Related papers: Zero-One Laws for Random Feasibility Problems

We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…

Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…

We consider an optimization problem in a convex space $E$ with an affine objective function, subject to $J$ constraints in the forms of inequalities on some other affine functions, where $J$ is a given nonnegative integer. Under suitable…

We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…

The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…

In the same spirit as Tsybakov (2003), we define the optimality of an aggregation procedure in the problem of classification. Using an aggregate with exponential weights, we obtain an optimal rate of convex aggregation for the hinge risk…

In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…

We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample average estimator for a stochastic…

We consider the bound-constrained global optimization of functions with low effective dimensionality, that are constant along an (unknown) linear subspace and only vary over the effective (complement) subspace. We aim to implicitly explore…

Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…

The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually…

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional)…

We study the problem of maximizing R{\'e}nyi entropy of order $2$ (equivalently, minimizing the index of coincidence) over the set of joint distributions with prescribed marginals. A closed-form optimizer is known under a feasibility…

In this paper, we study the tradeoff between the approximation guarantee and adaptivity for the problem of maximizing a monotone submodular function subject to a cardinality constraint. The adaptivity of an algorithm is the number of…

There is a long history in machine learning of model ensembling, beginning with boosting and bagging and continuing to the present day. Much of this history has focused on combining models for classification and regression, but recently…

The model averaging problem is to average multiple models to achieve a prediction accuracy not much worse than that of the best single model in terms of mean squared error. It is known that if the models are misspecified, model averaging is…

We study a typical optimization model where the optimization variable is composed of multiple probability distributions. Though the model appears frequently in practice, such as for policy problems, it lacks specific analysis in the general…

Let $A$ be a random $m\times n$ matrix over the finite field $F_q$ with precisely $k$ non-zero entries per row and let $y\in F_q^m$ be a random vector chosen independently of $A$. We identify the threshold $m/n$ up to which the linear…

Meaningful comparison between sets of observations often necessitates alignment or registration between them, and the resulting optimization problems range in complexity from those admitting simple closed-form solutions to those requiring…