Prediction Revisited

Оглавление

Mark P. Kritzman. Prediction Revisited

Table of Contents

List of Tables

List of Illustrations

Guide

Pages

PREDICTION REVISITED. THE IMPORTANCE OF OBSERVATION

Timeline of Innovations

Essential Concepts

Preface

1 Introduction

Relevance

Informativeness

Similarity

Roadmap

Note

2 Observing Information

Observing Information Conceptually

Central Tendency

Spread

Information Theory

The Strong Pull of Normality

A Constant of Convenience

Key Takeaways

Observing Information Mathematically

Average

Spread

Information Distance

Observing Information Applied

Appendix 2.1: On the Inflection Point of the Normal Distribution

References

Notes

3 Co-occurrence

Co-occurrence Conceptually

Correlation as an Information-Weighted Average of Co-occurrence

Pairs of Pairs

Across Many Attributes

Key Takeaways

Co-occurrence Mathematically

The Covariance Matrix

Co-occurrence Applied

References

Note

4 Relevance

Relevance Conceptually

Informativeness

Similarity

Relevance and Prediction

How Much Have You Regressed?

Partial Sample Regression

Asymmetry

Sensitivity

Memory and Bias

Key Takeaways

Relevance Mathematically

Prediction

Equivalence to Linear Regression

Partial Sample Regression

Asymmetry

Relevance Applied

Appendix 4.1: Predicting Binary Outcomes. Predicting Binary Outcomes Conceptually

Predicting Binary Outcomes Mathematically

References

Notes

5 Fit

Fit Conceptually

Failing Gracefully

Why Fit Varies

Avoiding Bias

Precision

Focus

Key Takeaways

Fit Mathematically

Components of Fit

Precision

Fit Applied

Notes

6 Reliability

Reliability Conceptually

Key Takeaways

Reliability Mathematically

Reliability Applied

References

Notes

7 Toward Complexity

Toward Complexity Conceptually

Learning by Example

Expanding on Relevance

Key Takeaways

Toward Complexity Mathematically

Complexity Applied

References

8 Foundations of Relevance

Observations and Relevance: A Brief Review of the Main Insights

Spread

Co-occurrence

Relevance

Asymmetry

Fit and Reliability

Partial Sample Regression and Machine Learning Algorithms

Abraham de Moivre (1667–1754)

Pierre-Simon Laplace (1749–1827)

Carl Friedrich Gauss (1777–1853)

Francis Galton (1822–1911)

Karl Pearson (1857–1936)

Ronald Fisher (1890–1962)

Prasanta Chandra Mahalanobis (1893–1972)

Claude Shannon (1916–2001)

References. Abraham de Moivre

Pierre-Simon Laplace

Carl Friedrich Gauss

Francis Galton

Karl Pearson

Ronald Fisher

Prasanta Chandra Mahalanobis

Claude Shannon

Notes

Concluding Thoughts

Perspective

Insights

Prescriptions

Index

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MEGAN CZASONIS

MARK KRITZMAN

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Informativeness is related to information theory, the creation of Claude Shannon, arguably the greatest genius of the twentieth century.1 As we discuss in Chapter 2, information theory posits that information is inversely related to probability. In other words, observations that are unusual contain more information than those that are common. We could stop here and rest on Shannon's formidable reputation to validate our inclusion of informativeness as one of the two components of relevance. But it never hurts to appeal to intuition. Therefore, let us consider the following example.

Suppose we would like to measure the relationship between the performance of the stock market and a collection of economic attributes (think variables) such as inflation, interest rates, energy prices, and economic growth. Our initial thought might be to examine how stock returns covary with changes in these attributes. If these economic attributes behaved in an ordinary way, it would be difficult to tell which of the attributes were driving stock returns or even if the performance of the stock market was instead responding to hidden forces. However, if one of the attributes behaved in an unusual way, and the stock market return we observed was also notable, we might suspect that these two occurrences are linked by more than mere coincidence. It could be evidence of a fundamental relationship. We provide a more formal explanation of informativeness in Chapter 2, but for now let us move on to similarity.

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