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We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex…

Optimization and Control · Mathematics 2014-11-20 Ting Kei Pong , Hao Sun , Ningchuan Wang , Henry Wolkowicz

We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…

Classical Analysis and ODEs · Mathematics 2025-07-15 Luis Gomez , Jonathan Jaimangal , Azita Mayeli , Tasfia Proma

We study the parameter estimation problem for a varying index coefficient model in high dimensions. Unlike the most existing works that iteratively estimate the parameters and link functions, based on the generalized Stein's identity, we…

Machine Learning · Statistics 2019-10-29 Sen Na , Zhuoran Yang , Zhaoran Wang , Mladen Kolar

Predictive models ground many state-of-the-art developments in statistical brain image analysis: decoding, MVPA, searchlight, or extraction of biomarkers. The principled approach to establish their validity and usefulness is…

Quantitative Methods · Quantitative Biology 2017-06-26 Gaël Varoquaux

Graphical and sparse (inverse) covariance models have found widespread use in modern sample-starved high dimensional applications. A part of their wide appeal stems from the significantly low sample sizes required for the existence of…

Statistics Theory · Mathematics 2023-11-28 Benjamin Roycraft , Bala Rajaratnam

We explore the limiting empirical eigenvalue distributions arising from matrices of the form \[A_{n+1} = \begin{bmatrix} A_n & I\\ I & A_n \end{bmatrix} , \]where $A_0$ is the adjacency matrix of a $k$-regular graph. We find that for…

Discrete Mathematics · Computer Science 2018-07-23 Clark Alexander , Tara Nenninger , Danielle Tucker

This paper investigates the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. In the special case where all edges of a graph are subdivided, we find the exact limits of the $k$-th largest…

Combinatorics · Mathematics 2023-03-21 Hitesh Kumar , Bojan Mohar , Shivaramakrishna Pragada , Hanmeng Zhan

We present an efficient method to estimate cross-validation bandwidth parameters for kernel density estimation in very large datasets where ordinary cross-validation is rendered highly inefficient, both statistically and computationally.…

Methodology · Statistics 2016-09-02 Anirban Bhattacharya , Jeffrey D. Hart

We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…

Social and Information Networks · Computer Science 2020-10-29 Nicolò Ruggeri , Caterina De Bacco

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple…

Machine Learning · Statistics 2012-01-11 Shuheng Zhou , Philipp Rutimann , Min Xu , Peter Buhlmann

We give an upper bound on the total variation distance between the linear eigenvalue statistic, properly scaled and centred, of a random matrix with a variance profile and the standard Gaussian random variable. The second order Poincar\'e…

Probability · Mathematics 2019-01-29 Kartick Adhikari , Indrajit Jana , Koushik Saha

In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problem in multivariate statistical analysis and there have been…

Statistics Theory · Mathematics 2015-04-28 Jiang Hu , Zhidong Bai , Chen Wang , Wei Wang

We introduce a novel covariance estimator for portfolio selection that adapts to the non-stationary or persistent heteroskedastic environments of financial time series by employing exponentially weighted averages and nonlinearly shrinking…

Machine Learning · Statistics 2023-01-23 Vincent Tan , Stefan Zohren

Intertwining analysis, algebra, numerical analysis and optimization, computing conjugate co-gradients of real-valued quotients gives rise to eigenvalue problems. In the linear Hermitian case, by inspecting optimal quotients in terms of…

Spectral Theory · Mathematics 2022-11-14 Marko Huhtanen , Olavi Nevanlinna

We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…

Methodology · Statistics 2013-01-17 Nicolas Städler , Sach Mukherjee

Least-squares models such as linear regression and Linear Discriminant Analysis (LDA) are amongst the most popular statistical learning techniques. However, since their computation time increases cubically with the number of features, they…

Machine Learning · Computer Science 2018-03-28 Matthias S. Treder

Recent technological advances in many domains including both genomics and brain imaging have led to an abundance of high-dimensional and correlated data being routinely collected. Classical multivariate approaches like Multivariate Analysis…

Methodology · Statistics 2018-11-20 Maxime Turgeon , Celia MT Greenwood , Aurelie Labbe

Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension $p$ is large in…

Statistics Theory · Mathematics 2018-11-26 Zeng Li , Clifford Lam , Jianfeng Yao , Qiwei Yao

In this paper, we characterize the asymptotic and large scale behavior of the eigenvalues of wavelet random matrices in high dimensions. We assume that possibly non-Gaussian, finite-variance $p$-variate measurements are made of a…

Statistics Theory · Mathematics 2024-06-11 Patrice Abry , B. Cooper Boniece , Gustavo Didier , Herwig Wendt

Information about intrinsic dimension is crucial to perform dimensionality reduction, compress information, design efficient algorithms, and do statistical adaptation. In this paper we propose an estimator for the intrinsic dimension of a…

Machine Learning · Statistics 2017-11-09 Paulo Serra , Michel Mandjes