Related papers: Function Spaces Without Kernels: Learning Compact …
This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…
Reproducing kernel Hilbert spaces provide a foundational framework for kernel-based learning, where regularization and interpolation problems admit finite-dimensional solutions through classical representer theorems. Many modern learning…
Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
Although reinforcement learning (RL) can solve many challenging sequential decision making problems, achieving zero-shot transfer across related tasks remains a challenge. The difficulty lies in finding a good representation for the current…
Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the…
We study feature learning in a compositional variant of kernel ridge regression in which the predictor is applied to a learnable linear transformation of the input. When the response depends on the input only through a low-dimensional…
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…
Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…
We develop a functional encoder-decoder approach to supervised meta-learning, where labeled data is encoded into an infinite-dimensional functional representation rather than a finite-dimensional one. Furthermore, rather than directly…
Artificial neural networks show promising performance in detecting correlations within data that are associated with specific outcomes. However, the black-box nature of such models can hinder the knowledge advancement in research fields by…
Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…
The theory of positive kernels and associated reproducing kernel Hilbert spaces, especially in the setting of holomorphic functions, has been an important tool for the last several decades in a number of areas of complex analysis and…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors.…
In recent years, there has been growing interest in the field of functional neural networks. They have been proposed and studied with the aim of approximating continuous functionals defined on sets of functions on Euclidean domains. In this…
This paper investigates a novel algorithmic approach to data representation based on kernel methods. Assuming that the observations lie in a Hilbert space X, the introduced Kernel Autoencoder (KAE) is the composition of mappings from…
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…
We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particular these functions include all the homogeneous polynomials…
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…