Related papers: A global structure-preserving kernel method for th…

This paper introduces Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR), a novel tensor regression framework that enhances interpretability and performance through mode-specific hybrid regularization and nonnegativity…

We study stochastic Poisson integrators for a class of stochastic Poisson systems driven by Stratonovich noise. Such geometric integrators preserve Casimir functions and the Poisson map property. For this purpose, we propose explicit…

In this paper we show how to augment classical methods for inverse problems with artificial neural networks. The neural network acts as a prior for the coefficient to be estimated from noisy data. Neural networks are global, smooth function…

The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude…

Poisson Surface Reconstruction is a widely-used algorithm for reconstructing a surface from an oriented point cloud. To facilitate applications where only partial surface information is available, or scanning is performed sequentially, a…

Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…

In this paper we prove discrete to continuum convergence rates for Poisson Learning, a graph-based semi-supervised learning algorithm that is based on solving the graph Poisson equation with a source term consisting of a linear combination…

Kernel ridge regression (KRR) is widely used for nonparametric regression over reproducing kernel Hilbert spaces. It offers powerful modeling capabilities at the cost of significant computational costs, which typically require $O(n^3)$…

Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…

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…

In this work, we introduce a spatio-temporal kernel for Gaussian process (GP) regression-based sound field estimation. Notably, GPs have the attractive property that the sound field is a linear function of the measurements, allowing the…

Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…

For nonrigid image registration, matching the particular structures (or the outliers) that have missing correspondence and/or local large deformations, can be more difficult than matching the common structures with small deformations in the…

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…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

We introduce Neural Poisson Surface Reconstruction (nPSR), an architecture for shape reconstruction that addresses the challenge of recovering 3D shapes from points. Traditional deep neural networks face challenges with common 3D shape…

Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity…