Related papers: Scalable random number generation for truncated lo…

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…

The past several years have seen remarkable progress in generative models which produce convincing samples of images and other modalities. A shared component of many powerful generative models is a decoder network, a parametric deep neural…

We study the basic statistical problem of testing whether normally distributed $n$-dimensional data has been truncated, i.e. altered by only retaining points that lie in some unknown truncation set $S \subseteq \mathbb{R}^n$. As our main…

In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…

Source localization is the inverse problem of graph information dissemination and has broad practical applications. However, the inherent intricacy and uncertainty in information dissemination pose significant challenges, and the ill-posed…

For certain types of statistical models, the characteristic function (Fourier transform) is available in closed form, whereas the probability density function has an intractable form, typically as an infinite sum of probability weighted…

Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving…

In Bayesian statistical inference and computationally intensive frequentist inference, one is interested in obtaining samples from a high dimensional, and possibly multi-modal target density. The challenge is to obtain samples from this…

We consider random instances of non-convex perceptron problems in the high-dimensional limit of a large number of examples $M$ and weights $N$, with finite load $\alpha = M/N$. We develop a formalism based on replica theory to predict the…

We propose a new distribution, called the soft tMVN distribution, which provides a smooth approximation to the truncated multivariate normal (tMVN) distribution with linear constraints. An efficient blocked Gibbs sampler is developed to…

We study and develop multilevel methods for the numerical approximation of a log-concave probability $\pi$ on $\mathbb{R}^d$, based on (over-damped) Langevin diffusion. In the continuity of \cite{art:egeapanloup2021multilevel} concentrated…

Stochastic gradient Markov Chain Monte Carlo algorithms are popular samplers for approximate inference, but they are generally biased. We show that many recent versions of these methods (e.g. Chen et al. (2014)) cannot be corrected using…

The conventional classification schemes -- notably multinomial logistic regression -- used in conjunction with convolutional networks (convnets) are classical in statistics, designed without consideration for the usual coupling with…

Transformers are often the go-to architecture to build foundation models that ingest a large amount of training data. But these models do not estimate the probability density distribution when trained on regression problems, yet obtaining…

We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…

Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion…

Score-based diffusion models have significantly advanced high-dimensional data generation across various domains, by learning a denoising oracle (or score) from datasets. From a Bayesian perspective, they offer a realistic modeling of data…

Inverse Probability Weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of "small denominators," trimming is routinely employed as a regularization…