Related papers: Generative diffusion for perceptron problems: stat…

We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the plane. We identify a large class of lattices, or more generally…

This paper explores the use of score-based diffusion models for Bayesian image reconstruction. Diffusion models are an efficient tool for generative modeling. Diffusion models can also be used for solving image reconstruction problems. We…

Statistical inference on large-dimensional tensor data has been extensively studied in the literature and widely used in economics, biology, machine learning, and other fields, but how to generate a structured tensor with a target…

Speech super-resolution (SR) is the task that restores high-resolution speech from low-resolution input. Existing models employ simulated data and constrained experimental settings, which limit generalization to real-world SR. Predictive…

The encoder and decoder for lossy data compression of binary memoryless sources are developed on the basis of a specific-type nonmonotonic perceptron. Statistical mechanical analysis indicates that the potential ability of the…

Score-based diffusion models are a powerful class of generative models, but their practical use often depends on training neural networks to approximate the score function. Training-free diffusion models provide an attractive alternative by…

We focus on \emph{row sampling} based approximations for matrix algorithms, in particular matrix multipication, sparse matrix reconstruction, and \math{\ell_2} regression. For \math{\matA\in\R^{m\times d}} (\math{m} points in \math{d\ll m}…

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…

We establish the limiting distribution of $\frac{{(\log \log x)}^{1/4}}{\sqrt{x}} \sum_{n\le x}\alpha(n)$ where $\alpha$ is a Steinhaus random multiplicative function, answering a question of Harper. The distributional convergence is proved…

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…

Efficient feature selection from high-dimensional datasets is a very important challenge in many data-driven fields of science and engineering. We introduce a statistical mechanics inspired strategy that addresses the problem of sparse…

In this work, we address the systematic biases and random errors stemming from finite step sizes encountered in diffusion simulations. We introduce the Effective Geometry Monte Carlo (EG-MC) simulation algorithm which modifies the geometry…

When presented with a binary classification problem where the data exhibits severe class imbalance, most standard predictive methods may fail to accurately model the minority class. We present a model based on Generative Adversarial…

Diffusion-based generative models provide a powerful framework for learning to sample from a complex target distribution. The remarkable empirical success of these models applied to high-dimensional signals, including images and video,…

Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a…

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using…

We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in…

Computational sampling has been central to the sciences since the mid-20th century. While machine-learning-based approaches have recently enabled major advances, their behavior remains poorly understood, with limited theoretical control…

Recent literature has effectively leveraged diffusion models trained on continuous variables as priors for solving inverse problems. Notably, discrete diffusion models with discrete latent codes have shown strong performance, particularly…