Related papers: A Langevin-like Sampler for Discrete Distributions

We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with…

Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks…

This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling. Focusing on two mainstream samplers -- the denoising diffusion implicit model (DDIM) and the denoising diffusion…

A canonical algorithm for log-concave sampling is the Langevin Algorithm, aka the Langevin Diffusion run with some discretization stepsize $\eta > 0$. This discretization leads the Langevin Algorithm to have a stationary distribution…

In this paper we propose a new approach for sampling from probability measures in, possibly, high dimensional spaces. By perturbing the standard overdamped Langevin dynamics by a suitable Stratonovich perturbation that preserves the…

In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a…

Langevin algorithms are gradient descent methods with additive noise. They have been used for decades in Markov chain Monte Carlo (MCMC) sampling, optimization, and learning. Their convergence properties for unconstrained non-convex…

The Langevin Dynamics (LD), which aims to sample from a probability distribution using its score function, has been widely used for analyzing and developing score-based generative modeling algorithms. While the convergence behavior of LD in…

Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have…

The paper provides a thorough investigation of Direct loss minimization (DLM), which optimizes the posterior to minimize predictive loss, in sparse Gaussian processes. For the conjugate case, we consider DLM for log-loss and DLM for square…

Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density $\pi(\theta)\propto \exp(-U(\theta)) $, LMC…

Differentially private collaborative filtering is a challenging task, both in terms of accuracy and speed. We present a simple algorithm that is provably differentially private, while offering good performance, using a novel connection of…

Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…

Diffusion large language models (dLLMs) have emerged as a promising alternative for text generation, distinguished by their native support for parallel decoding. In practice, block inference is crucial for avoiding order misalignment in…

Diffusion models (DMs) have emerged as powerful image priors in Bayesian computational imaging. Two primary strategies have been proposed for leveraging DMs in this context: Plug-and-Play methods, which are zero-shot and highly flexible but…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for strongly log-concave distributions suggest that, as the dimension…

The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm that incorporates the gradient of the logarithm of the target density in its proposal distribution. In an earlier joint work \citet{pill:stu:12}, the author had…

Discrete diffusion models have emerged as powerful tools for high-quality data generation. Despite their success in discrete spaces, such as text generation tasks, the acceleration of discrete diffusion models remains under-explored. In…

In this paper we combine the Alias method with the concept of systematic sampling, a method commonly used in particle filters for efficient low-variance resampling. The proposed method allows very fast sampling from a discrete distribution:…