Related papers: A Gaussian limit process for optimal FIND algorith…

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…

Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…

The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the…

In this paper, we present a detailed convergence analysis of a recently developed approximate Newton-type fully distributed optimization method for smooth, strongly convex local loss functions, called Network-GIANT, which has been…

We determine the computational complexity of approximately counting and sampling independent sets of a given size in bounded-degree graphs. That is, we identify a critical density $\alpha_c(\Delta)$ and provide (i) for $\alpha <…

Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…

Low-rank approximation is a popular strategy to tackle the "big n problem" associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified.…

High-fidelity simulations and physical experiments are essential for engineering analysis and design, yet their high cost often makes two critical tasks--global sensitivity analysis (GSA) and optimization--prohibitively expensive. This…

We study the problem of estimating the mean of an identity covariance Gaussian in the truncated setting, in the regime when the truncation set comes from a low-complexity family $\mathcal{C}$ of sets. Specifically, for a fixed but unknown…

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…

We investigate in this paper the estimation of Gaussian graphs by model selection from a non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and focus on the disadvantageous case where n is smaller than p. To…

In this paper we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian NN and (the law of) a random Gaussian vector. Our results concern both shallow random Gaussian neural networks with…

The Median of Medians (also known as BFPRT) algorithm, although a landmark theoretical achievement, is seldom used in practice because it and its variants are slower than simple approaches based on sampling. The main contribution of this…

We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector $X$ has finite mean and covariance. In this setting, the radius of confidence intervals achieved…

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…

We propose a sampling algorithm that achieves superior complexity bounds in all the classical settings (strongly log-concave, log-concave, Logarithmic-Sobolev inequality (LSI), Poincar\'e inequality) as well as more general settings with…

We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting…

We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$. Under mild assumptions on the non-linearity, we obtain…