Related papers: Parsimonious Mahalanobis Kernel for the Classifica…
In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. To handle this kind of data, Grassmann kernels were proposed to measure the space structure and used with classifiers,…
This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…
We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors…
Metric learning is a key problem for many data mining and machine learning applications, and has long been dominated by Mahalanobis methods. Recent advances in nonlinear metric learning have demonstrated the potential power of…
The parameters of support vector machines (SVMs) such as the penalty parameter and the kernel parameters have a great impact on the classification accuracy and the complexity of the SVM model. Therefore, the model selection in SVM involves…
Gaussian processes offers a convenient way to perform nonparametric reconstructions of observational data assuming only a kernel which describes the covariance between neighbouring points in a data set. We approach the ambiguity in the…
Tree kernels have demonstrated their ability to deal with hierarchical data, as the intrinsic tree structure often plays a discriminative role. While such kernels have been successfully applied to various domains such as nature language…
We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and…
We introduce the loss kernel, an interpretability method for measuring similarity between data points according to a trained neural network. The kernel is the covariance matrix of per-sample losses computed under a distribution of…
We consider the problem of causal structure learning in the setting of heterogeneous populations, i.e., populations in which a single causal structure does not adequately represent all population members, as is common in biological and…
Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…
Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is sampled from a low-dimensional structure.…
We present a new kernel-based algorithm for modeling evenly distributed multidimensional datasets that does not rely on input space sparsification. The presented method reorganizes the typical single-layer kernel-based model into a deep…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…
The product moment covariance is a cornerstone of multivariate data analysis, from which one can derive correlations, principal components, Mahalanobis distances and many other results. Unfortunately the product moment covariance and the…
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…
This article presents a quantum computing approach to designing of similarity measures and kernels for classification of stochastic symbolic time series. In the area of machine learning, kernels are important components of various…
A holonomic system of linear partial differential equations is, roughly speaking, a system whose solution space is finite dimensional. A distribution that is a solution of a holonomic system is called a holonomic distribution. We give…
We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…