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Quantum kernel methods are among the leading candidates for achieving quantum advantage in supervised learning. A key bottleneck is the cost of inference: evaluating a trained model on new data requires estimating a weighted sum…

The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely-wide neural networks trained under least squares loss by gradient descent. Recent works also report that NTK regression can outperform finitely-wide neural networks…

Quadratic programming is a ubiquitous prototype in convex programming. Many machine learning problems can be formulated as quadratic programming, including the famous Support Vector Machines (SVMs). Linear and kernel SVMs have been among…

Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density.…

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…

Graph kernels based on the $1$-dimensional Weisfeiler-Leman algorithm and corresponding neural architectures recently emerged as powerful tools for (supervised) learning with graphs. However, due to the purely local nature of the…

We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple…

Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For $m$-edge and $n$-vertex graphs, it is well-known to be solvable in $O(m\sqrt{n})$ time; however, for several applications…

Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…

Spectral clustering and diffusion maps are celebrated dimensionality reduction algorithms built on eigen-elements related to the diffusive structure of the data. The core of these procedures is the approximation of a Laplacian through a…

We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…

Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…

Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…

Graph is an usual representation of relational data, which are ubiquitous in manydomains such as molecules, biological and social networks. A popular approach to learningwith graph structured data is to make use of graph kernels, which…

Kernel method is a very powerful tool in machine learning. The trick of kernel has been effectively and extensively applied in many areas of machine learning, such as support vector machine (SVM) and kernel principal component analysis…

Principal Component Analysis (PCA) is a popular method for dimension reduction and has attracted an unfailing interest for decades. More recently, kernel PCA (KPCA) has emerged as an extension of PCA but, despite its use in practice, a…

A fundamental problem on graph-structured data is that of quantifying similarity between graphs. Graph kernels are an established technique for such tasks; in particular, those based on random walks and return probabilities have proven to…

Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large…