Related papers: Nonparametric functionals as generalized functions

Fisher's linear discriminant analysis is a classical method for classification, yet it is limited to capturing linear features only. Kernel discriminant analysis as an extension is known to successfully alleviate the limitation through a…

This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…

A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…

We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve…

The main purpose of this paper is to estimate the regression function by using a recursive nonparametric kernel approach. We derive the asymptotic normality for a general class of recursive kernel estimate of the regression function, under…

A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…

We reprove the well known fact that the energy distance defines a metric on the space of Borel probability measures on a Hilbert space with finite first moment by a new approach, by analyzing the behavior of the Gaussian kernel on Hilbert…

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

This paper deals with the nonparametric density estimation of the regression error term assuming its independence with the covariate. The difference between the feasible estimator which uses the estimated residuals and the unfeasible one…

Kernel expansions are a topic of considerable interest in machine learning, also because of their relation to the so-called feature maps introduced in machine learning. Properties of the associated basis functions and weights (corresponding…

In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning…

A scheme within density functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [H. Rydberg, et al., Phys. Rev. Lett. 91, 126402…

If $\Lambda $ is a measure space, $u:\Lambda ^{m}\rightarrow \Bbb{R}$ is a given function and $N\geq m,$ the function $U(x_{1},...,x_{N})=\left( \begin{array}{l} N \\ m \end{array} \right) ^{-1}\sum_{1\leq i_{1}<\cdots <i_{m}\leq…

Certain extremum estimators have asymptotic distributions that are non-Gaussian, yet characterizable as the distribution of the $\argmax$ of a Gaussian process. This paper presents high-level sufficient conditions under which such…

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…

The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

The distributional statistical framework replaces classical probability densities by distribution-kernel pairs $(T, \varphi)$, where $T$ is a tempered distribution and $\varphi$ is a rapidly decaying kernel. We develop the thesis that the…

Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…