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We explore the problem of deriving a posteriori probabilities of being defective for the members of a population in the non-adaptive group testing framework. Both noiseless and noisy testing models are addressed. The technique, which relies…

Information Theory · Computer Science 2021-02-11 Gianluigi Liva , Enrico Paolini , Marco Chiani

In this paper, we study the problem of non-adaptive group testing, in which one seeks to identify which items are defective given a set of suitably-designed tests whose outcomes indicate whether or not at least one defective item was…

Information Theory · Computer Science 2025-09-26 Lan V. Truong , Matthew Aldridge , Jonathan Scarlett

This paper considers the problem of Quantitative Group Testing (QGT). Consider a set of $N$ items among which $K$ items are defective. The QGT problem is to identify (all or a sufficiently large fraction of) the defective items, where the…

Information Theory · Computer Science 2019-04-25 Esmaeil Karimi , Fatemeh Kazemi , Anoosheh Heidarzadeh , Krishna R. Narayanan , Alex Sprintson

In group testing, the task is to identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability $\alpha$, independent of all other…

Discrete Mathematics · Computer Science 2024-11-15 Lukas Hintze , Lena Krieg , Olga Scheftelowitsch , Haodong Zhu

In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the…

Statistics Theory · Mathematics 2010-11-30 Fengrong Wei , Jian Huang

Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find…

Data Structures and Algorithms · Computer Science 2016-06-13 Annalisa De Bonis

In a group testing scheme, a set of tests is designed to identify a small number $t$ of defective items that are present among a large number $N$ of items. Each test takes as input a group of items and produces a binary output indicating…

Information Theory · Computer Science 2016-11-17 Arya Mazumdar

The study in group testing aims to develop strategies to identify a small set of defective items among a large population using a few pooled tests. The established techniques have been highly beneficial in a broad spectrum of applications…

Information Theory · Computer Science 2025-01-23 Venkata Gandikota , Nikita Polyanskii , Haodong Yang

In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…

Statistics Theory · Mathematics 2020-11-16 Yisha Yao , Cun-Hui Zhang

Automated test-generation research overwhelmingly assumes the correctness of focal methods, yet practitioners routinely face non-regression scenarios where the focal method may be defective. A baseline evaluation of EVOSUITE and two leading…

Software Engineering · Computer Science 2026-02-03 Pengyu Xue , Yuxiang Zhang , Zhen Yang , Xiaoxue Ren , Xiang Li , Pengfei Hu , Linhao Wu , Kainan Li

The basic goal in combinatorial group testing is to identify a set of up to $d$ defective items within a large population of size $n \gg d$ using a pooling strategy. Namely, the items can be grouped together in pools, and a single…

Discrete Mathematics · Computer Science 2013-01-21 Mahdi Cheraghchi

In the problem of classical group testing one aims to identify a small subset (of size $d$) diseased individuals/defective items in a large population (of size $n$). This process is based on a minimal number of suitably-designed group tests…

Information Theory · Computer Science 2022-09-26 Xiwei Cheng , Sidharth Jaggi , Qiaoqiao Zhou

This work focuses on non-adaptive combinatorial group testing, with a primary goal of efficiently identifying a set of at most $d$ defective elements among a given set of $n$ elements using the fewest possible tests. Non-adaptive…

Information Theory · Computer Science 2026-04-28 Daniil Goshkoder , Nikita Polyanskii , Ilya Vorobyev

The fundamental task of group testing is to recover a small distinguished subset of items from a large population while efficiently reducing the total number of tests (measurements). The key contribution of this paper is in adopting a new…

Information Theory · Computer Science 2015-03-13 George Kamal Atia , Venkatesh Saligrama

Group testing is a technique which avoids individually testing $n$ samples for a rare disease and instead tests $n < p$ pools, where a pool consists of a mixture of small, equal portions of a subset of the $p$ samples. Group testing saves…

Statistics Theory · Mathematics 2023-08-29 Richeek Das , Aaron Jerry Ninan , Adithya Bhaskar , Ajit Rajwade

Group-testing refers to the problem of identifying (with high probability) a (small) subset of $D$ defectives from a (large) set of $N$ items via a "small" number of "pooled" tests. For ease of presentation in this work we focus on the…

Information Theory · Computer Science 2013-07-11 Sheng Cai , Mohammad Jahangoshahi , Mayank Bakshi , Sidharth Jaggi

Modern machine learning models may be susceptible to learning spurious correlations that hold on average but not for the atypical group of samples. To address the problem, previous approaches minimize the empirical worst-group risk. Despite…

Machine Learning · Computer Science 2023-03-13 Soumya Suvra Ghosal , Yixuan Li

We consider some computationally efficient and provably correct algorithms with near-optimal sample-complexity for the problem of noisy non-adaptive group testing. Group testing involves grouping arbitrary subsets of items into pools. Each…

Information Theory · Computer Science 2016-11-18 Chun Lam Chan , Sidharth Jaggi , Venkatesh Saligrama , Samar Agnihotri

Natural language understanding (NLU) models often rely on dataset biases rather than intended task-relevant features to achieve high performance on specific datasets. As a result, these models perform poorly on datasets outside the training…

Computation and Language · Computer Science 2023-01-05 Yougang Lyu , Piji Li , Yechang Yang , Maarten de Rijke , Pengjie Ren , Yukun Zhao , Dawei Yin , Zhaochun Ren

In combinatorial group testing (CGT), the objective is to identify the set of at most $d$ defective items from a pool of $n$ items using as few tests as possible. The celebrated result for the CGT problem is that the number of tests $t$ can…

Information Theory · Computer Science 2019-01-29 Huseyin A. Inan , Peter Kairouz , Ayfer Ozgur