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We study a principal component analysis problem under the spiked Wishart model in which the structure in the signal is captured by a class of union-of-subspace models. This general class includes vanilla sparse PCA as well as its variants…

Machine Learning · Statistics 2024-01-02 Guanyi Wang , Mengqi Lou , Ashwin Pananjady

One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…

Statistics Theory · Mathematics 2022-06-22 Tselil Schramm , Alexander S. Wein

This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal…

Methodology · Statistics 2024-10-02 Jianqing Fan , Yuling Yan , Yuheng Zheng

This paper develops a unified information-theoretic framework for artificial-intelligence (AI)-aided integrated sensing and communication (ISAC), where a learning component with limited representational capacity is embedded within the…

Information Theory · Computer Science 2025-12-16 Farshad Rostami Ghadi , F. Javier Lopez-Martinez , Kai-Kit Wong , Christos Masouros

We present novel algorithmic techniques to efficiently verify the Kruskal rank of matrices that arise in sparse linear regression, tensor decomposition, and latent variable models. Our unified framework combines randomized hashing…

Data Structures and Algorithms · Computer Science 2025-03-10 Fengqin Zhou

We consider the problem of grouping items into clusters based on few random pairwise comparisons between the items. We introduce three closely related algorithms for this task: a belief propagation algorithm approximating the Bayes optimal…

Social and Information Networks · Computer Science 2016-08-26 Alaa Saade , Marc Lelarge , Florent Krzakala , Lenka Zdeborová

In this paper we study sharp thresholds for detecting sparse signals in $\beta$-models for potentially sparse random graphs. The results demonstrate interesting interplay between graph sparsity, signal sparsity, and signal strength. In…

Statistics Theory · Mathematics 2017-05-30 Rajarshi Mukherjee , Sumit Mukherjee , Subhabrata Sen

This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly…

Information Theory · Computer Science 2013-09-10 Junhong Lin , Song Li

We consider the problem of inferring the conditional independence graph (CIG) of a multivariate stationary dicrete-time Gaussian random process based on a finite length observation. Using information-theoretic methods, we derive a lower…

Statistics Theory · Mathematics 2014-03-06 Gabor Hannak , Alexander Jung , Norbert Goertz

We study the statistical problem of estimating a rank-one sparse tensor corrupted by additive Gaussian noise, a model also known as sparse tensor PCA. We show that for Bernoulli and Bernoulli-Rademacher distributed signals and \emph{for…

Statistics Theory · Mathematics 2020-09-08 Jonathan Niles-Weed , Ilias Zadik

Although federated learning has gained prominence as a privacy-preserving framework tailored for distributed Internet of Things (IoT) environments, current federated principal component analysis (PCA) methods lack integration of sparsity, a…

Machine Learning · Computer Science 2025-10-29 Chenyi Huang , Xianchao Xiu

In this paper, we analyze the information theoretic lower bound on the necessary number of samples needed for recovering a sparse signal under different compressed sensing settings. We focus on the weighted graph model, a model-based…

Information Theory · Computer Science 2022-09-16 Adarsh Barik , Jean Honorio

Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…

Machine Learning · Statistics 2025-09-09 Amnon Balanov , Tamir Bendory , Wasim Huleihel

In the machine learning era, sparsity continues to attract significant interest due to the benefits it provides to learning models. Algorithms aiming to optimise the \(\ell_0\)- and \(\ell_1\)-norm are the common choices to achieve…

Image and Video Processing · Electrical Eng. & Systems 2020-11-25 Perla Mayo , Robin Holmes , Alin Achim

We study a random graph model for small-world networks which are ubiquitous in social and biological sciences. In this model, a dense cycle of expected bandwidth $n \tau$, representing the hidden one-dimensional geometry of vertices, is…

Statistics Theory · Mathematics 2024-02-02 Cheng Mao , Alexander S. Wein , Shenduo Zhang

We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…

Machine Learning · Statistics 2023-07-07 Gabriel Arpino , Ramji Venkataramanan

The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…

Machine Learning · Statistics 2025-04-07 Jinhang Chai , Jianqing Fan

Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated from genomics, imaging and other fields.…

Methodology · Statistics 2016-04-05 Chao Gao , Zongming Ma , Harrison H. Zhou

Consider a network consisting of two subnetworks (communities) connected by some external edges. Given the network topology, the community detection problem can be cast as a graph partitioning problem that aims to identify the external…

Social and Information Networks · Computer Science 2023-07-19 Pin-Yu Chen , Alfred O. Hero

We study the fundamental tradeoffs between statistical accuracy and computational tractability in the analysis of high dimensional heterogeneous data. As examples, we study sparse Gaussian mixture model, mixture of sparse linear…

Statistics Theory · Mathematics 2018-08-22 Jianqing Fan , Han Liu , Zhaoran Wang , Zhuoran Yang