Related papers: Optimal Nested Test Plan for Combinatorial Quantit…
We consider the problem of non-adaptive group testing of $N$ items out of which $K$ or less items are known to be defective. We propose a testing scheme based on left-and-right-regular sparse-graph codes and a simple iterative decoder. We…
We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional…
We consider the task of distinguishing whether a quantum system is prepared in a state from one of several sets of quantum states. Assuming their convexity and stability under tensor product, we prove that the optimal error exponent for…
Characterization of quantum systems from experimental data is a central problem in quantum science and technology. But which measurements should be used to gather data in the first place? While optimal measurement choices can be worked out…
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…
We consider the problem of identifying infected individuals in a population of size N. We introduce a group testing approach that uses significantly fewer than N tests when infection prevalence is low. The most common approach to group…
We study the problem of detecting planted solutions in a random satisfiability formula. Adopting the formalism of hypothesis testing in statistical analysis, we describe the minimax optimal rates of detection. Our analysis relies on the…
In this paper, we propose a computer-oriented method of construction of optimal group sequential hypothesis tests with variable group sizes. In particular, for independent and identically distributed observations we obtain the form of…
The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient…
Inspired by applications in testing for Covid-19, we consider a variant of two-stage group testing called "conservative" (or "trivial") two-stage testing, where every item declared to be defective must be definitively confirmed by being…
We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…
We study a ranking and selection problem of learning from choice-based feedback with dynamic assortments. In this problem, a company sequentially displays a set of items to a population of customers and collects their choices as feedback.…
Group testing is a well known search problem that consists in detecting up to $s$ defective elements of the set $[t]=\{1,\ldots,t\}$ by carrying out tests on properly chosen subsets of $[t]$. In classical group testing the goal is to find…
Combinatorial group testing (CGT) is used to identify defective items from a set of items by grouping them together and performing a small number of tests on the groups. Recently, group testing has been used to design efficient COVID-19…
We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…
Quantum state tomography is an indispensable but costly part of many quantum experiments. Typically, it requires measurements to be carried in a number of different settings on a fixed experimental setup. The collected data is often…
Group testing is an active area of current research and has important applications in medicine, biotechnology, genetics, and product testing. There have been recent advances in design and estimation, but the simple Dorfman procedure…
In this paper, we consider the problem of designing optimal pooling matrix for group testing (for example, for COVID-19 virus testing) with the constraint that no more than $r>0$ samples can be pooled together, which we call "dilution…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…