Related papers: Kernel Methods on Riemannian Manifolds with Gaussi…

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…

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…

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…

Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

This study investigates the application of Riemannian geometry-based methods for brain decoding using invasive electrophysiological recordings. Although previously employed in non-invasive, the utility of Riemannian geometry for invasive…

Geometric Machine Learning (GML) has shown that respecting non-Euclidean geometry in data spaces can significantly improve performance over naive Euclidean assumptions. In parallel, Quantum Machine Learning (QML) has emerged as a promising…

The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Lo\`eve transforms, and…

In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…

Despite the recent deep learning (DL) revolution, kernel machines still remain powerful methods for action recognition. DL has brought the use of large datasets and this is typically a problem for kernel approaches, which are not scaling up…

The isometric embedding problem for Riemannian manifolds, which connects intrinsic and extrinsic geometry, is a central question in differential geometry with deep theoretical significance and wide-ranging applications. Despite extensive…

Filtration of quantifiable objects by smoothing kernels on Riemannian manifolds for visualisation is an ongoing research. However, using common filters created for linear domains on manifolds with non-Euclidean topologies can yield…

Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric…

Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data…

Deep neural networks (DNNs) on Riemannian manifolds have garnered increasing interest in various applied areas. For instance, DNNs on spherical and hyperbolic manifolds have been designed to solve a wide range of computer vision and nature…

Methods and algorithms that work with data on nonlinear manifolds are collectively summarized under the term `Riemannian computing'. In practice, curvature can be a key limiting factor for the performance of Riemannian computing methods.…

Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process…

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…

The aim of the paper is to create a link between the theory of reproducing kernel Hilbert spaces (RKHS) and the notion of a unitary representation of a group or of a groupoid. More specifically, it is demonstrated on one hand, how to…

Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…