Related papers: ANOVA kernels and RKHS of zero mean functions for …
We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas…
We propose a novel framework for matching estimators for causal effect from observational data that is based on minimizing the dual norm of estimation error when expressed as an operator. We show that many popular matching estimators can be…
Kernels are often developed and used as implicit mapping functions that show impressive predictive power due to their high-dimensional feature space representations. In this study, we gradually construct a series of simple feature maps that…
We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…
This note characterizes multiplicative linear functionals on reproducing kernel Hilbert spaces of functions on the Euclidean unit ball in complex d-dimensional space, in terms of their action on kernel functions. The kernels considered are…
This paper considers the construction of Reproducing Kernel Hilbert Spaces (RKHS) on the sphere as an alternative to the conventional Hilbert space using the inner product that yields the L^2(S^2) function space of finite energy signals. In…
Function encoders are a recent technique that learn neural network basis functions to form compact, adaptive representations of Hilbert spaces of functions. We show that function encoders provide a principled connection to feature learning…
Motivated by the need of processing functional-valued data, or more general, operatorvalued data, we introduce the notion of the operator reproducing kernel Hilbert space (ORKHS). This space admits a unique operator reproducing kernel which…
In $\mathbb R^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert…
We present a novel variation of online kernel machines in which we exploit a consensus based optimization mechanism to guide the evolution of decision functions drawn from a reproducing kernel Hilbert space, which efficiently models the…
This paper presents a kernel formulation of the recently introduced diff-hash algorithm for the construction of similarity-sensitive hash functions. Our kernel diff-hash algorithm that shows superior performance on the problem of image…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition…
Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…
As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…
High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…
In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with…
We present a general kernel-based framework for learning operators between Banach spaces along with a priori error analysis and comprehensive numerical comparisons with popular neural net (NN) approaches such as Deep Operator Net (DeepONet)…