Utility-Based Learning from Data: 1st Edition (Hardback) book cover

Utility-Based Learning from Data

1st Edition

By Craig Friedman, Sven Sandow

Chapman and Hall/CRC

417 pages | 34 B/W Illus.

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Description

Utility-Based Learning from Data provides a pedagogical, self-contained discussion of probability estimation methods via a coherent approach from the viewpoint of a decision maker who acts in an uncertain environment. This approach is motivated by the idea that probabilistic models are usually not learned for their own sake; rather, they are used to make decisions. Specifically, the authors adopt the point of view of a decision maker who

(i) operates in an uncertain environment where the consequences of every possible outcome are explicitly monetized,

(ii) bases his decisions on a probabilistic model, and

(iii) builds and assesses his models accordingly.

These assumptions are naturally expressed in the language of utility theory, which is well known from finance and decision theory. By taking this point of view, the book sheds light on and generalizes some popular statistical learning approaches, connecting ideas from information theory, statistics, and finance. It strikes a balance between rigor and intuition, conveying the main ideas to as wide an audience as possible.

Reviews

Utility-Based Learning from Data is an excellent treatment of data-driven statistics for decision-making. Friedman and Sandow lucidly describe the connections between different branches of statistics and econometrics, such as utility theory, maximum entropy, and Bayesian analysis. A must-read for serious statisticians!

—Marco Avellaneda, Professor of Mathematics, New York University, and Risk Magazine Quant of the Year 2010

Combining insights from both theory and practice, this is a model trade book about modeling trading books.

—Peter Carr, Global Head of Market Modeling, Morgan Stanley, and Executive Director, Masters in Math Finance, New York University

Utility-Based Learning from Data connects key ideas from utility theory with methods from statistics, machine learning, and information theory. It presents, using decision-theoretic principles, a framework for building models that can be used by decision makers. By adopting the utility-based approach, Friedman and Sandow are able to adapt models to the risk preferences of the model user, while maintaining tractability. It is a much-needed and comprehensive book, which should help put model-building for use by decision makers on more solid ground.

—Gregory Piatetsky-Shapiro, editor of KDnuggets.com, co-founder and past Chair of SIGKDD, and founder of the Knowledge Discovery and Data Mining (KDD) conferences

Table of Contents

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.

About the Authors

Craig Friedman is a managing director and head of research in the Quantitative Analytics group at Standard & Poor’s in New York. Dr. Friedman is also a fellow of New York University’s Courant Institute of Mathematical Sciences. He is an associate editor of both the International Journal of Theoretical and Applied Finance and the Journal of Credit Risk.

Sven Sandow is an executive director in risk management at Morgan Stanley in New York. Dr. Sandow is also a fellow of New York University’s Courant Institute of Mathematical Sciences. He holds a Ph.D. in physics and has published articles in scientific journals on various topics in physics, finance, statistics, and machine learning.

The contents of this book are Dr. Sandow’s opinions and do not represent Morgan Stanley.

About the Series

Chapman & Hall/CRC Machine Learning & Pattern Recognition

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
BUS061000
BUSINESS & ECONOMICS / Statistics
COM000000
COMPUTERS / General
COM012040
COMPUTERS / Programming / Games
MAT000000
MATHEMATICS / General