Related papers: Non-commutative error correcting codes and proper …
We consider nonparametric sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution with some loose constraints. We…
In group testing, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether at least one defective item is present. This problem is relevant in areas such as medical…
In the context of fault-detection problems, the objective is to identify all defective items among a set of $n$ binary-state items using the minimum number of tests. The {group testing} paradigm, which allows testing a subset of items in a…
Property testing has been extensively studied and its target is to determine whether a given object satisfies a certain property or it is far from the property. In this paper, we construct an efficient quantum algorithm which tests if a…
In the classical combinatorial (adaptive) group testing problem, one is given two integers \(d\) and \(n\), where \(0\le d\le n\), and a population of \(n\) items, exactly \(d\) of which are known to be defective. The question is to devise…
We examine the extent to which sublinear-sample property testing and estimation apply to settings where samples are independently but not identically distributed. Specifically, we consider the following distributional property testing…
Property Testing is a formal framework to study the computational power and complexity of sampling from combinatorial objects. A central goal in standard graph property testing is to understand which graph properties are testable with…
Helly's theorem is a fundamental result in discrete geometry, describing the ways in which convex sets intersect with each other. If $S$ is a set of $n$ points in $R^d$, we say that $S$ is $(k,G)$-clusterable if it can be partitioned into…
A set family ${\cal F}$ is called intersecting if every two members of ${\cal F}$ intersect, and it is called uniform if all members of ${\cal F}$ share a common size. A uniform family ${\cal F} \subseteq \binom{[n]}{k}$ of $k$-subsets of…
In group testing, the task is to identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability $\alpha$, independent of all other…
In many statistical applications, the dimension is too large to handle for standard high-dimensional machine learning procedures. This is particularly true for graphical models, where the interpretation of a large graph is difficult and…
The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…
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.…
Many algorithms are designed to work well on average over inputs. When running such an algorithm on an arbitrary input, we must ask: Can we trust the algorithm on this input? We identify a new class of algorithmic problems addressing this,…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…
In this paper we study a new, generalized version of the well-known group testing problem. In the classical model of group testing we are given n objects, some of which are considered to be defective. We can test certain subsets of the…
We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical…
The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…