Related papers: Gaussian Multiplier Bootstrap Procedure for the $k…
Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…
There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…
Most of the modern literature on robust mean estimation focuses on designing estimators which obtain optimal sub-Gaussian concentration bounds under minimal moment assumptions and sometimes also assuming contamination. This work looks at…
Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused…
Laplace approximation is a very useful tool in Bayesian inference and it claims a nearly Gaussian behavior of the posterior. \cite{SpLaplace2022} established some rather accurate finite sample results about the quality of Laplace…
While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings…
Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…
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…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and…
We propose a general framework using spike-and-slab prior distributions to aid with the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function. We show that highly…
Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool to generate more general high frequency solutions to…
We propose multiplier bootstrap procedures for nonparametric inference and uncertainty quantification of the target mean function, based on a novel framework of integrating target and source data. We begin with the relatively easier…
Training Gaussian process-based models typically involves an $ O(N^3)$ computational bottleneck due to inverting the covariance matrix. Popular methods for overcoming this matrix inversion problem cannot adequately model all types of latent…
In this paper, we obtain the Berry-Esseen bound for multivariate normal approximation for the Polyak-Ruppert averaged iterates of the linear stochastic approximation (LSA) algorithm with decreasing step size. Moreover, we prove the…
Clustering and estimating cluster means are core problems in statistics and machine learning, with k-means and Expectation Maximization (EM) being two widely used algorithms. In this work, we provide a theoretical explanation for the…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
A primary goal of computer experiments is to reconstruct the function given by the computer code via scattered evaluations. Traditional isotropic Gaussian process models suffer from the curse of dimensionality, when the input dimension is…
We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…