Related papers: Local Kernels and the Geometric Structure of Data

We present a unified framework to study graph kernels, special cases of which include the random walk graph kernel \citep{GaeFlaWro03,BorOngSchVisetal05}, marginalized graph kernel \citep{KasTsuIno03,KasTsuIno04,MahUedAkuPeretal04}, and…

Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…

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…

The main result of this paper is that determinantal point processes on the real line corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact…

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

We present a Gaussian kernel loss function and training algorithm for convolutional neural networks that can be directly applied to both distance metric learning and image classification problems. Our method treats all training features…

Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base…

We present a data-driven framework for the modeling of nonlocal heat transport in plasmas using a nonlocal theory informed neural network trained on kinetic Particle-in-Cell simulations that span both local and nonlocal regimes. The model…

We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be…

Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-based methods such as Gaussian processes are becoming increasingly important in applications where quantifying uncertainty is of key interest. In…

Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning. In this work, we aim to understand when and how deep networks -- with…

We propose kernel-gradient drifting, a one-step generative modeling framework that replaces the fixed Euclidean displacement direction in drifting models with directions induced by the kernel itself. Standard drifting is attractive because…

A novel strategy that combines a given collection of $\pi$-reversible Markov kernels is proposed. At each Markov transition, one of the available kernels is selected via a state-dependent probability distribution. In contrast to random-scan…

We survey the recent progress in the study of heat kernels for a class of non-symmetric non-local operators. We focus on the existence and sharp two-sided estimates of the heat kernels and their connection to jump diffusions.

Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…

In recent years, kernel methods are widespread in tasks of similarity measuring. Specifically, graph kernels are widely used in fields of bioinformatics, chemistry and financial data analysis. However, existing methods, especially entropy…

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…

Understanding how neural networks transform input data across layers is fundamental to unraveling their learning and generalization capabilities. Although prior work has used insights from kernel methods to study neural networks, a global…

In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations.…

This paper introduces a new and effective algorithm for learning kernels in a Multi-Task Learning (MTL) setting. Although, we consider a MTL scenario here, our approach can be easily applied to standard single task learning, as well. As…