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We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet…

Methodology · Statistics 2011-11-02 Matthew A. Taddy , Athanasios Kottas

An extension of reproducing kernel Hilbert space (RKHS) theory provides a new framework for modeling functional regression models with functional responses. The approach only presumes a general nonlinear regression structure as opposed to…

Statistics Theory · Mathematics 2008-12-17 Heng Lian

This short technical report presents some learning theory results on vector-valued reproducing kernel Hilbert space (RKHS) regression, where the input space is allowed to be non-compact and the output space is a (possibly…

Machine Learning · Statistics 2022-02-17 Junhyunng Park , Krikamol Muandet

We develop a new framework for estimating joint probability distributions using tensor product reproducing kernel Hilbert spaces (RKHS). Our framework accommodates a low-dimensional, normalized and positive model of a Radon--Nikodym…

Machine Learning · Statistics 2024-09-25 Damir Filipovic , Michael Multerer , Paul Schneider

Forsstr\"om et al. [8] recently introduced a large class of $\{0,1\}$-valued processes that they named Poisson representable. In addition to deriving several interesting properties for these processes, their main focus was determining which…

Probability · Mathematics 2025-01-27 Stein Andreas Bethuelsen , Malin Palö Forsström

A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear…

Statistics Theory · Mathematics 2023-04-20 Yoshihito Kazashi , Fabio Nobile

The X-ray transform is one of the most fundamental integral operators in image processing and reconstruction. In this article, we revisit the formalism of the X-ray transform by considering it as an operator between Reproducing Kernel…

Functional Analysis · Mathematics 2024-06-26 Ho Yun , Victor M. Panaretos

This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely…

Machine Learning · Statistics 2025-06-24 Motonobu Kanagawa , Philipp Hennig , Dino Sejdinovic , Bharath K. Sriperumbudur

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…

Machine Learning · Statistics 2016-10-27 Yang Song , Jun Zhu , Yong Ren

We present a novel Bayesian framework for inverse problems in which the pos terior distribution is interpreted as the intensity measure of a Poisson point process (PPP). The posterior density is approximated using kernel density estimation,…

Numerical Analysis · Mathematics 2025-10-08 Zhiliang Deng , Zhiyuan Wang , Xiaomei Yang , Xiaofei Guan

Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space.…

Machine Learning · Computer Science 2017-04-26 Pantelis Bouboulis , Sergios Theodoridis

This work studies nonparametric Bayesian estimation of the intensity function of an inhomogeneous Poisson point process in the important case where the intensity depends on covariates, based on the observation of a single realisation of the…

Statistics Theory · Mathematics 2025-05-09 Matteo Giordano , Alisa Kirichenko , Judith Rousseau

We study recursive regularized learning algorithms in the reproducing kernel Hilbert space (RKHS) with non-stationary online data streams. We introduce the concept of random Tikhonov regularization path and decompose the tracking error of…

Machine Learning · Computer Science 2025-10-24 Xiwei Zhang , Yan Chen , Tao Li

We propose a novel Bayesian methodology for inference in functional linear and logistic regression models based on the theory of reproducing kernel Hilbert spaces (RKHS's). We introduce general models that build upon the RKHS generated by…

Methodology · Statistics 2025-09-09 José R. Berrendero , Antonio Coín , Antonio Cuevas

We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…

Statistics Theory · Mathematics 2022-08-24 Daren Wang , Zifeng Zhao , Yi Yu , Rebecca Willett

We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. We exhibit a prior on intensities which both leads to a computationally feasible method and enjoys…

Statistics Theory · Mathematics 2013-11-28 Eduard Belitser , Paulo Serra , Harry van Zanten

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…

Machine Learning · Statistics 2019-07-25 Seth Flaxman , Michael Chirico , Pau Pereira , Charles Loeffler

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…

Optimization and Control · Mathematics 2020-05-19 Shaoyan Guo , Huifu Xu , Liwei Zhang

Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…

Methodology · Statistics 2021-09-14 Jiayi Wang , Raymond K. W. Wong , Xiaoke Zhang

We propose a hierarchical learning strategy aimed at generating sparse representations and associated models for large noisy datasets. The hierarchy follows from approximation spaces identified at successively finer scales. For promoting…

Machine Learning · Computer Science 2020-06-11 Prashant Shekhar , Abani Patra