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Performing signal processing over graphs requires knowledge of the underlying fixed topology. However, graphs often grow in size with new nodes appearing over time, whose connectivity is typically unknown; hence, making more challenging the…

This paper presents and analyses a new family of linear subdivision schemes to refine noisy data given on triangular meshes. The subdivision rules consist of locally fitting and evaluating a weighted least squares approximating first-degree…

This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational science and engineering. The methods entail global…

In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed…

We consider the problem of approximating $[0,1]^{d}$-periodic functions by convolution with a scaled Gaussian kernel. We start by establishing convergence rates to functions from periodic Sobolev spaces and we show that the saturation rate…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

Many applications such as election forecasting, environmental monitoring, health policy, and graph based machine learning require taking expectation of functions defined on the vertices of a graph. We describe a construction of a sampling…

This paper proves joint convergence of the approximation error for several stochastic integrals with respect to local Brownian semimartingales, for nonequidistant and random grids. The conditions needed for convergence are that the Lebesgue…

Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such…

Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, can be exploited. A relevant tool for analysing sparse…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…

Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…

Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…

Modern supervised learning techniques, particularly those using deep nets, involve fitting high dimensional labelled data sets with functions containing very large numbers of parameters. Much of this work is empirical. Interesting phenomena…

We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise.…

Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…

We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…

Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…