The analogy between combinatorial optimization and statistical mechanics has proven to be a fruitful object of study. Simulated annealing, a metaheuristic for combinatorial optimization problems, is based on this analogy. In this paper we use the statistical mechanics formalism based on the above mentioned analogy to analyze the asymptotic behavior of a special class of combinatorial optimizati...

Accurate yield optimization and statistical analysis of microwave components are crucial ingredients for manufacturability-driven designs in a time-to-market development environment. Yield optimization requires intensive simulations to cover the entire statistic of possible outcomes of a given manufacturing process. Performing direct yield optimization using accurate full-wave electromagnetic s...

Statistics and Optimization have been closely linked from the very outset. The search for a ‘best’ estimator (least squares, maximum likelihood, etc.) certainly relies on optimization tools. On the other hand, Statistics has often provided the motivation for the development of algorithmic procedures for certain classes of optimization problems. However, it’s only relatively recently, more speci...

The statistical notion of variable interaction is relevant to learning diiculty. This is substantiated by an empirical study that examines the relationship between concept variation and predictive accuracy, extended by analizing the variable interaction as a cause of concept variation. One of six learning systems empirically studied, MRP, exhibits a distinctive advantage ascribed to characteris...

Existing nonconvex statistical optimization theory and methods crucially rely on the correct specification of the underlying “true” statistical models. To address this issue, we take a first step towards taming model misspecification by studying the high-dimensional sparse phase retrieval problem with misspecified link functions. In particular, we propose a simple variant of the thresholded Wir...

Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics—e.g., or the expected length of a shortest path between two nodes, or the expected weight of a minimum spanning tree of the graph, etc. These statistics provide insight into the structure of a graph, and they can help predic...

This paper treats the application of statistical principles for 3D computer vision purposes. Both the automatic generation of probabilistic object models, and the localization as well as the classification of objects in compound scenes result in complex optimization problems within the introduced statistical framework. Different methods are discussed for solving the associated optimization prob...

We discuss in this paper asymptotic statistical inference of stochastic optimization problems. These are optimization problems where the “true” objective function, and probably some of the constraints, are estimated, typically by averaging a random sample. The classical maximum likelihood estimation can be considered in that framework. Recently statistical analysis of such problems has been mot...

ix Title: Statistical Physics of Hard Optimization Problems Author: Lenka Zdeborová Abstract: Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems ...

General purpose graphics processing units (GPGPUs) suitable for general purpose programming have become sufficiently affordable in the last three years to be used in personal workstations. In this paper we assess the usefulness of such hardware in the statistical analysis of simulation input and output data. In particular we consider the fitting of complex parametric statistical metamodels to l...