Related papers: Optimizing Over Radial Kernels on Compact Manifold…

This work deals with the optimization of computer programs targeting Graphics Processing Units (GPUs). The goal is to lift, from programmers to optimizing compilers, the heavy burden of determining program details that are dependent on the…

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

Support vector machines and kernel methods have recently gained considerable attention in chemoinformatics. They offer generally good performance for problems of supervised classification or regression, and provide a flexible and…

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)…

We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation with compactly-supported kernels and also classical…

Deformable medical image registration is an essential task in computer-assisted interventions. This problem is particularly relevant to oncological treatments, where precise image alignment is necessary for tracking tumor growth, assessing…

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…

Anomaly detection based on one-class classification algorithms is broadly used in many applied domains like image processing (e.g. detection of whether a patient is "cancerous" or "healthy" from mammography image), network intrusion…

Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…

Kernel-based methods are heavily used in machine learning. However, they suffer from $O(N^2)$ complexity in the number $N$ of considered data points. In this paper, we propose an approximation procedure, which reduces this complexity to…

Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive…

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular…

We present a necessary and sufficient condition for the strict positive definiteness of a real, continuous, isotropic and positive definite kernel on a two-point compact homogeneous space. The characterization adds to others previously…

Kernels for structured data are commonly obtained by decomposing objects into their parts and adding up the similarities between all pairs of parts measured by a base kernel. Assignment kernels are based on an optimal bijection between the…

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…

Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and robotics. While the underlying theory is classical, existing…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as…

In the recent past, automatic selection or combination of kernels (or features) based on multiple kernel learning (MKL) approaches has been receiving significant attention from various research communities. Though MKL has been extensively…

Random Fourier features (RFFs) provide a promising way for kernel learning in a spectral case. Current RFFs-based kernel learning methods usually work in a two-stage way. In the first-stage process, learning the optimal feature map is often…