Related papers: Kernel Mean Embedding Topology: Weak and Strong Fo…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
Kernel approximation is widely used to scale up kernel SVM training and prediction. However, the memory and computation costs of kernel approximation models are still too high if we want to deploy them on memory-limited devices such as…
Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…
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 consider weakly positive semidefinite kernels valued in ordered $*$-spaces with or without certain topological properties, and investigate their linearisations (Kolmogorov decompositions) as well as their reproducing kernel spaces. The…
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…
We propose a kernel-based nonparametric framework for mean-variance optimization that enables inference on economically motivated shape constraints in finance, including positivity, monotonicity, and convexity. Many central hypotheses in…
The K-means algorithm is among the most commonly used data clustering methods. However, the regular K-means can only be applied in the input space and it is applicable when clusters are linearly separable. The kernel K-means, which extends…
Motivated by applications, we consider here new operator theoretic approaches to Conditional mean embeddings (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and…
Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $\mu$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two…
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…
Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels…
Function encoders are a recent technique that learn neural network basis functions to form compact, adaptive representations of Hilbert spaces of functions. We show that function encoders provide a principled connection to feature learning…
We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…
Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…
The consistency of a learning method is usually established under the assumption that the observations are a realization of an independent and identically distributed (i.i.d.) or mixing process. Yet, kernel methods such as support vector…
We introduce a framework for learning continuous neural representations of formal specifications by distilling the geometry of their semantics into a latent space. Existing approaches rely either on symbolic kernels -- which preserve…
Highly localized kernels constructed by orthogonal polynomials have been fundamental in recent development of approximation and computational analysis on the unit sphere, unit ball and several other regular domains. In this work we first…
Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that machine learning enhanced by quantum computing is…
Quantum kernels quantify similarity between data points by measuring the inner product between quantum states, computed through quantum circuit measurements. By embedding data into quantum systems, quantum kernel feature maps, that may be…