Related papers: Group testing and local search: is there a computa…
How to detect a small community in a large network is an interesting problem, including clique detection as a special case, where a naive degree-based $\chi^2$-test was shown to be powerful in the presence of an Erd\H{o}s-Renyi background.…
Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such…
We consider the problem of sequential hypothesis testing by betting. For a general class of composite testing problems -- which include bounded mean testing, equal mean testing for bounded random tuples, and some key ingredients of…
We study Probabilistic Group Testing of a set of N items each of which is defective with probability p. We focus on the double limit of small defect probability, p<<1, and large number of variables, N>>1, taking either p->0 after…
Practitioners conducting adaptive experiments often encounter two competing priorities: maximizing total welfare (or `reward') through effective treatment assignment and swiftly concluding experiments to implement population-wide…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
Motivated by applications in domains such as social networks and computational biology, we study the problem of community recovery in graphs with locality. In this problem, pairwise noisy measurements of whether two nodes are in the same…
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 present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to…
We introduce an extension of a variationally optimized perturbation method, by combining it with renormalization group properties in a straightforward (perturbative) form. This leads to a very transparent and efficient procedure, with a…
We consider the problem of diagnosing faults in a system represented by a Bayesian network, where diagnosis corresponds to recovering the most likely state of unobserved nodes given the outcomes of tests (observed nodes). Finding an optimal…
In this paper, we consider the problem of estimating the underlying graph associated with an Ising model given a number of independent and identically distributed samples. We adopt an \emph{approximate recovery} criterion that allows for a…
In this paper, we obtain new results on the weak and strong consistency of the maximum and integrated conditional likelihood estimators for the community detection problem in the Stochastic Block Model with $k$ communities and unknown…
Discovery problems often require deciding whether additional sampling is needed to detect all categories whose prevalence exceeds a prespecified threshold. We study this question under a Bernoulli product (incidence) model, where categories…
Grover's search algorithm is one of the basic building block in the world of quantum algorithms. Successfully applying it to combinatorial optimization problems is a subtle challenge. As a quadratic speedup is not enough to naively search…
We study the general integer programming (IP) problem of optimizing a separable convex function over the integer points of a polytope: $\min \{f(\mathbf{x}) \mid A\mathbf{x} = \mathbf{b}, \, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \,…
We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…
We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…
We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model has a number of new applications, including…