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In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…

Combinatorics · Mathematics 2021-10-15 Bingchen Qian , Xin Wang , Gennian Ge

We consider the problem of estimating an unknown coordinate-wise monotone function given noisy measurements, known as the isotonic regression problem. Often, only a small subset of the features affects the output. This motivates the sparse…

Statistics Theory · Mathematics 2019-07-04 David Gamarnik , Julia Gaudio

In this research paper, structured bi-matrix variate, matrix quadratic equations are considered. Some lemmas related to determining the eigenvalues of unknown matrices are proved. Also, a method of determining the diagonalizabe unknown…

General Mathematics · Mathematics 2012-07-26 Garimella Rama Murthy

Isotonic regression is a nonparametric approach for fitting monotonic models to data that has been widely studied from both theoretical and practical perspectives. However, this approach encounters computational and statistical overfitting…

Methodology · Statistics 2012-03-21 Ronny Luss , Saharon Rosset , Moni Shahar

In this paper, state and noise covariance estimation problems for linear system with unknown multiplicative noise are considered. The measurement likelihood is modelled as a mixture of two Gaussian distributions and a Student's t…

Signal Processing · Electrical Eng. & Systems 2023-08-29 Xingkai Yu , Ziyang Meng

Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…

Statistical Mechanics · Physics 2015-03-13 Fabrizio Altarelli , Alfredo Braunstein , Abolfazl Ramezanpour , Riccardo Zecchina

We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…

Optimization and Control · Mathematics 2021-12-07 Roman Pogodin , Mikhail Krechetov , Yury Maximov

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…

Systems and Control · Computer Science 2016-08-09 Laurent Bako , Henrik Ohlsson

In this paper, we consider the problem of seriation of a permuted structured matrix based on noisy observations. The entries of the matrix relate to an expected quantification of interaction between two objects: the higher the value, the…

Statistics Theory · Mathematics 2025-07-21 Clément Berenfeld , Alexandra Carpentier , Nicolas Verzelen

Isotonic regression is a shape-constrained nonparametric regression in which the regression is an increasing step function. For $n$ data points, the number of steps in the isotonic regression may be as large as $n$. As a result, standard…

Computation · Statistics 2014-12-10 Janis Hardwick , Quentin F. Stout

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

Statistics Theory · Mathematics 2016-07-05 Olga Klopp , Karim Lounici , Alexandre B. Tsybakov

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…

Machine Learning · Statistics 2017-05-23 Mohammadreza Soltani , Chinmay Hegde

The Nystr\"om method is a popular choice for finding a low-rank approximation to a symmetric positive semi-definite matrix. The method can fail when applied to symmetric indefinite matrices, for which the error can be unboundedly large. In…

Numerical Analysis · Mathematics 2023-10-10 Taejun Park , Yuji Nakatsukasa

We have recently presented a method to solve an overdetermined linear system of equations with multiple right hand side vectors, where the unknown matrix is to be symmetric and positive definite. The coefficient and the right hand side…

Optimization and Control · Mathematics 2014-09-19 Negin Bagherpour , Nezam Mahdavi-Amiri

We study alternating minimization for matrix completion in the simplest possible setting: completing a rank-one matrix from a revealed subset of the entries. We bound the asymptotic convergence rate by the variational characterization of…

Machine Learning · Computer Science 2020-08-13 Rui Liu , Alex Olshevsky

The problem of fast point-to-point MIMO channel mutual information estimation is addressed, in the situation where the receiver undergoes unknown colored interference, whereas the channel with the transmitter is perfectly known. The…

Probability · Mathematics 2012-03-14 Abla Kammoun , Romain Couillet , Jamal Najim , Merouane Debbah

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

Machine Learning · Statistics 2010-09-07 Mehryar Mohri , Ameet Talwalkar

We study the problem of solving a linear sensing system when the observations are unlabeled. Specifically we seek a solution to a linear system of equations y = Ax when the order of the observations in the vector y is unknown. Focusing on…

Information Theory · Computer Science 2015-12-02 Jayakrishnan Unnikrishnan , Saeid Haghighatshoar , Martin Vetterli

Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…

Statistics Theory · Mathematics 2022-05-31 Edgar Dobriban

We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare…

Optimization and Control · Mathematics 2024-12-17 Aida Khajavirad , Yakun Wang