Related papers: Two new Probability inequalities and Concentration…
This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…
Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the…
It has been shown experimentally that a decimation algorithm based on Survey Propagation (SP) equations allows to solve efficiently some combinatorial problems over random graphs. We show that these equations can be derived as sum-product…
Arkin et al.~\cite{ArkinBCCJKMM17} recently introduced \textit{partitioned pairs} network optimization problems: given a metric-weighted graph on $n$ pairs of nodes, the task is to color one node from each pair red and the other blue, and…
We prove invariance theorems for general inequalities of different metrics and apply them to limit relations between the sharp constants in the multivariate Markov-Bernstein-Nikolskii type inequalities with the polyharmonic operator for…
We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…
We begin our journey by recalling the fundamentals of Probability Theory that underlie one of its most significant applications to real-world problems: Parametric Estimation. Throughout the text, we systematically develop this theme by…
This paper introduces a version of decoupling and randomization to establish concentration inequalities for double-indexed permutation statistics. The results yield, among other applications, a new combinatorial Hanson-Wright inequality and…
We provide a simple, general argument to obtain improvements of concentration-type inequalities starting from improvements of their corresponding isoperimetric-type inequalities. We apply this argument to obtain robust improvements of the…
Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by…
We establish distributional estimates for noncommutative martingales, in the sense of decreasing rearrangements of the spectra of unbounded operators, which generalises the study of distributions of random variables. Our results include…
The Promise Constraint Satisfaction Problem (PCSP) is a recently introduced vast generalization of the Constraint Satisfaction Problem (CSP). We investigate the computational complexity of a class of PCSPs beyond the most studied cases -…
Recent development in high-dimensional statistical inference has necessitated concentration inequalities for a broader range of random variables. We focus on sub-Weibull random variables, which extend sub-Gaussian or sub-exponential random…
We address two important statistical problems: that of estimating mixtures of multivariate normal distributions and mixtures of $t$-distributions based on univariate projections, and that of quantifying a discrepancy between mixture…
In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
We derive sufficient conditions for a probability measure on a finite product space (a spin system) to satisfy a (modified) logarithmic Sobolev inequality. We establish these conditions for various examples, such as the (vertex-weighted)…
The mixing set with a knapsack constraint arises as a substructure in mixed-integer programming reformulations of chance-constrained programs with stochastic right-hand-sides over a finite discrete distribution. Recently, Luedtke et al.…
Probabilistic graphical models (PGMs) are tools for solving complex probabilistic relationships. However, suboptimal PGM structures are primarily used in practice. This dissertation presents three contributions to the PGM literature. The…
We prove anti-concentration results for polynomials of independent random variables with arbitrary degree. Our results extend the classical Littlewood-Offord result for linear polynomials, and improve several earlier estimates. We discuss…