Related papers: Kernel methods and minimum contrast estimators for…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…

Existing ultrasound deconvolution approaches unrealistically assume, primarily for computational reasons, that the convolution model relies on a spatially invariant kernel and circulant boundary conditions. We discard both restrictions and…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…

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…

In this work we consider the problem of learning a positive semidefinite kernel matrix from relative comparisons of the form: "object A is more similar to object B than it is to C", where comparisons are given by humans. Existing solutions…

We provide new general kernel selection rules thanks to penalized least-squares criteria. We derive optimal oracle inequalities using adequate concentration tools. We also investigate the problem of minimal penalty as described in [BM07].

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

A particularly interesting instance of supervised learning with kernels is when each training example is associated with two objects, as in pairwise classification (Brunner et al., 2012), and in supervised learning of preference relations…

The technique of kernelization consists in extracting, from an instance of a problem, an essentially equivalent instance whose size is bounded in a parameter k. Besides being the basis for efficient param-eterized algorithms, this method…

Nonparametric estimation of copula density functions using kernel estimators presents significant challenges. One issue is the potential unboundedness of certain copula density functions at the corners of the unit square. Another is the…

Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…

Since the entry of kernel theory in the field of quantum machine learning, quantum kernel methods (QKMs) have gained increasing attention with regard to both probing promising applications and delivering intriguing research insights.…

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…

Continuous treatments (e.g., doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We…

In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…

Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…

Convolution is a fundamental operation in image processing and machine learning. Aimed primarily at maintaining image size, padding is a key ingredient of convolution, which, however, can introduce undesirable boundary effects. We present a…

Motivated by the need for the rigorous analysis of the numerical stability of variational least-squares kernel-based methods for solving second-order elliptic partial differential equations, we provide previously lacking stability…

In low light or short-exposure photography the image is often corrupted by noise. While longer exposure helps reduce the noise, it can produce blurry results due to the object and camera motion. The reconstruction of a noise-less image is…