Related papers: On a Hypergraph Approach to Multistage Group Testi…

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…

In medical documents, it is possible that an entity of interest not only contains a discontiguous sequence of words but also overlaps with another entity. Entities of such structures are intrinsically hard to recognize due to the large…

We consider the quantitative group testing problem where the objective is to identify defective items in a given population based on results of tests performed on subsets of the population. Under the quantitative group testing model, the…

The goal of group testing is to efficiently identify a few specific items, called positives, in a large population of items via tests. A test is an action on a subset of items which returns positive if the subset contains at least one…

Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…

Given a fixed-sample-size test that controls the error probabilities under two specific, but arbitrary, distributions, a 3-stage and two 4-stage tests are proposed and analyzed. For each of them, a novel, concrete, non-asymptotic,…

The goal of combinatorial group testing is to efficiently identify up to $d$ defective items in a large population of $n$ items, where $d \ll n$. Defective items satisfy certain properties while the remaining items in the population do not.…

In this paper, we consider the group testing problem with adaptive test designs and noisy outcomes. We propose a computationally efficient four-stage procedure with components including random binning, identification of bins containing…

Pathogenic infections pose a significant threat to global health, affecting millions of people every year and presenting substantial challenges to healthcare systems worldwide. Efficient and timely testing plays a critical role in disease…

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…

Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary…

Subgraph Isomorphism is a very basic graph problem, where given two graphs $G$ and $H$ one is to check whether $G$ is a subgraph of $H$. Despite its simple definition, the Subgraph Isomorphism problem turns out to be very broad, as it…

Automated debugging techniques, such as Fault Localisation (FL) or Automated Program Repair (APR), are typically designed under the Single Fault Assumption (SFA). However, in practice, an unknown number of faults can independently cause…

In multistage perfect matching problems we are given a sequence of graphs on the same vertex set and asked to find a sequence of perfect matchings, corresponding to the sequence of graphs, such that consecutive matchings are as similar as…

A massive dataset often consists of a growing number of (potentially) heterogeneous sub-populations. This paper is concerned about testing various forms of heterogeneity arising from massive data. In a general nonparametric framework, a set…

Screening is the problem of finding a superset of the set of non-zero entries in an unknown p-dimensional vector \beta* given n noisy observations. Naturally, we want this superset to be as small as possible. We propose a novel framework…

In this work, we introduce bidirectional collision detection --- a new algorithmic tool that applies to the collision problems that arise in many isomorphism problems. For the group isomorphism problem, we show that bidirectional collision…

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…

Hypothesis testing for graphs has been an important tool in applied research fields for more than two decades, and still remains a challenging problem as one often needs to draw inference from few replicates of large graphs. Recent studies…

A general theory of topological classification of defects is introduced. We illustrate the application of tools from algebraic topology, including homotopy and cohomology groups, to classify defects including several explicit calculations…