Related papers: Symmetric Group Testing and Superimposed Codes
We study the question of local testability of low (constant) degree functions from a product domain $S_1 \times \dots \times {S}_n$ to a field $\mathbb{F}$, where ${S_i} \subseteq \mathbb{F}$ can be arbitrary constant sized sets. We show…
A hypothesis testing algorithm is replicable if, when run on two different samples from the same distribution, it produces the same output with high probability. This notion, defined by by Impagliazzo, Lei, Pitassi, and Sorell [STOC'22],…
Independence testing is a classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
In this paper, we consider the problem of noiseless non-adaptive group testing under the for-each recovery guarantee, also known as probabilistic group testing. In the case of $n$ items and $k$ defectives, we provide an algorithm attaining…
Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…
Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…
When minimizing the empirical risk in binary classification, it is a common practice to replace the zero-one loss with a surrogate loss to make the learning objective feasible to optimize. Examples of well-known surrogate losses for binary…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
Group sequential design (GSD) is widely used in clinical trials in which correlated tests of multiple hypotheses are used. Multiple primary objectives resulting in tests with known correlations include evaluating 1) multiple experimental…
The evaluation of noisy binary classifiers on unlabeled data is treated as a streaming task: given a data sketch of the decisions by an ensemble, estimate the true prevalence of the labels as well as each classifier's accuracy on them. Two…
The optimizations of the track fittings require complex simulations of silicon strip detectors to be compliant with the fundamental properties of the hit heteroscedasticity. Many different generations of random numbers must be available…
The goal of group testing is to identify a small number of defective items within a large population. In the non-adaptive setting, tests are designed in advance and represented by a measurement matrix $\mM$, where rows correspond to tests…
In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…
We study the group testing problem where the goal is to identify a set of k infected individuals carrying a rare disease within a population of size n, based on the outcomes of pooled tests which return positive whenever there is at least…
Convex rank tests are partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. Each class consists of the…
We formulate and analyze a stochastic threshold group testing problem motivated by biological applications. Here a set of $n$ items contains a subset of $d \ll n$ defective items. Subsets (pools) of the $n$ items are tested -- the test…
We consider the problem of two-sample testing in a semi-supervised setting with abundant unlabeled covariate data. Standard two-sample tests neglect covariate information, which has the potential to significantly boost performance. However,…
In one-stage or non-adaptive group testing, instead of testing every sample unit individually, they are split, bundled in pools, and simultaneously tested. The results are then decoded to infer the states of the individual items. This…
The group testing problem is concerned with identifying a small number $k \sim n^\theta$ for $\theta \in (0,1)$ of infected individuals in a large population of size $n$. At our disposal is a testing procedure that allows us to test groups…