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Substring kernels are classical tools for representing biological sequences or text. However, when large amounts of annotated data are available, models that allow end-to-end training such as neural networks are often preferred. Links…

A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…

Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations,…

We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…

Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…

A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…

Interpretability benefits the theoretical understanding of representations. Existing word embeddings are generally dense representations. Hence, the meaning of latent dimensions is difficult to interpret. This makes word embeddings like a…

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…

For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…

To afford flexible behaviour, the brain must build internal representations that mirror the structure of variables in the external world. For example, 2D space obeys rules: the same set of actions combine in the same way everywhere (step…

Building spatial process models that capture nonstationary behavior while delivering computationally efficient inference is challenging. Nonstationary spatially varying kernels (see, e.g., Paciorek, 2003) offer flexibility and richness, but…

Representations that can compactly and effectively capture the temporal evolution of semantic content are important to computer vision and machine learning algorithms that operate on multi-variate time-series data. We investigate such…

Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…

We propose a spherical kernel for efficient graph convolution of 3D point clouds. Our metric-based kernels systematically quantize the local 3D space to identify distinctive geometric relationships in the data. Similar to the regular grid…

Recently the use of neural networks has been introduced in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. This new technique has introduced…

This work concerns the construction and characterization of product kernels for multivariate approximation from a finite set of discrete samples. To this end, we consider composing different component kernels, each acting on a…

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated…

We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…