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This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and…

Statistics Theory · Mathematics 2018-01-03 T. Tony Cai , Yihong Wu

We consider a Gaussian contamination (i.e., mixture) model where the contamination manifests itself as a change in variance. We study this model in various asymptotic regimes, in parallel with the work of Ingster (1997) and Donoho and Jin…

Statistics Theory · Mathematics 2018-07-31 Ery Arias-Castro , Rong Huang

Mixed Poisson distributions provide a flexible approach to the analysis of count data with overdispersion, zero inflation, or heavy tails. Since the Poisson mean must be nonnegative, the mixing distribution is typically assumed to have…

Probability · Mathematics 2025-08-20 F. William Townes

In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…

Statistics Theory · Mathematics 2022-02-17 Bhaswar B. Bhattacharya , Rajarshi Mukherjee

We consider Gaussian mixture models in high dimensions and concentrate on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive information bounds and establish the performance…

Statistics Theory · Mathematics 2016-10-04 Nicolas Verzelen , Ery Arias-Castro

We suggest partial logarithmic binning as the method of choice for uncovering the nature of many distributions encountered in information science (IS). Logarithmic binning retrieves information and trends "not visible" in noisy power-law…

Physics and Society · Physics 2012-04-03 Staša Milojević

Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…

Data Structures and Algorithms · Computer Science 2023-04-05 Renato Ferreira Pinto , Nathaniel Harms

Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…

Machine Learning · Computer Science 2022-12-06 Maryam Aliakbarpour , Amartya Shankha Biswas , Kavya Ravichandran , Ronitt Rubinfeld

The problem of signal detection using sparse, faint information is closely related to a variety of contemporary statistical problems, including the control of false-discovery rate, and classification using very high-dimensional data. Each…

Statistics Theory · Mathematics 2008-12-18 Peter Hall , Jiashun Jin

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…

Statistics Theory · Mathematics 2015-03-06 Rajarshi Mukherjee , Natesh S. Pillai , Xihong Lin

We consider a collection of independent random variables that are identically distributed, except for a small subset which follows a different, anomalous distribution. We study the problem of detecting which random variables in the…

Information Theory · Computer Science 2018-06-21 Natalie Durgin , Rachel Grotheer , Chenxi Huang , Shuang Li , Anna Ma , Deanna Needell , Jing Qin

This paper studies the trade-off between two different kinds of pure exploration: breadth versus depth. The most biased coin problem asks how many total coin flips are required to identify a "heavy" coin from an infinite bag containing both…

Machine Learning · Computer Science 2016-03-29 Kevin Jamieson , Daniel Haas , Ben Recht

We consider the problem of detecting the presence of a submatrix with larger-than-usual values in a large data matrix. This problem was considered in (Butucea and Ingster, 2013) under a one-parameter exponential family, and one of the test…

Statistics Theory · Mathematics 2016-04-27 Ery Arias-Castro , Yuchao Liu

This paper addresses detecting anomalous patterns in images, time-series, and tensor data when the location and scale of the pattern is unknown a priori. The multiscale scan statistic convolves the proposed pattern with the image at various…

Statistics Theory · Mathematics 2018-06-22 James Sharpnack

In this paper, we develop asymptotic theory for the mixing detection methodology proposed by M. Magdziarz and A. Weron [Physical Review E, 84:051138 (2011)]. The assumptions cover a broad family of Gaussian stochastic processes including…

Probability · Mathematics 2021-06-16 Kui Zhang , Gustavo Didier

As one of the most important types of (weaker) supervised information in machine learning and pattern recognition, pairwise constraint, which specifies whether a pair of data points occur together, has recently received significant…

Computer Vision and Pattern Recognition · Computer Science 2015-02-23 Zhenyong Fu , Zhiwu Lu

Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…

Information Theory · Computer Science 2022-12-05 James Melbourne , Saurav Talukdar , Shreyas Bhaban , Mokshay Madiman , Murti V. Salapaka

We consider the estimation of the mixing distribution of a normal distribution where both the shift and scale are unobserved random variables. We argue that in general, the model is not identifiable. We give an elegant non-constructive…

Statistics Theory · Mathematics 2024-08-20 Ya'acov Ritov

In object tracking and state estimation problems, ambiguous evidence such as imprecise measurements and the absence of detections can contain valuable information and thus be leveraged to further refine the probabilistic belief state. In…

Signal Processing · Electrical Eng. & Systems 2023-05-23 Keith A. LeGrand , Silvia Ferrari

We investigate the performance of the scan (maximum likelihood ratio statistic) and of the average likelihood ratio statistic in the problem of detecting a deterministic signal with unknown spatial extent in the prototypical univariate…

Methodology · Statistics 2014-02-26 Hock Peng Chan , Guenther Walther