Related papers: Functional Autoregressive Processes in Reproducing…
We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ…
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…
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…
In this paper, we present a unified approach to function approximation in reproducing kernel Hilbert spaces (RKHS) that establishes a previously unrecognized optimality property for several well-known function approximation techniques, such…
Large-scale hypothesis testing is central to modern science, where controlling the False Discovery Rate (FDR) has become the standard approach to managing false positives across many simultaneous tests. Hypotheses rarely exist in isolation;…
This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact…
In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is…
We propose a general framework for policy representation for reinforcement learning tasks. This framework involves finding a low-dimensional embedding of the policy on a reproducing kernel Hilbert space (RKHS). The usage of RKHS based…
In this paper, an adaptive non-parametric method is proposed to estimate the scalar-valued nonlinear function that appears in uncertain systems governed by ordinary differential equations (ODEs). By employing an infinite-dimensional…
We introduce a novel framework for change point detection in spherical functional autoregressive (SPHAR) processes, enabling the identification of structural breaks in spatio-temporal random fields on the sphere. Our LASSO-regularized…
The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an…
For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard…
This paper presents new results on Functional Analysis of Variance for fixed effect models with correlated Hilbert-valued Gaussian error components. The geometry of the Reproducing Kernel Hilbert Space (RKHS) of the error term is considered…
Many modern spatio-temporal data sets, in sociology, epidemiology or seismology, for example, exhibit self-exciting characteristics, triggering and clustering behaviors both at the same time, that a suitable Hawkes space-time process can…
In statistical learning, identifying underlying structures of true target functions based on observed data plays a crucial role to facilitate subsequent modeling and analysis. Unlike most of those existing methods that focus on some…
The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and…
This paper introduces a new kind of seasonal fractional autoregressive process (SFAR) driven by fractional Gaussian noise (fGn). The new model includes a standard seasonal AR model and fGn. {The estimation of the parameters of this new…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system…
This paper proposes a method for constructing one-step prediction tubes for nonlinear systems using reproducing kernel Hilbert spaces. We approximate a bounded reproducing kernel Hilbert space (RKHS) hypothesis set by a finite-dimensional…