Related papers: On the optimality of some group testing algorithms
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
We consider the well-studied dueling bandit problem, where a learner aims to identify near-optimal actions using pairwise comparisons, under the constraint of differential privacy. We consider a general class of utility-based preference…
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…
In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential…
An algorithm is given for determining an optimal $b$-step approximation of weighted data, where the error is measured with respect to the $L_\infty$ norm. For data presorted by the independent variable the algorithm takes $\Theta(n + \log n…
Traditionally, robust statistics has focused on designing estimators tolerant to a minority of contaminated data. Robust list-decodable learning focuses on the more challenging regime where only a minority $\frac 1 k$ fraction of the…
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…
Given $n$ elements, an integer $k$ and a parameter $\varepsilon$, we study to select an element with rank in $(k-n\varepsilon,k+n\varepsilon]$ using unreliable comparisons where the outcome of each comparison is incorrect independently with…
What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…
Most discovery systems for silent failures work in two phases: a continuous monitoring phase that detects presence of failures through probe packets and a localization phase that pinpoints the faulty element(s). This separation is important…
In recent years, algorithmic breakthroughs in stringology, computational social choice, scheduling, etc., were achieved by applying the theory of so-called $n$-fold integer programming. An $n$-fold integer program (IP) has a highly uniform…
This paper studies the problem of differentially private empirical risk minimization (DP-ERM) for binary linear classification. We obtain an efficient $(\varepsilon,\delta)$-DP algorithm with an empirical zero-one risk bound of…
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
Test-time training (TTT) adapts language models through gradient-based updates at inference. But is adaptation the right strategy? We study compute-optimal test-time strategies for verifiable execution-grounded (VEG) tasks, domains like GPU…
The challenge of identifying the best feasible arm within a fixed budget has attracted considerable interest in recent years. However, a notable gap remains in the literature: the exact exponential rate at which the error probability…
This paper considers the noisy group testing problem where among a large population of items some are defective. The goal is to identify all defective items by testing groups of items, with the minimum possible number of tests. The focus of…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
Recent papers initiated the study of a generalization of group testing where the potentially contaminated sets are the members of a given hypergraph F=(V,E). This generalization finds application in contexts where contaminations can be…
We consider search by mobile agents for a hidden, idle target, placed on the infinite line. Feasible solutions are agent trajectories in which all agents reach the target sooner or later. A special feature of our problem is that the agents…
This paper investigates a novel offline change-point detection problem from an information-theoretic perspective. In contrast to most related works, we assume that the knowledge of the underlying pre- and post-change distributions are not…