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We introduce a nonparametric prior on the conditional distribution of a (univariate or multivariate) response given a set of predictors. The prior is constructed in the form of a two-stage generative procedure, which in the first stage…

In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…

Priors in Bayesian analyses often encode informative domain knowledge that can be useful in making the inference process more efficient. Occasionally, however, priors may be unrepresentative of the parameter values for a given dataset,…

Fully connected layers are a primary source of memory and computational overhead in deep neural networks due to their dense, often redundant parameterization. While various compression techniques exist, they frequently introduce complex…

Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…

Optimizing expensive-to-evaluate black-box functions of discrete (and potentially continuous) design parameters is a ubiquitous problem in scientific and engineering applications. Bayesian optimization (BO) is a popular, sample-efficient…

Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…

This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank (PPR) computation. At each stage of the process, we employ a localized inexact proximal point iteration to solve a simplified…

This paper proposes a nonparametric multivariate density forecast model based on deep learning. It not only offers the whole marginal distribution of each random variable in forecasting targets, but also reveals the future correlation…

The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models for density estimation and clustering. The goal of this paper is to illustrate…

We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of…

We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…

We develop a novel framework to accelerate Gaussian process regression (GPR). In particular, we consider localization kernels at each data point to down-weigh the contributions from other data points that are far away, and we derive the GPR…

Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which the simple pieces of the…

Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…

We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…

In reinforcement learning (RL), Q-learning is a fundamental algorithm whose convergence is guaranteed in the tabular setting. However, this convergence guarantee does not hold under linear function approximation. To overcome this…

We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…

Regularization is a critical component in deep learning. The most commonly used approach, weight decay, applies a constant penalty coefficient uniformly across all parameters. This may be overly restrictive for some parameters, while…