Related papers: Reproducing kernels based schemes for nonparametri…
We consider the theory of bond discounts, defined as the difference between the terminal payoff of the contract and its current price. Working in the setting of finite-dimensional realizations in the HJM framework, under suitable notions of…
We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice's (NIJ) Real-Time Crime Forecasting Challenge. Our method is a spatiotemporal forecasting model combining scalable…
This paper considers different facets of the interplay between reproducing kernel Hilbert spaces (RKHS) and stable analysis/synthesis processes: First, we analyze the structure of the reproducing kernel of a RKHS using frames and…
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regularization schemes have been studied to produce robust and stable…
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 consider expected risk minimization problems when the range of the estimator is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. To facilitate nonlinear…
In many remote sensing applications one wants to estimate variables or parameters of interest from observations. When the target variable is available at a resolution that matches the remote sensing observations, standard algorithms such as…
This work constructs a hypothesis test for detecting whether an data-generating function $h: R^p \rightarrow R$ belongs to a specific reproducing kernel Hilbert space $\mathcal{H}_0$ , where the structure of $\mathcal{H}_0$ is only…
The paper introduces a new efficient nonlinear one-class classifier formulated as the Rayleigh quotient criterion optimisation. The method, operating in a reproducing kernel Hilbert space, minimises the scatter of target distribution along…
Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…
We generalize Jan Willems' behavioral approach to a class of discrete-time nonlinear systems in a vector-valued reproducing kernel Hilbert space (RKHS). Apart from linear time-invariant systems, this class covers nonlinear systems modeled…
In this article, we study nonparametric inference problems in the context of multivariate or functional time series, including testing for goodness-of-fit, the presence of a change point in the marginal distribution, and the independence of…
A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…
In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…
This paper studies convergence of empirical risks in reproducing kernel Hilbert spaces (RKHS). A conventional assumption in the existing research is that empirical training data do not contain any noise but this may not be satisfied in some…
We focus on the problem of finding a non-linear classification function that lies in a Reproducing Kernel Hilbert Space (RKHS) both from the primal point of view (finding a perfect separator when one exists) and the dual point of view…
This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
We propose a novel online learning paradigm for nonlinear-function estimation tasks based on the iterative projections in the L2 space with probability measure reflecting the stochastic property of input signals. The proposed learning…