Related papers: Learning from Non-Random Data in Hilbert Spaces: A…
Motivated by the learned iterative soft thresholding algorithm (LISTA), we introduce a general class of neural networks suitable for sparse reconstruction from few linear measurements. By allowing a wide range of degrees of weight-sharing…
Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…
Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
Learning a smooth graph signal from partially observed data is a well-studied task in graph-based machine learning. We consider this task from the perspective of optimal recovery, a mathematical framework for learning a function from…
We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of…
In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…
We construct a least squares approximation method for the recovery of complex-valued functions from a reproducing kernel Hilbert space on $D \subset \mathbb{R}^d$. The nodes are drawn at random for the whole class of functions and the error…
While large training datasets generally offer improvement in model performance, the training process becomes computationally expensive and time consuming. Distributed learning is a common strategy to reduce the overall training time by…
We present statistical convergence results for the learning of (possibly) non-linear mappings in infinite-dimensional spaces. Specifically, given a map $G_0:\mathcal X\to\mathcal Y$ between two separable Hilbert spaces, we analyze the…
In many linear inverse problems, we want to estimate an unknown vector belonging to a high-dimensional (or infinite-dimensional) space from few linear measurements. To overcome the ill-posed nature of such problems, we use a low-dimension…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
In recent years, transfer learning has garnered significant attention. Its ability to leverage knowledge from related studies to improve generalization performance in a target study has made it highly appealing. This paper focuses on…
The problem of domain generalization is to learn, given data from different source distributions, a model that can be expected to generalize well on new target distributions which are only seen through unlabeled samples. In this paper, we…
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
Established approaches to obtain generalization bounds in data-driven optimization and machine learning mostly build on solutions from empirical risk minimization (ERM), which depend crucially on the functional complexity of the hypothesis…
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…