrete Distributions
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…
The diffusion models (DMs) have demonstrated the remarkable capability of generating images via learning the noised score function of data distribution. Current DM sampling techniques typically rely on first-order Langevin dynamics at each…
We present a robust Distributed and Localized Model Predictive Control (rDLMPC) framework for large-scale structured linear systems. The proposed algorithm uses the System Level Synthesis to provide a distributed closed-loop model…
In this paper, we study the problem of sampling from log-concave distributions supported on convex, compact sets, with a particular focus on the randomized midpoint discretization of both vanilla and kinetic Langevin diffusions in this…
High-dimensional data that evolve dynamically feature predominantly in the modern data era. As a partial response to this, recent years have seen increasing emphasis to address the dimensionality challenge. However, the non-static nature of…
Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient at each iteration. This modest change allows…
We develop and analyze an asynchronous algorithm for distributed convex optimization when the objective writes a sum of smooth functions, local to each worker, and a non-smooth function. Unlike many existing methods, our distributed…
We introduce the DNNLikelihood, a novel framework to easily encode, through Deep Neural Networks (DNN), the full experimental information contained in complicated likelihood functions (LFs). We show how to efficiently parametrise the LF,…
We revisit the problem of sampling from a target distribution that has a smooth strongly log-concave density everywhere in $\mathbb R^p$. In this context, if no additional density information is available, the randomized midpoint…
Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based…
This paper introduces and analyses interacting underdamped Langevin algorithms, termed Kinetic Interacting Particle Langevin Monte Carlo (KIPLMC) methods, for statistical inference in latent variable models. We propose a diffusion process…
In contrast to the study of Langevin equations in a homogeneous environment in the literature, the study on Langevin equations in randomly-varying environments is relatively scarce. Almost all the existing works require random environments…
Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of…
We introduce a novel generative model, the Discrete Distribution Networks (DDN), that approximates data distribution using hierarchical discrete distributions. We posit that since the features within a network inherently capture…
Discrete choice models (DCMs) are used to analyze individual decision-making in contexts such as transportation choices, political elections, and consumer preferences. DCMs play a central role in applied econometrics by enabling inference…
Sampling from the full posterior distribution of high-dimensional non-linear, non-Gaussian latent dynamical models presents significant computational challenges. While Particle Gibbs (also known as conditional sequential Monte Carlo) is…
Many methods that build powerful variational distributions based on unadjusted Langevin transitions exist. Most of these were developed using a wide range of different approaches and techniques. Unfortunately, the lack of a unified analysis…
A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian…
We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show that it achieves $\varepsilon$ error (in 2-Wasserstein…
Adaptive sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. A sequential adaptive sampling-and-refinement procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form of…