Related papers: Distributed Learning with Discretely Observed Func…

We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…

Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to…

Convolutional dictionary learning (CDL) estimates shift invariant basis adapted to multidimensional data. CDL has proven useful for image denoising or inpainting, as well as for pattern discovery on multivariate signals. As estimated…

This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…

Data-driven spectral analysis of Koopman operators is a powerful tool for understanding numerous real-world dynamical systems, from neuronal activity to variations in sea surface temperature. The Koopman operator acts on a function space…

In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem…

The problem of heterogeneous clients in federated learning has recently drawn a lot of attention. Spectral model sharding, i.e., partitioning the model parameters into low-rank matrices based on the singular value decomposition, has been…

Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, kernel methods offer a natural nonparametric approach with…

The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer,…

We consider the problem of distributed learning, where a network of agents collectively aim to agree on a hypothesis that best explains a set of distributed observations of conditionally independent random processes. We propose a…

When concept shifts and sample scarcity are present in the target domain of interest, nonparametric regression learners often struggle to generalize effectively. The technique of transfer learning remedies these issues by leveraging data or…

It is often said that control and estimation problems are in duality. Recently, in (Aubin-Frankowski,2021), we found new reproducing kernels in Linear-Quadratic optimal control by focusing on the Hilbert space of controlled trajectories,…

We propose an efficient distributed online learning protocol for low-latency real-time services. It extends a previously presented protocol to kernelized online learners that represent their models by a support vector expansion. While such…

Learning mappings between infinite-dimensional function spaces has achieved empirical success in many disciplines of machine learning, including generative modeling, functional data analysis, causal inference, and multi-agent reinforcement…

Randomized methods of neural network learning suffer from a problem with the generation of random parameters as they are difficult to set optimally to obtain a good projection space. The standard method draws the parameters from a fixed…

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions…

In deep learning models, learning more with less data is becoming more important. This paper explores how neural networks with normalized Radial Basis Function (RBF) kernels can be trained to achieve better sample efficiency. Moreover, we…

In recent studies, the generalization properties for distributed learning and random features assumed the existence of the target concept over the hypothesis space. However, this strict condition is not applicable to the more common…

We study linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general (generic) inhomogeneous boundary conditions in Sobolev spaces. We investigate the character of solvability of…

Operator learning is the approximation of operators between infinite dimensional Banach spaces using machine learning approaches. While most progress in this area has been driven by variants of deep neural networks such as the Deep Operator…