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The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel such as the Gaussian, however, limits its…

The majority of popular graph kernels is based on the concept of Haussler's $\mathcal{R}$-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering…

With the rise of large language models (LLMs) for flexibly processing information as strings, a natural application is regression, specifically by preprocessing string representations into LLM embeddings as downstream features for metric…

Kernels are often developed and used as implicit mapping functions that show impressive predictive power due to their high-dimensional feature space representations. In this study, we gradually construct a series of simple feature maps that…

This paper investigates the convergence properties of spectral algorithms -- a class of regularization methods originating from inverse problems -- under covariate shift. In this setting, the marginal distributions of inputs differ between…

An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…

We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…

Kernel classifiers and regressors designed for structured data, such as sequences, trees and graphs, have significantly advanced a number of interdisciplinary areas such as computational biology and drug design. Typically, kernels are…

In this paper, we consider the problem of estimating the eigenvalues and eigenfunctions of the covariance kernel (i.e., the functional principal components) from sparse and irregularly observed longitudinal data. We approach this problem…

Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…

For a class of integral operators with kernels metric functions on manifold we find some necessary and sufficient conditions to have finite rank. The problem we pose has a stochastic nature and boils down to the following alternative…

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…

Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…

We characterize a Hawkes point process with kernel proportional to the probability density function of Mittag-Leffler random variables. This kernel decays as a power law with exponent $\beta +1 \in (1,2]$. Several analytical results can be…

Outlier detection methods have become increasingly relevant in recent years due to increased security concerns and because of its vast application to different fields. Recently, Pauwels and Lasserre (2016) noticed that the sublevel sets of…

We study linear function approximation in a finite basis under finite-precision arithmetic. In a highly non-orthogonal basis, certain directions are only weakly represented, so that rounding errors can significantly distort the effectively…

Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…

The leverage effect-- the correlation between an asset's return and its volatility-- has played a key role in forecasting and understanding volatility and risk. While it is a long standing consensus that leverage effects exist and improve…

The kernel estimator is known not to be adequate for estimating the density of a positive random variable X. The main reason is the well-known boundary bias problems that it suffers from, but also its poor behaviour in the long right tail…

We propose the adaptive random Fourier features Gaussian kernel LMS (ARFF-GKLMS). Like most kernel adaptive filters based on stochastic gradient descent, this algorithm uses a preset number of random Fourier features to save computation…