相关论文: Chain of Log-Concave Markov Chains
This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…
This paper presents a new Metropolis-adjusted Langevin algorithm (MALA) that uses convex analysis to simulate efficiently from high-dimensional densities that are log-concave, a class of probability distributions that is widely used in…
Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…
We introduce a new framework for efficient sampling from complex probability distributions, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core idea is to use continuous transportation to transform…
In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a non-stationary piecewise-deterministic Markov process, from only one observation of the path within a long time. In this…
We examine challenges to sampling from Boltzmann distributions associated with multiscale energy landscapes. The multiscale features, or "roughness," corresponds to highly oscillatory, but bounded, perturbations of a smooth landscape.…
To overcome topological constraints and improve the expressiveness of normalizing flow architectures, Wu, K\"ohler and No\'e introduced stochastic normalizing flows which combine deterministic, learnable flow transformations with stochastic…
In large-data applications, such as the inference process of diffusion models, it is desirable to design sampling algorithms with a high degree of parallelization. In this work, we study the adaptive complexity of sampling, which is the…
Phylogenetic trees are key data objects in biology, and the method of phylogenetic reconstruction has been highly developed. The space of phylogenetic trees is a nonpositively curved metric space. Recently, statistical methods to analyze…
Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…
This paper focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude.…
This paper is concerned with sampling from probability distributions $\pi$ on $\mathbb{R}^d$ admitting a density of the form $\pi(x) \propto e^{-U(x)}$, where $U(x)=F(x)+G(Kx)$ with $K$ being a linear operator and $G$ being…
We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove an information theoretic lower bound on the number of stochastic gradient queries of the log density needed. Several popular sampling…
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…
A well-known first-order method for sampling from log-concave probability distributions is the Unadjusted Langevin Algorithm (ULA). This work proposes a new annealing step-size schedule for ULA, which allows to prove new convergence…
Log-concave sampling has witnessed remarkable algorithmic advances in recent years, but the corresponding problem of proving lower bounds for this task has remained elusive, with lower bounds previously known only in dimension one. In this…
The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…
Pseudo-marginal Markov chain Monte Carlo methods for sampling from intractable distributions have gained recent interest and have been theoretically studied in considerable depth. Their main appeal is that they are exact, in the sense that…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
We focus on the parametric estimation of the distribution of a Markov environment from the observation of a single trajectory of a one-dimensional nearest-neighbor path evolving in this random environment. In the ballistic case, as the…