Related papers: Super-Samples from Kernel Herding

We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…

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…

Kernel methods have great promise for learning rich statistical representations of large modern datasets. However, compared to neural networks, kernel methods have been perceived as lacking in scalability and flexibility. We introduce a…

The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…

Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of…

We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice's (NIJ) Real-Time Crime Forecasting Challenge. Our method is a spatiotemporal forecasting model combining scalable…

The recent discovery of the equivalence between infinitely wide neural networks (NNs) in the lazy training regime and Neural Tangent Kernels (NTKs) (Jacot et al., 2018) has revived interest in kernel methods. However, conventional wisdom…

We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a vector-valued reproducing kernel Hilbert space induced by an…

This paper introduces a diagonal adaptive kernel model that dynamically learns kernel eigenvalues and output coefficients simultaneously during training. Unlike fixed-kernel methods tied to the neural tangent kernel theory, the diagonal…

Random Forests and Gradient Boosting are among the most effective algorithms for supervised learning on tabular data. Both belong to the class of tree-based ensemble methods, where predictions are obtained by aggregating many randomized…

We introduce a nonparametric algorithm to learn interaction kernels of mean-field equations for 1st-order systems of interacting particles. The data consist of discrete space-time observations of the solution. By least squares with…

Dictionary learning algorithms have been successfully used in both reconstructive and discriminative tasks, where the input signal is represented by a linear combination of a few dictionary atoms. While these methods are usually developed…

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…

We study strictly proper scoring rules in the Reproducing Kernel Hilbert Space. We propose a general Kernel Scoring rule and associated Kernel Divergence. We consider conditions under which the Kernel Score is strictly proper. We then…

Measuring similarity between incomplete data is a fundamental challenge in web mining, recommendation systems, and user behavior analysis. Traditional approaches either discard incomplete data or perform imputation as a preprocessing step,…

Inverse Optimization (IO) is a framework for learning the unknown objective function of an expert decision-maker from a past dataset. In this paper, we extend the hypothesis class of IO objective functions to a reproducing kernel Hilbert…

We use a suitable version of the so-called "kernel trick" to devise two-sample (homogeneity) tests, especially focussed on high-dimensional and functional data. Our proposal entails a simplification related to the important practical…

We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels…

Many real-world applications generate continuous data streams for regression. Hoeffding trees and their variants have a long-standing tradition due to their effectiveness, either alone or as base models in broader ensembles. Recent…

Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…