Related papers: A class of kernel-based scalable algorithms for da…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the…
In this paper, we study an online learning algorithm with a robust loss function $\mathcal{L}_{\sigma}$ for regression over a reproducing kernel Hilbert space (RKHS). The loss function $\mathcal{L}_{\sigma}$ involving a scaling parameter…
Owing to the advantages of increased accuracy and the potential to detect unseen patterns, provided by data mining techniques they have been widely incorporated for standard classification problems. They have often been used for high…
Probabilistic predictions are probability distributions over the set of possible outcomes. Such predictions quantify the uncertainty in the outcome, making them essential for effective decision making. By combining multiple predictions, the…
In this paper, we study the problem of early stopping for iterative learning algorithms in a reproducing kernel Hilbert space (RKHS) in the nonparametric regression framework. In particular, we work with the gradient descent and (iterative)…
The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the…
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…
Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…
This paper presents a novel approach to formulating the actor-critic method for optimal control by casting policy iteration in reproducing kernel Hilbert spaces (RKHSs -- also known as native spaces). By tailoring the reproducing kernel and…
Accurate energy demand forecasting is crucial for sustainable and resilient energy development. To meet the Net Zero Representative Concentration Pathways (RCP) $4.5$ scenario in the DACH countries, increased renewable energy production,…
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…
We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularly relevant when the function is assumed to belong to a…
Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have…
Divide-and-conquer is a general strategy to deal with large scale problems. It is typically applied to generate ensemble instances, which potentially limits the problem size it can handle. Additionally, the data are often divided by random…
In this paper, the framework of kernel machines with two layers is introduced, generalizing classical kernel methods. The new learning methodology provide a formal connection between computational architectures with multiple layers and the…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…
Thanks to their easy implementation via Radial Basis Functions (RBFs), meshfree kernel methods have been proved to be an effective tool for e.g. scattered data interpolation, PDE collocation, classification and regression tasks. Their…
Recent studies indicate that kernel machines can often perform similarly or better than deep neural networks (DNNs) on small datasets. The interest in kernel machines has been additionally bolstered by the discovery of their equivalence to…
Estimating Kullback Leibler (KL) divergence from samples of two distributions is essential in many machine learning problems. Variational methods using neural network discriminator have been proposed to achieve this task in a scalable…