Related papers: KerJEPA: Kernel Discrepancies for Euclidean Self-S…

Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not…

We propose ULFS-KDPE, a kernel debiased plug-in estimator based on the universal least favorable submodel, for estimating pathwise differentiable parameters in nonparametric models. The method constructs a data-adaptive debiasing flow in a…

In this paper, we show two new variants of multi-view k-means (MVKM) algorithms to address multi-view data. The general idea is to outline the distance between $h$-th view data points $x_i^h$ and $h$-th view cluster centers $a_k^h$ in a…

In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of $\ell^p$ regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that…

Deep kernel learning (DKL) and related techniques aim to combine the representational power of neural networks with the reliable uncertainty estimates of Gaussian processes. One crucial aspect of these models is an expectation that, because…

Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…

This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…

Self-supervised learning (SSL) has emerged as a powerful paradigm for representation learning by optimizing geometric objectives, such as invariance to augmentations, variance preservation, and feature decorrelation, without requiring…

Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) methods based on kernels will be investigated. One example is…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

Gaussian processes (GPs) are Bayesian non-parametric models popular in a variety of applications due to their accuracy and native uncertainty quantification (UQ). Tuning GP hyperparameters is critical to ensure the validity of prediction…

We propose a learning framework for graph kernels, which is theoretically grounded on regularizing optimal transport. This framework provides a novel optimal transport distance metric, namely Regularized Wasserstein (RW) discrepancy, which…

Joint-Embedding Predictive Architectures (JEPAs), a powerful class of self-supervised models, exhibit an unexplained ability to cluster time-series data by their underlying dynamical regimes. We propose a novel theoretical explanation for…

Kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of…

Large language models (LLMs) are increasingly adapted to downstream tasks via reinforcement learning (RL) methods like Group Relative Policy Optimization (GRPO), which often require thousands of rollouts to learn new tasks. We argue that…

Our understanding of learning input-output relationships with neural nets has improved rapidly in recent years, but little is known about the convergence of the underlying representations, even in the simple case of linear autoencoders…

Recently, manifold regularized semi-supervised learning (MRSSL) received considerable attention because it successfully exploits the geometry of the intrinsic data probability distribution including both labeled and unlabeled samples to…

In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…

We study a semi-supervised learning method based on the similarity graph and RegularizedLaplacian. We give convenient optimization formulation of the Regularized Laplacian method and establishits various properties. In particular, we show…