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Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…
Under covariate shift, training (source) data and testing (target) data differ in input space distribution, but share the same conditional label distribution. This poses a challenging machine learning task. Robust Bias-Aware (RBA)…
Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…
This work explores new classes of nonstationary stochastic sequences associated with polynomial hypergroups. Their covariance structures are analyzed through positive definite kernels and corresponding Hilbert spaces. Novel consistent…
Quantum kernel methods promise enhanced expressivity for learning structured data, but their usefulness has been limited by kernel concentration and barren plateaus. Both effects are mathematically equivalent and suppress trainability. We…
Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base…
Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and…
Kernel smoothers are considered near the boundary of the interval. Kernels which minimize the expected mean square error are derived. These kernels are equivalent to using a linear weighting function in the local polynomial regression. It…
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…
Kernels ensuing from tree ensembles such as random forest (RF) or gradient boosted trees (GBT), when used for kernel learning, have been shown to be competitive to their respective tree ensembles (particularly in higher dimensional…
Previously, we showed that computational mechanic's causal states -- predictively-equivalent trajectory classes for a stochastic dynamical system -- can be cast into a reproducing kernel Hilbert space. The result is a widely-applicable…
Kernel methods are ubiquitous in classical machine learning, and recently their formal similarity with quantum mechanics has been established. To grasp the potential advantage of quantum machine learning, it is necessary to understand the…
The state-of-the-art CNN models give good performance on sentence classification tasks. The purpose of this work is to empirically study desirable properties such as semantic coherence, attention mechanism and reusability of CNNs in these…
Clifford-Steerable CNNs (CSCNNs) provide a unified framework that allows incorporating equivariance to arbitrary pseudo-Euclidean groups, including isometries of Euclidean space and Minkowski spacetime. In this work, we demonstrate that the…
We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…
Kulldorff's (1997) seminal paper on spatial scan statistics (SSS) has led to many methods considering different regions of interest, different statistical models, and different approximations while also having numerous applications in…
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)…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
Kernel methods play a critical role in many machine learning algorithms. They are useful in manifold learning, classification, clustering and other data analysis tasks. Setting the kernel's scale parameter, also referred to as the kernel's…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…