Related papers: Robust, randomized preconditioning for kernel ridg…

Deep neural networks excel in high-dimensional problems, outperforming models such as kernel methods, which suffer from the curse of dimensionality. However, the theoretical foundations of this success remain poorly understood. We follow…

We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct a wide range of convex…

Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on…

We use reproducing kernel methods to study various rigidity problems. The methods and setting allow us to also consider the non-positive case.

The ever-growing size of the datasets renders well-studied learning techniques, such as Kernel Ridge Regression, inapplicable, posing a serious computational challenge. Divide-and-conquer is a common remedy, suggesting to split the dataset…

Kernel ridge regression (KRR) and Gaussian processes (GPs) are fundamental tools in statistics and machine learning, with recent applications to highly over-parameterized deep neural networks. The ability of these tools to learn a target…

For many high-dimensional studies, additional information on the variables, like (genomic) annotation or external p-values, is available. In the context of binary and continuous prediction, we develop a method for adaptive group-regularized…

We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an RKHS framework. The data set of size n is partitioned into $m=O(n^\alpha)$ disjoint subsets. On each subset, some…

Kernel machines have sustained continuous progress in the field of quantum chemistry. In particular, they have proven to be successful in the low-data regime of force field reconstruction. This is because many equivariances and invariances…

Subspace clustering methods have been widely studied recently. When the inputs are 2-dimensional (2D) data, existing subspace clustering methods usually convert them into vectors, which severely damages inherent structures and relationships…

The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…

This paper introduces PROMISE ($\textbf{Pr}$econditioned Stochastic $\textbf{O}$ptimization $\textbf{M}$ethods by $\textbf{I}$ncorporating $\textbf{S}$calable Curvature $\textbf{E}$stimates), a suite of sketching-based preconditioned…

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and $\varepsilon$-support vector regression. By assuming the ground-truth…

Motivated by the studies of neural networks (e.g.,the neural tangent kernel theory), we perform a study on the large-dimensional behavior of kernel ridge regression (KRR) where the sample size $n \asymp d^{\gamma}$ for some $\gamma > 0$.…

This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and bi-conjugate gradient…

We propose KROM, a kernel-based reduced-order framework for fast solution of nonlinear partial differential equations. KROM formulates PDE solution as a minimum-norm (Gaussian-process) recovery problem in an RKHS, and accelerates the…

I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select…

We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate subspace, Dollar, Gould, Schilders, and Wathen (2006) describe how to apply the…

Compositional disorder is common in crystal compounds. In these compounds, some atoms are randomly distributed at some crystallographic sites. For such compounds, randomness forms many non-identical independent structures. Thus, calculating…

We address the problem of causal effect estimation in the presence of unobserved confounding, but where proxies for the latent confounder(s) are observed. We propose two kernel-based methods for nonlinear causal effect estimation in this…