Related papers: Optimal Estimation of Structured Covariance Operat…
We consider a family of gradient Gaussian vector fields on $\Z^d$, where the covariance operator is not translation invariant. A uniform finite range decomposition of the corresponding covariance operators is proven, i.e., the covariance…
We consider the problem of learning an unknown, possibly nonlinear operator between separable Hilbert spaces from supervised data. Inputs are drawn from a prescribed probability measure on the input space, and outputs are (possibly noisy)…
Last decade witnesses significant methodological and theoretical advances in estimating large precision matrices. In particular, there are scientific applications such as longitudinal data, meteorology and spectroscopy in which the ordering…
Covariance tapering is a popular approach for reducing the computational cost of spatial prediction and parameter estimation for Gaussian process models. However, tapering can have poor performance when the process is sampled at spatially…
We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered…
In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…
In this paper, we investigate the supremum-norm generalization error and the uniform inference for a specific class of kernel regression methods, namely the kernel gradient flows. Under the widely adopted capacity-source condition framework…
Let a family of gradient Gaussian vector fields on $ \mathbb{Z}^d $ be given. We show the existence of a uniform finite range decomposition of the corresponding covariance operators, that is, the covariance operator can be written as a sum…
We derive optimal rates of convergence in the supremum norm for estimating the H\"older-smooth mean function of a stochastic process which is repeatedly and discretely observed with additional errors at fixed, multivariate, synchronous…
We propose a novel approach to computationally efficient GP training based on the observation that square-exponential (SE) covariance matrices contain several off-diagonal entries extremely close to zero. We construct a principled procedure…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy,…
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…
Centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds are determined by their covariance operators. We consider centered GRFs given as variational…
Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
We derive improved regression and classification rates for support vector machines using Gaussian kernels under the assumption that the data has some low-dimensional intrinsic structure that is described by the box-counting dimension. Under…