Related papers: Conformal Transformation of Kernels: A Geometric P…

Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…

The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…

Cross-lingual semantic textual similarity systems estimate the degree of the meaning similarity between two sentences, each in a different language. State-of-the-art algorithms usually employ machine translation and combine vast amount of…

Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…

Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher-order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non-Gaussian…

For management, documents are categorized into a specific category, and to do these, most of the organizations use manual labor. In today's automation era, manual efforts on such a task are not justified, and to avoid this, we have so many…

Although Convolutional Neural Networks (CNNs) are widely used, their translation invariance (ability to deal with translated inputs) is still subject to some controversy. We explore this question using translation-sensitivity maps to…

Kernel expansions are a topic of considerable interest in machine learning, also because of their relation to the so-called feature maps introduced in machine learning. Properties of the associated basis functions and weights (corresponding…

Molecular geometry prediction of flexible molecules, or conformer search, is a long-standing challenge in computational chemistry. This task is of great importance for predicting structure-activity relationships for a wide variety of…

This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…

We propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our algorithm simultaneously computes support vectors and a proxy kernel matrix…

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…

Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a…

Transformers have revolutionized machine learning across diverse domains, yet understanding their behavior remains crucial, particularly in high-stakes applications. This paper introduces the contextual counting task, a novel toy problem…

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…

Gaussian processes (GP) are widely used as a metamodel for emulating time-consuming computer codes. We focus on problems involving categorical inputs, with a potentially large number L of levels (typically several tens), partitioned in G <<…

3D action recognition was shown to benefit from a covariance representation of the input data (joint 3D positions). A kernel machine feed with such feature is an effective paradigm for 3D action recognition, yielding state-of-the-art…

Self-attention (SA) based models have recently achieved significant performance improvements in hybrid and end-to-end automatic speech recognition (ASR) systems owing to their flexible context modeling capability. However, it is also known…

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…

Graph models are relevant in many fields, such as distributed computing, intelligent tutoring systems or social network analysis. In many cases, such models need to take changes in the graph structure into account, i.e. a varying number of…