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Multi-scale representations deeply learned via convolutional neural networks have shown tremendous importance for various pixel-level prediction problems. In this paper we present a novel approach that advances the state of the art on…
A simple yet effective architectural design of radial basis function neural networks (RBFNN) makes them amongst the most popular conventional neural networks. The current generation of radial basis function neural network is equipped with…
We start with a brief survey on H\"offding's kernels, its properties, related spectral decompositions, and discuss marginal distributions of H\"offding measures. In the second part of this note, one-dimensional covariance representations…
Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer…
Standard kernels such as Mat\'ern or RBF kernels only encode simple monotonic dependencies within the input space. Spectral mixture kernels have been proposed as general-purpose, flexible kernels for learning and discovering more…
Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…
Graph kernels have been successfully applied to many graph classification problems. Typically, a kernel is first designed, and then an SVM classifier is trained based on the features defined implicitly by this kernel. This two-stage…
Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional…
We introduce the notion of multiplication kernels of birational and $D$-module type and give various examples. We also introduce the notion of a semi-classical multiplication kernel associated with an integrable system and discuss its…
Graph hypernetworks (GHNs), constructed by combining graph neural networks (GNNs) with hypernetworks (HNs), leverage relational data across various domains such as neural architecture search, molecular property prediction and federated…
We show, in a formal way, how a class of complex quasiprobability distribution functions may be introduced by using the fractional Fourier transform. This leads to the Fresnel transform of a characteristic function instead of the usual…
While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of…
Kernel-based statistical methods are efficient, but their performance depends heavily on the selection of kernel parameters. In literature, the optimization studies on kernel-based chemometric methods is limited and often reduced to grid…
We present a new paradigm for creating random features to approximate bi-variate functions (in particular, kernels) defined on general manifolds. This new mechanism of Manifold Random Features (MRFs) leverages discretization of the manifold…
A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…
Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an…
Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be proved in the most general possible setting. Two important…
The theory of positive kernels and associated reproducing kernel Hilbert spaces, especially in the setting of holomorphic functions, has been an important tool for the last several decades in a number of areas of complex analysis and…
Radial basis function (RBF) network is a third layered neural network that is widely used in function approximation and data classification. Here we propose a quantum model of the RBF network. Similar to the classical case, we still use the…
In this paper we study two extensions of the complex-valued Gaussian radial basis function (RBF) kernel and discuss their connections with Fock spaces in two different settings. First, we introduce the quaternonic Gaussian RBF kernel…