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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…

Machine learning provides a novel avenue for the study of experimental realizations of many-body systems, and has recently been proven successful in analyzing properties of experimental data of ultracold quantum gases. We here show that…

We propose a new probabilistic framework that allows mobile robots to autonomously learn deep, generative models of their environments that span multiple levels of abstraction. Unlike traditional approaches that combine engineered models…

Many statistical problems include model parameters that are defined as the solutions to optimization sub-problems. These include classical approaches such as profile likelihood as well as modern applications involving flow networks or…

We design a simple ascending-price algorithm to compute a $(1+\varepsilon)$-approximate equilibrium in Arrow-Debreu exchange markets with weak gross substitute (WGS) property, which runs in time polynomial in market parameters and $\log…

Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…

The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It…

In several recent works on infinite-dimensional systems of ODEs \cite{cao_derivation_2021,cao_explicit_2021,cao_iterative_2024,cao_sticky_2024}, which arise from the mean-field limit of agent-based models in economics and social sciences…

We present an approach to quantifying both aleatoric and epistemic uncertainty for deep neural networks in image classification, based on generative adversarial networks (GANs). While most works in the literature that use GANs to generate…

Gaussian processes are an important regression tool with excellent analytic properties which allow for direct integration of derivative observations. However, vanilla GP methods scale cubically in the amount of observations. In this work,…

We consider the problem of estimating the conditional probability distribution of missing values given the observed ones. We propose an approach, which combines the flexibility of deep neural networks with the simplicity of Gaussian mixture…

The lack of well-calibrated confidence estimates makes neural networks inadequate in safety-critical domains such as autonomous driving or healthcare. In these settings, having the ability to abstain from making a prediction on…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

Latent-variable energy-based models (LVEBMs) assign a single normalized energy to joint pairs of observed data and latent variables, offering expressive generative modeling while capturing hidden structure. We recast maximum-likelihood…

Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…

Graph Neural Networks (GNNs) are a broad class of connectionist models for graph processing. Recent studies have shown that GNNs can approximate any function on graphs, modulo the equivalence relation on graphs defined by the…

We study how well generative adversarial networks (GAN) learn probability distributions from finite samples by analyzing the convergence rates of these models. Our analysis is based on a new oracle inequality that decomposes the estimation…

Distributed systems have been widely used in practice to accomplish data analysis tasks of huge scales. In this work, we target on the estimation problem of generalized linear models on a distributed system with nonrandomly distributed…

Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…

In this paper, we study the problem of signal estimation from noisy non-linear measurements when the unknown $n$-dimensional signal is in the range of an $L$-Lipschitz continuous generative model with bounded $k$-dimensional inputs. We make…