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The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference…
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…
Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address…
This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…
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…
In this paper, we discuss the problem of system identification when frequency domain side information is available on the system. Initially, we consider the case where the prior knowledge is provided as being the $\Hcal_{\infty}$-norm of…
This paper presents a novel feature of the kernel-based system identification method. We prove that the regularized kernel-based approach for the estimation of a finite impulse response is equivalent to a robust least-squares problem with a…
Kernel survival analysis models estimate individual survival distributions with the help of a kernel function, which measures the similarity between any two data points. Such a kernel function can be learned using deep kernel survival…
We consider the problem of clustering a sample of probability distributions from a random distribution on $\mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing…
Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
In the study of stochastic systems, the committor function describes the probability that a system starting from an initial configuration $x$ will reach a set $B$ before a set $A$. This paper introduces an efficient and interpretable…
Regularized kernel methods such as support vector machines (SVM) and support vector regression (SVR) constitute a broad and flexible class of methods which are theoretically well investigated and commonly used in nonparametric…
The ability of a human being to extrapolate previously gained knowledge to other domains inspired a new family of methods in machine learning called transfer learning. Transfer learning is often based on the assumption that objects in both…
In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…