Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence

Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector $w^* \in \mathbb{R}^d$ that represents the "qualities" of the $d$ items being compared; this class of models includes the two most widely used parametric models--the Bradley-Terry-Luce (BTL) and the Thurstone models. Working within a standard minimax framework, we provide tight upper and lower bounds on the optimal error in estimating the quality score vector $w^*$ under this class of models. The bounds depend on the topology of the comparison graph induced by the subset of pairs being compared via its Laplacian spectrum. Thus, in settings where the subset of pairs may be chosen, our results provide principled guidelines for making this choice. Finally, we compare these error rates to those under cardinal measurement models and show that the error rates in the ordinal and cardinal settings have identical scalings apart from constant pre-factors.Comment: 39 pages, 5 figures. Significant extension of arXiv:1406.661

Information Theory and Machine Learning

The recent successes of machine learning, especially regarding systems based on deep neural networks, have encouraged further research activities and raised a new set of challenges in understanding and designing complex machine learning algorithms. New applications require learning algorithms to be distributed, have transferable learning results, use computation resources efficiently, convergence quickly on online settings, have performance guarantees, satisfy fairness or privacy constraints, incorporate domain knowledge on model structures, etc. A new wave of developments in statistical learning theory and information theory has set out to address these challenges. This Special Issue, "Machine Learning and Information Theory", aims to collect recent results in this direction reflecting a diverse spectrum of visions and efforts to extend conventional theories and develop analysis tools for these complex machine learning systems

On Connections Between Machine Learning And Information Elicitation, Choice Modeling, And Theoretical Computer Science

Machine learning, which has its origins at the intersection of computer science and statistics, is now a rapidly growing area of research that is being integrated into almost every discipline in science and business such as economics, marketing and information retrieval. As a consequence of this integration, it is necessary to understand how machine learning interacts with these disciplines and to understand fundamental questions that arise at the resulting interfaces. The goal of my thesis research is to study these interdisciplinary questions at the interface of machine learning and other disciplines including mechanism design/information elicitation, preference/choice modeling, and theoretical computer science

Model-Oriented Data Analysis; Proceedings of an IIASA Workshop, Eisenach, GDR, March 9-13, 1987)

The main topics of this workshop were (1) optimal experimental design, (2) regression analysis, and (3) model testing and applications. Under the topic "Optimal experimental design" new optimality criteria based on asymptotic properties of relevant statistics were discussed. The use of additional restrictions on the designs were also discussed, inadequate and nonlinear models were considered and Bayesian approaches to the design problem in the nonlinear case were a focal point of the special session. It was emphasized that experimental design is a field of much current interest. During the sessions devoted to "Regression analysis" it became clear that there is an essential progress in statistics for nonlinear models. Here, besides the asymptotic behavior of several estimators the non-asymptotic properties of some interesting statistics were discussed. The distribution of the maximum-likelihood (ML) estimator in normal models and alternative estimators to the least-squares or ML estimators were discussed intensively. Several approaches to "resampling" were considered in connection with linear, nonlinear and semiparametric models. Some new results were reported concerning simulated likelihoods which provide a powerful tool for statistics in several types of models. The advantages and problems of bootstrapping, jackknifing and related methods were considered in a number of papers. Under the topic of "Model testing and applications" the papers covered a broad spectrum of problems. Methods for the detection of outliers and the consequences of transformations of data were discussed. Furthermore, robust regression methods, empirical Bayesian approaches and the stability of estimators were considered, together with numerical problems in data analysis and the use of computer packages

New Perspectives on Games and Interaction

This volume is a collection of papers presented at the 2007 colloquium on new perspectives on games and interaction at the Royal Dutch Academy of Sciences in Amsterdam. The purpose of the colloquium was to clarify the uses of the concepts of game theory, and to identify promising new directions. This important collection testifies to the growing importance of game theory as a tool to capture the concepts of strategy, interaction, argumentation, communication, cooperation and competition. Also, it provides evidence for the richness of game theory and for its impressive and growing application

Economic Structural Change: Analysis and Forecasting

In modern economic model building, structural change is a key concept. Economic growth and events like the oil price shocks have impacts on the economic system such that models with fixed structure are illusions. Considerable progress has been made in the last few years concerning statistical and econometric tools. Methods for identification of structural change, models that are robust to changes and assimilate their effects, and adequate forecasting techniques have been developed. Under the auspices of IIASA a very active community of statisticians and econometricians has made a very influential effort in this area. The purpose of this volume is to document these activities, to present new methods and developments in this area, and to demonstrate applications. Particular weight is given to nonparametric and robust methods for identification of and modeling under structural change, a Bayesian approach to forecast combination, and time-varying parameter cointegration. This book has four parts: (1) Identification of structural change, (2) Model building in the presence of structural change, (3) Forecasting in the presence of structural change, and (4) Economic modeling and the use of empirical data. The book provides an up-to-date status report on the field and should stimulate applications of the methods in empirical work as well as further research