Related papers: High-dimensional Gaussian and bootstrap approximat…
We investigate popular resampling methods for estimating the uncertainty of statistical models, such as subsampling, bootstrap and the jackknife, and their performance in high-dimensional supervised regression tasks. We provide a tight…
This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…
Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…
Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexible modeling approach of the relationship between predictors and count response variables. The applications of HBPRMs to large-scale datasets require efficient…
Approximate message passing (AMP) methods and their variants have attracted considerable recent attention for the problem of estimating a random vector $\mathbf{x}$ observed through a linear transform $\mathbf{A}$. In the case of large…
This article establishes novel strong uniform laws of large numbers for randomly weighted sums such as bootstrap means. By leveraging recent advances, these results extend previous work in their general applicability to a wide range of…
This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…
Distribution of the sum of independent identically distributed symmetric lattice vectors is approximated by the accompanying compound Poisson law and the second-order Hipp-type signed compound Poisson measure. Bergstr\"om -type asymptotic…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
Recent advances have equipped 3D Gaussian Splatting with texture parameterizations to capture spatially varying attributes, improving the performance of both appearance modeling and downstream tasks. However, the added texture parameters…
This paper develops distribution theory and bootstrap-based inference methods for a broad class of convex pairwise difference estimators. These estimators minimize a kernel-weighted convex-in-parameter function over observation pairs with…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
In a two-stage cluster sampling procedure, $n$ random populations are drawn independently from independent populations and a sub-sample of observations is taken in each of them. The estimator of the general mean of the observed variables is…
Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
Theoretical results for importance sampling rely on the existence of certain moments of the importance weights, which are the ratios between the proposal and target densities. In particular, a finite variance ensures square root convergence…