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Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

Machine Learning · Computer Science 2012-03-19 Yuan , Qi , Ahmed H. Abdel-Gawad , Thomas P. Minka

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…

Probability · Mathematics 2009-11-11 V. Shcherbakov

We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

Statistics Theory · Mathematics 2015-02-10 Weining Shen , Subhashis Ghosal

We propose a new method for simplification of Gaussian process (GP) models by projecting the information contained in the full encompassing model and selecting a reduced number of variables based on their predictive relevance. Our results…

Methodology · Statistics 2017-12-18 Juho Piironen , Aki Vehtari

In this paper, we precisely quantify the wavelet compressibility of compound Poisson processes. To that end, we expand the given random process over the Haar wavelet basis and we analyse its asymptotic approximation properties. By only…

Information Theory · Computer Science 2021-12-20 Shayan Aziznejad , Julien Fageot

We present an approximate Bayesian inference approach for estimating the intensity of an inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the…

Machine Learning · Statistics 2019-05-06 Christian Donner , Manfred Opper

Deep Gaussian processes have recently been proposed as natural objects to fit, similarly to deep neural networks, possibly complex features present in modern data samples, such as compositional structures. Adopting a Bayesian nonparametric…

Statistics Theory · Mathematics 2025-02-04 Ismaël Castillo , Thibault Randrianarisoa

We define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns. The three distributions we consider are derived from the gamma-Poisson, gamma-negative binomial, and…

Methodology · Statistics 2015-07-14 Mingyuan Zhou , Oscar Hernan Madrid Padilla , James G. Scott

Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…

Methodology · Statistics 2013-10-08 Antonio Canale , David B. Dunson

While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own right. Current…

Machine Learning · Statistics 2017-04-17 Anirban Roychowdhury , Brian Kulis

BayesianOptimization(BO) is a sample-efficient black-box optimizer, and extensive methods have been proposed to build the absolute function response of the black-box function through a probabilistic surrogate model, including…

Machine Learning · Computer Science 2024-02-07 Xiaoxing Wang , Jiaxing Li , Chao Xue , Wei Liu , Weifeng Liu , Xiaokang Yang , Junchi Yan , Dacheng Tao

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

Machine Learning · Computer Science 2016-03-08 Z. Zhang , K. Duraisamy , N. A. Gumerov

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…

Machine Learning · Statistics 2019-08-27 David Reeb , Andreas Doerr , Sebastian Gerwinn , Barbara Rakitsch

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

Methodology · Statistics 2013-10-07 Rajesh Talluri , Veerabhadran Baladandayuthapani , Bani K. Mallick

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Methodology · Statistics 2011-06-29 Anjishnu Banerjee , David Dunson , Surya Tokdar

The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…

Statistics Theory · Mathematics 2014-07-03 Antonio Lijoi , Bernardo Nipoti , Igor Prünster

We investigate the class of $\sigma$-stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs which encompasses most of the the popular…

Computation · Statistics 2018-02-22 María Lomelí , Stefano Favaro , Yee Whye Teh

The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem…

Probability · Mathematics 2016-09-07 Louis H. Y. Chen , Aihua Xia

In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as…

Machine Learning · Statistics 2016-08-22 Yves-Laurent Kom Samo , Stephen Roberts

The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…

Machine Learning · Statistics 2023-10-09 Eliezer de Souza da Silva , Tomasz Kuśmierczyk , Marcelo Hartmann , Arto Klami