Related papers: Group testing via residuation and partial geometri…
We propose a general, modular method for significance testing of groups (or clusters) of variables in a high-dimensional linear model. In presence of high correlations among the covariables, due to serious problems of identifiability, it is…
The usual problem for group testing is this: For a given number of individuals and a given prevalence, how many tests T* are required to find every infected individual? In real life, however, the problem is usually different: For a given…
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…
The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of tests, and is relevant in applications such as medical testing, communication protocols, pattern matching, and…
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…
In the pooled data problem, the goal is to identify the categories associated with a large collection of items via a sequence of pooled tests. Each pooled test reveals the number of items in the pool belonging to each category. A prominent…
We consider an efficiently decodable non-adaptive group testing (NAGT) problem that meets theoretical bounds. The problem is to find a few specific items (at most $d$) satisfying certain characteristics in a colossal number of $N$ items as…
We propose and analyze a novel scheme based on LDPC codes for quantitative group testing. The key underlying idea is to augment the bipartite graph by introducing hidden non-binary variables to strengthen the message-passing decoder. This…
Generative models typically sample outputs independently, and recent inference-time guidance and scaling algorithms focus on improving the quality of individual samples. However, in real-world applications, users are often presented with a…
The outbreak of the novel coronavirus (COVID-19) is unfolding as a major international crisis whose influence extends to every aspect of our daily lives. Effective testing allows infected individuals to be quarantined, thus reducing the…
Group testing (GT) is the Boolean version of spare signal recovery and, due to its simplicity, a marketplace for ideas that can be brought to bear upon related problems, such as heavy hitters, compressed sensing, and multiple access…
The problem of distributed matrix-vector product is considered, where the server distributes the task of the computation among $n$ worker nodes, out of which $L$ are compromised (but non-colluding) and may return incorrect results.…
In this paper, an information theoretic analysis on non-adaptive group testing schemes based on sparse pooling graphs is presented. The binary status of the objects to be tested are modeled by i.i.d. Bernoulli random variables with…
In this work, we consider the sparsity-constrained community-based group testing problem, where the population follows a community structure. In particular, the community consists of $F$ families, each with $M$ members. A number $k_f$ out…
Up to date, only lower and upper bounds for the optimal configuration of a Square Array (A2) Group Testing (GT) algorithm are known. We establish exact analytical formulae and provide a couple of applications of our result. First, we…
We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of "interpretable"…
In high dimensional settings, sparse structures are crucial for efficiency, either in term of memory, computation or performance. In some contexts, it is natural to handle more refined structures than pure sparsity, such as for instance…
Covariance matrices of random vectors contain information that is crucial for modelling. Specific structures and patterns of the covariances (or correlations) may be used to justify parametric models, e.g., autoregressive models. Until now,…