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Machine Learning (ML) has widely been used for modeling and predicting physical systems. These techniques offer high expressive power and good generalizability for interpolation within observed data sets. However, the disadvantage of…

Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…

An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…

Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…

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…

Much recent work in bioinformatics has focused on the inference of various types of biological networks, representing gene regulation, metabolic processes, protein-protein interactions, etc. A common setting involves inferring network edges…

Multi-manifold modeling is increasingly used in segmentation and data representation tasks in computer vision and related fields. While the general problem, modeling data by mixtures of manifolds, is very challenging, several approaches…

Modern single-cell flow and mass cytometry technologies measure the expression of several proteins of the individual cells within a blood or tissue sample. Each profiled biological sample is thus represented by a set of hundreds of…

This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to…

This chapter deals with kernel methods as a special class of techniques for surrogate modeling. Kernel methods have proven to be efficient in machine learning, pattern recognition and signal analysis due to their flexibility, excellent…

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…

Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance),…

Recent advances in self-supervised learning and neural network scaling have enabled the creation of large models, known as foundation models, which can be easily adapted to a wide range of downstream tasks. The current paradigm for…

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.…

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…

In the last few decades, significant achievements have been attained in predicting where humans look at images through different computational models. However, how to determine contributions of different visual features to overall saliency…

This paper presents a novel approach for multi-kernel estimation by enhancing the KernelGAN algorithm, which traditionally estimates a single kernel for the entire image. We introduce Multi-KernelGAN, which extends KernelGAN's capabilities…

With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum…

Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several…

Pairwise learning corresponds to the supervised learning setting where the goal is to make predictions for pairs of objects. Prominent applications include predicting drug-target or protein-protein interactions, or customer-product…