Utility-Based Learning from Data

ISBN: 9780367452322 出版年：2016 页码：418 Friedman, Craig Sandow, Sven CRC Press

Introduction Notions from Utility Theory Model Performance Measurement Model Estimation The Viewpoint of This Book Organization of This Book Examples Mathematical Preliminaries Some Probabilistic Concepts Convex Optimization Entropy and Relative Entropy The Horse Race The Basic Idea of an Investor in a Horse Race The Expected Wealth Growth Rate The Kelly Investor Entropy and Wealth Growth Rate The Conditional Horse Race Elements of Utility Theory Beginnings: The St. Petersburg Paradox Axiomatic Approach Risk Aversion Some Popular Utility Functions Field Studies Our Assumptions The Horse Race and Utility The Discrete Unconditional Horse Races Discrete Conditional Horse Races Continuous Unconditional Horse Races Continuous Conditional Horse Races Select Methods for Measuring Model Performance Rank-Based Methods for Two-State Models Likelihood Performance Measurement via Loss Function A Utility-Based Approach to Information Theory Interpreting Entropy and Relative Entropy in the Discrete Horse Race Context (U,O)-Entropy and Relative (U,O)-Entropy for Discrete Unconditional Probabilities Conditional (U,O)-Entropy and Conditional Relative (U,O)-Entropy for Discrete Probabilities U-Entropy for Discrete Unconditional Probabilities Utility-Based Model Performance Measurement Utility-Based Performance Measures for Discrete Probability Models Revisiting the Likelihood Ratio Utility-Based Performance Measures for Discrete Conditional Probability Models Utility-Based Performance Measures for Probability Density Models Utility-Based Performance Measures for Conditional Probability Density Models Monetary Value of a Model Upgrade Some Proofs Select Methods for Estimating Probabilistic Models Classical Parametric Methods Regularized Maximum Likelihood Inference Bayesian Inference Minimum Relative Entropy (MRE) Methods A Utility-Based Approach to Probability Estimation Discrete Probability Models Conditional Density Models Probability Estimation via Relative U-Entropy Minimization Expressing the Data Constraints in Purely Economic Terms Some Proofs Extensions Model Performance Measures and MRE for Leveraged Investors Model Performance Measures and MRE for Investors in Incomplete Markets Utility-Based Performance Measures for Regression Models Select Applications Three Credit Risk Models The Gail Breast Cancer Model A Text Classification Model References Index Exercises appear at the end of most chapters.