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

Efficient and elastic LiDAR reconstruction for large-scale exploration tasks

High-quality reconstructions and understanding the environment are essential for robotic tasks such as localisation, navigation and exploration. Applications like planners and controllers can make decisions based on them. International competitions such as the DARPA Subterranean Challenge demonstrate the difficulties that reconstruction methods must address in the real world, e.g. complex surfaces in unstructured environments, accumulation of localisation errors in long-term explorations, and the necessity for methods to be scalable and efficient in large-scale scenarios. Guided by these motivations, this thesis presents a multi-resolution volumetric reconstruction system, supereight-Atlas (SE-Atlas). SE-Atlas efficiently integrates long-range LiDAR scans with high resolution, incorporates motion undistortion, and employs an Atlas of submaps to produce an elastic 3D reconstruction. These features address limitations of conventional reconstruction techniques that were revealed in real-world experiments of an initial active perceptual planning prototype. Our experiments with SE-Atlas show that it can integrate LiDAR scans at 60m range with ∼5 cm resolution at ∼3 Hz, outperforming state-of-the-art methods in integration speed and memory efficiency. Reconstruction accuracy evaluation also proves that SE-Atlas can correct the map upon SLAM loop closure corrections, maintaining global consistency. We further propose four principled strategies for spawning and fusing submaps. Based on spatial analysis, SE-Atlas spawns new submaps when the robot transitions into an isolated space, and fuses submaps of the same space together. We focused on developing a system which scales against environment size instead of exploration length. A new formulation is proposed to compute relative uncertainties between poses in a SLAM pose graph, improving submap fusion reliability. Our experiments show that the average error in a large-scale map is approximately 5 cm. A further contribution was incorporating semantic information into SE-Atlas. A recursive Bayesian filter is used to maintain consistency in per-voxel semantic labels. Semantics is leveraged to detect indoor-outdoor transitions and adjust reconstruction parameters online

Online decision problems with large strategy sets

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.Includes bibliographical references (p. 165-171).In an online decision problem, an algorithm performs a sequence of trials, each of which involves selecting one element from a fixed set of alternatives (the "strategy set") whose costs vary over time. After T trials, the combined cost of the algorithm's choices is compared with that of the single strategy whose combined cost is minimum. Their difference is called regret, and one seeks algorithms which are efficient in that their regret is sublinear in T and polynomial in the problem size. We study an important class of online decision problems called generalized multi- armed bandit problems. In the past such problems have found applications in areas as diverse as statistics, computer science, economic theory, and medical decision-making. Most existing algorithms were efficient only in the case of a small (i.e. polynomial- sized) strategy set. We extend the theory by supplying non-trivial algorithms and lower bounds for cases in which the strategy set is much larger (exponential or infinite) and the cost function class is structured, e.g. by constraining the cost functions to be linear or convex. As applications, we consider adaptive routing in networks, adaptive pricing in electronic markets, and collaborative decision-making by untrusting peers in a dynamic environment.by Robert David Kleinberg.Ph.D