Related papers: Functional learning through kernels
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
In this article, a novel approach to learning a complex function which can be written as the system of linear equations is introduced. This learning is grounded upon the observation that solving the system of linear equations by a…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and…
Motivated by the abundance of functional data such as time series and images, there has been a growing interest in integrating such data into neural networks and learning maps from function spaces to R (i.e., functionals). In this paper, we…
We characterize the reproducing kernel Hilbert spaces whose elements are $p$-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for $p=2$ we show that the spectral…
We discuss how to define a kernel for Signal Temporal Logic (STL) formulae. Such a kernel allows us to embed the space of formulae into a Hilbert space, and opens up the use of kernel-based machine learning algorithms in the context of STL.…
Gaussian Radial Basis Function (RBF) Kernels are the most-often-employed kernels in artificial intelligence and machine learning routines for providing optimally-best results in contrast to their respective counter-parts. However, a little…
The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…
The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…
We derive analytical expressions for the generalization performance of kernel regression as a function of the number of training samples using theoretical methods from Gaussian processes and statistical physics. Our expressions apply to…
We discuss a general method to learn data representations from multiple tasks. We provide a justification for this method in both settings of multitask learning and learning-to-learn. The method is illustrated in detail in the special case…
By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…
Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or…
Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…
The primary hyperparameter in kernel regression (KR) is the choice of kernel. In most theoretical studies of KR, one assumes the kernel is fixed before seeing the training data. Under this assumption, it is known that the optimal kernel is…
Feature learning in neural networks is crucial for their expressive power and inductive biases, motivating various theoretical approaches. Some approaches describe network behavior after training through a change in kernel scale from…
Learning the kernel functions used in kernel methods has been a vastly explored area in machine learning. It is now widely accepted that to obtain 'good' performance, learning a kernel function is the key challenge. In this work we focus on…
Many kinds of data are naturally amenable to being treated as sequences. An example is text data, where a text may be seen as a sequence of words. Another example is clickstream data, where a data instance is a sequence of clicks made by a…
In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for…