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We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

Machine Learning · Computer Science 2015-11-10 Francis Bach

We study the problem of optimal estimation of the density cluster tree under various assumptions on the underlying density. Building up from the seminal work of Chaudhuri et al. [2014], we formulate a new notion of clustering consistency…

Statistics Theory · Mathematics 2019-12-05 Daren Wang , Xinyang Lu , Alessandro Rinaldo

In response to the U.S.\ Food and Drug Administration's (FDA) Project Optimus, a paradigm shift is underway in the design of early-phase oncology trials. To accelerate drug development, seamless Phase I/II designs have gained increasing…

Methodology · Statistics 2025-11-04 Kana Makino , Natsumi Makigusa , Masahiro Kojima

Linear regression models depend directly on the design matrix and its properties. Techniques that efficiently estimate model coefficients by partitioning rows of the design matrix are increasingly popular for large-scale problems because…

Machine Learning · Statistics 2019-07-23 Michael J. Kane , Bryan Lewis , Sekhar Tatikonda , Simon Urbanek

We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…

Methodology · Statistics 2018-07-19 Madhurima Nath , Stephen Eubank

We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…

Machine Learning · Computer Science 2013-06-05 Alex Gittens , Michael W. Mahoney

We consider inference for the mean and covariance functions of covariate adjusted functional data using Local Linear Kernel (LLK) estimators. By means of a double asymptotic, we differentiate between sparse and dense covariate adjusted…

Methodology · Statistics 2018-02-28 Dominik Liebl

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…

Machine Learning · Statistics 2021-11-05 Cristopher Salvi , Maud Lemercier , Chong Liu , Blanka Hovarth , Theodoros Damoulas , Terry Lyons

Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing networks. However, there has been little…

Statistics Theory · Mathematics 2015-11-18 Chao Gao , Yu Lu , Harrison H. Zhou

Motivated by portfolio allocation and linear discriminant analysis, we consider estimating a functional $\mathbf{\mu}^T \mathbf{\Sigma}^{-1} \mathbf{\mu}$ involving both the mean vector $\mathbf{\mu}$ and covariance matrix…

Statistics Theory · Mathematics 2021-02-12 Jianqing Fan , Haolei Weng , Yifeng Zhou

In this paper, we discuss the convergence analysis of the conjugate gradient-based algorithm for the functional linear model in the reproducing kernel Hilbert space framework, utilizing early stopping results in regularization against…

Statistics Theory · Mathematics 2023-10-05 Naveen Gupta , S. Sivananthan , Bharath K. Sriperumbudur

In the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial derivatives. We use a random series of…

Statistics Theory · Mathematics 2016-04-13 William Weimin Yoo , Subhashis Ghosal

The aim of this article is to propose a novel kernel estimator of the baseline function in a general high-dimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the…

Applications · Statistics 2015-07-07 Agathe Guilloux , Sarah Lemler , Marie-Luce Taupin

Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…

Methodology · Statistics 2022-04-20 Yichi Zhang , Weining Shen , Dehan Kong

We describe an asynchronous parallel stochastic coordinate descent algorithm for minimizing smooth unconstrained or separably constrained functions. The method achieves a linear convergence rate on functions that satisfy an essential strong…

Optimization and Control · Mathematics 2014-11-12 Ji Liu , Stephen J. Wright , Christopher Ré , Victor Bittorf , Srikrishna Sridhar

We first revisit the problem of estimating the spot volatility of an It\^o semimartingale using a kernel estimator. We prove a Central Limit Theorem with optimal convergence rate for a general two-sided kernel. Next, we introduce a new…

Econometrics · Economics 2022-02-08 José E. Figueroa-López , Bei Wu

Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely…

Statistics Theory · Mathematics 2009-09-29 Peter Hall , Alexander Meister

We use a suitable version of the so-called "kernel trick" to devise two-sample (homogeneity) tests, especially focussed on high-dimensional and functional data. Our proposal entails a simplification related to the important practical…

Statistics Theory · Mathematics 2024-04-24 Javier Cárcamo , Antonio Cuevas , Luis-Alberto Rodríguez

Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density.…

Statistics Theory · Mathematics 2019-01-03 Maciej Skorski

Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…

Methodology · Statistics 2022-12-06 Canhong Wen , Ruipeng Dong , Xueqin Wang , Weiyu Li , Heping Zhang