Related papers: On the probabilistic approach to the random satisf…
We study local search algorithms to solve instances of the random $k$-satisfiabi lity problem, equivalent to finding (if they exist) zero-energy ground states of statistical models with disorder on random hypergraphs. It is well known that…
We propose a rigorous decomposition of predictive error, highlighting that not all 'irreducible' error is genuinely immutable. Many domains stand to benefit from iterative enhancements in measurement, construct validity, and modeling. Our…
We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…
We study the structure of satisfying assignments of a random 3-SAT formula. In particular, we show that a random formula of density 4.453 or higher almost surely has no non-trivial "core" assignments. Core assignments are certain partial…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…
We study the susceptibility propagation, a message-passing algorithm to compute correlation functions. It is applied to constraint satisfaction problems and its accuracy is examined. As a heuristic method to find a satisfying assignment, we…
We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase…
We study the quantum version of the random $K$-Satisfiability problem in the presence of the external magnetic field $\Gamma$ applied in the transverse direction. We derive the replica-symmetric free energy functional within static…
We study a class of two-stage stochastic programs in which the second stage includes a set of components with uncertain capacity, and the expression for the distribution function of the uncertain capacity includes first-stage variables.…
We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…
We study the computational complexity of multi-stage robust optimization problems. Such problems are formulated with alternating min/max quantifiers and therefore naturally fall into a higher stage of the polynomial hierarchy. Despite this,…
Paper [1] derived the probability density function (PDF) of a sum of products of two correlated complex Gaussian zero-mean random variables (RVs) that has been applied to calculate the error probabilities of a \emph{M}-ary phase shift…
Phase III randomized clinical trials play a monumentally critical role in the evaluation of new medical products. Because of the intrinsic nature of uncertainty embedded in our capability in assessing the efficacy of a medical product,…
Randomized algorithms for deciding satisfiability were shown to be effective in solving problems with thousands of variables. However, these algorithms are not complete. That is, they provide no guarantee that a satisfying assignment, if…
We study the graph alignment problem over two independent Erd\H{o}s-R\'enyi graphs on $n$ vertices, with edge density $p$ falling into two regimes separated by the critical window around $p_c=\sqrt{\log n/n}$. Our result reveals an…
We consider a problem wherein jobs arrive at random times and assume random values. Upon each job arrival, the decision-maker must decide immediately whether or not to accept the job and gain the value on offer as a reward, with the…
Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and…
The goal of this chapter is to review the main ideas that underlie the cavity method for disordered models defined on random graphs, as well as present some of its outcomes, focusing on the random constraint satisfaction problems for which…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Random constraint satisfaction problems can exhibit a phase where the number of constraints per variable $\alpha$ makes the system solvable in theory on the one hand, but also makes the search for a solution hard, meaning that common…