Related papers: Functional Autoregressive Processes in Reproducing…
Kernel methods form a theoretically-grounded, powerful and versatile framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the \emph{kernel trick} to perform pairwise evaluations of…
Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control. In this domain, kernel methods such as Gaussian process…
In this paper, we develop a generalized theory of convolutional signal processing and neural networks for Reproducing Kernel Hilbert Spaces (RKHS). Leveraging the theory of algebraic signal processing (ASP), we show that any RKHS allows the…
We introduce a complex-valued counterpart of the representer theorem in machine learning. We study several learning and minimization problems in reproducing kernel Hilbert spaces (RKHSs), with the aim of identifying appropriate input-output…
This paper introduces a new periodic fractional autoregressive process (PFAR) driven by fractional Gaussian noise (fGn) to model time series of precipitation evapotranspiration. Compared with the similar model in [\emph{Water Resources…
Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…
A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic…
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 paper, we discuss the problem of system identification when frequency domain side information is available on the system. Initially, we consider the case where the prior knowledge is provided as being the $\Hcal_{\infty}$-norm of…
Nonlinear autoregressive models are very useful for modeling many natural processes, however, the size of the class of these models is large. Functional-coefficient autoregressive models (FCAR) are useful structures for reducing the size of…
We study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics. Based on the fluctuation-dissipation theory, this problem is reformulated as an unsupervised learning task…
Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependence and the attractive feature of being resolution-invariant.…
In this paper, we present sharp estimates for the covering numbers of the embedding of the reproducing kernel Hilbert space (RKHS) associated with the Weierstrass fractal kernel into the space of continuous functions. The method we apply is…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…
A methodological framework for ensemble-based estimation and simulation of high dimensional dynamical systems such as the oceanic or atmospheric flows is proposed. To that end, the dynamical system is embedded in a family of reproducing…
Random objects are complex non-Euclidean data taking value in general metric space, possibly devoid of any underlying vector space structure. Such data are getting increasingly abundant with the rapid advancement in technology. Examples…
Under the reproducing kernel Hilbert spaces (RKHS), we consider the penalized least-squares of the partially functional linear models (PFLM), whose predictor contains both functional and traditional multivariate parts, and the multivariate…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…