Utility-Based Learning from Data

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