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Learning and decision-making from rank data

Xia, Lirong, author

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Summary

  • The ubiquitous challenge of learning and decision-making from rank data arises in situations where intelligent systems collect preference and behavior data from humans, learn from the data, and then use the data to help humans make efficient, effective, and timely decisions. Often, such data are represented by rankings. This book surveys some recent progress toward addressing the challenge from the considerations of statistics, computation, and socio-economics. We will cover classical statistical models for rank data, including random utility models, distance-based models, and mixture models. We will discuss and compare classical and state-of-the-art algorithms, such as algorithms based on Minorize-Majorization (MM), Expectation-Maximization (EM), Generalized Method-of-Moments (GMM), rank breaking, and tensor decomposition. We will also introduce principled Bayesian preference elicitation frameworks for collecting rank data. Finally, we will examine socio-economic aspects of statistically desirable decision-making mechanisms, such as Bayesian estimators. This book can be useful in three ways: (1) for theoreticians in statistics and machine learning to better understand the considerations and caveats of learning from rank data, compared to learning from other types of data, especially cardinal data; (2) for practitioners to apply algorithms covered by the book for sampling, learning, and aggregation; and (3) as a textbook for graduate students or advanced undergraduate students to learn about the field. This book requires that the reader has basic knowledge in probability, statistics, and algorithms. Knowledge in social choice would also help but is not required.

Notes

  • Part of: Synthesis digital library of engineering and computer science.
  • Includes bibliographical references (pages 131-141).
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  • INSPEC
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Contents

  • 1. Introduction -- 1.1 The research problem -- 1.2 Overview of the book --
  • 2. Statistical models for rank data -- 2.1 Basics of statistical modeling -- 2.1.1 Modeling partial orders as events -- 2.2 Random utility models -- 2.2.1 The Plackett-Luce model -- 2.2.2 Properties of random utility models (RUMs) -- 2.2.3 Sampling from random utility models -- 2.2.4 Connection to discrete choice models -- 2.3 Distance-based models -- 2.3.1 Mallows' model -- 2.3.2 Repeated insertion model: efficient sampling from mallows -- 2.3.3 Condorcet's model -- 2.4 Datasets and model fitness -- 2.5 Bibliographical notes --
  • 3. Parameter estimation algorithms -- 3.1 Algorithms for the Plackett-Luce model -- 3.1.1 The minorize-maximization (MM) algorithm -- 3.1.2 The Luce spectral ranking (LSR) algorithm -- 3.1.3 Generalized method-of-moments (GMM) algorithm -- 3.2 Algorithms for general random utility models -- 3.2.1 The expectation-maximization (EM) algorithm -- 3.2.2 EM for RUMs: Monte Carlo E-step by Gibbs sampling -- 3.2.3 EM for RUMs: M-step -- 3.2.4 GMM for RUMs with location families -- 3.3 Algorithms for distance-based models -- 3.4 Bibliographical notes --
  • 4. The rank-breaking framework -- 4.1 Rank-breaking for random utility models -- 4.1.1 Breaking + GMM for Plackett-Luce -- 4.1.2 Uniqueness of outcome of algorithm 4.11 -- 4.1.3 Characterization of consistent breakings for Plackett-Luce -- 4.1.4 Computational and statistical efficiency of algorithms for Plackett-Luce -- 4.1.5 Rank-breaking for general random utility models with location families -- 4.2 Rank-breaking + composite marginal likelihood (RBCML) -- 4.2.1 Weighted breakings -- 4.2.2 Composite marginal likelihood methods (CML) -- 4.2.3 The RBCML framework -- 4.2.4 Consistency and asymptotic normality of RBCML -- 4.2.5 RBCML for Plackett-Luce -- 4.2.6 RBCML for RUMs with location families -- 4.2.7 The adaptive RBCML algorithm -- 4.2.8 Experiments -- 4.3 Bibliographical notes --
  • 5. Mixture models for rank data -- 5.1 Mixture models -- 5.1.1 Identifiability of mixture models -- 5.1.2 An EM algorithm for learning mixture models -- 5.2 Learning mixtures of Plackett-Luce -- 5.2.1 Algorithms for mixtures of Plackett-Luce -- 5.3 Learning mixtures of general RUMs with location families -- 5.4 Learning mixtures of mallows -- 5.5 Bibliographical notes --
  • 6. Bayesian preference elicitation -- 6.1 The Bayesian preference elicitation problem -- 6.1.1 Plackett-Luce model with features -- 6.1.2 Computing expected information gain -- 6.2 Bayesian preference elicitation for personal choice -- 6.2.1 Information criteria -- 6.2.2 Approximation techniques for personal choice -- 6.3 Bayesian preference elicitation for social choice -- 6.3.1 Approximating posterior distributions -- 6.3.2 Ranked-top-k questions -- 6.3.3 Social choice by randomized voting -- 6.4 Experimental results -- 6.4.1 Estimating the cost function -- 6.4.2 Comparing information criteria -- 6.5 Bibliographical notes --
  • 7. Socially desirable group decision-making from rank data -- 7.1 Statistical decision-theoretic framework -- 7.1.1 Measuring decision mechanisms: Bayesian loss and frequentist loss -- 7.1.2 Socio-economic criteria: social choice axioms -- 7.2 Minimax estimators in neutral frameworks -- 7.3 Socially desirable Bayesian estimators -- 7.3.1 An impossibility theorem on strict Condorcet criterion -- 7.3.2 Satisfiability of other axioms -- 7.4 An automated design framework -- 7.4.1 Data generation -- 7.4.2 Hypothesis space -- 7.4.3 Optimization -- 7.5 Bibliographical notes --
  • 8. Future directions -- Bibliography -- Author's biography
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