Related papers: The Generalised Kernel Covariance Measure
Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded…
We consider kernel based learning methods for regression and analyze what happens to the risk minimizer when new variables, statistically independent of input and target variables, are added to the set of input variables; this problem…
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…
We study the problem of testing the null hypothesis that X and Y are conditionally independent given Z, where each of X, Y and Z may be functional random variables. This generalises testing the significance of X in a regression model of…
Kernel-based methods are used in the context of Granger Causality to enable the identification of nonlinear causal relationships between time series variables. In this paper, we show that two state of the art kernel-based Granger Causality…
In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…
We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are…
Distance covariance is a popular dependence measure for two random vectors $X$ and $Y$ of possibly different dimensions and types. Recent years have witnessed concentrated efforts in the literature to understand the distributional…
The Generalized Additive Model (GAM) is a powerful tool and has been well studied. This model class helps to identify additive regression structure. Via available test procedures one may identify the regression structure even sharper if…
Discovering causal relationships from observational data is a fundamental yet challenging task. Invariant causal prediction (ICP, Peters et al., 2016) is a method for causal feature selection which requires data from heterogeneous settings…
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…
The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not…
We address the problem of filling missing entries in a kernel Gram matrix, given a related full Gram matrix. We attack this problem from the viewpoint of regression, assuming that the two kernel matrices can be considered as explanatory…
Conditional independence (CI) testing is frequently used in data analysis and machine learning for various scientific fields and it forms the basis of constraint-based causal discovery. Oftentimes, CI testing relies on strong, rather…
We prove that kernel covariance embeddings lead to information-theoretically perfect separation of distinct continuous probability distributions. In statistical terms, we establish that testing for the \emph{equality} of two non-atomic…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
Kernel-based testing has revolutionized the field of non-parametric tests through the embedding of distributions in an RKHS. This strategy has proven to be powerful and flexible, yet its applicability has been limited to the standard…
The Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth…
This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$, which plays an important role in statistical and machine learning applications. We propose…
High-dimensional variable selection is an important issue in many scientific fields, such as genomics. In this paper, we develop a sure independence feature screening pro- cedure based on kernel canonical correlation analysis (KCCA-SIS, for…