Mark P. Kritzman - Prediction Revisited

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MEGAN CZASONIS

MARK KRITZMAN

DAVID TURKINGTON

Copyright © 2022 by Megan Czasonis, Mark Kritzman, and David Turkington. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Relevance is the centerpiece of our approach to prediction. The key concepts that give rise to relevance were introduced over the past three centuries, as illustrated in this timeline. In Chapter 8, we offer more detail about the people who made these groundbreaking discoveries.

This book introduces a new approach to prediction, which requires a new vocabulary—not new words, but new interpretations of words that are commonly understood to have other meanings. Therefore, to facilitate a quicker understanding of what awaits you, we define some essential concepts as they are used throughout this book. And rather than follow the convention of presenting them alphabetically, we present them in a sequence that matches the progression of ideas as they unfold in the following pages.

Observation: One element among many that are described by a common set of attributes, distributed across time or space, and which collectively provide guidance about an outcome that has yet to be revealed. Classical statistics often refers to an observation as a multivariate data point.

Attribute: A recorded value that is used individually or alongside other attributes to describe an observation. In classical statistics, attributes are called independent variables.

Outcome: A measurement of interest that is usually observed alongside other attributes, and which one wishes to predict. In classical statistics, outcomes are called dependent variables.

Arithmetic average: A weighted summation of the values of attributes or outcomes that efficiently aggregates the information contained in a sample of observations. Depending on the context and the weights that are used, the result may be interpreted as a typical value or as a prediction of an unknown outcome.

Spread: The pairwise distance between observations of an attribute, measured in units of surprise. We compute this distance as the average of half the squared difference in values across every pair of observations. In classical statistics, the same quantity is usually computed as the average of squared deviations of observations from their mean and is referred to as variance. However, the equivalent evaluation of pairwise spreads reveals why we must divide by N – 1 rather than N to obtain an unbiased estimate of a sample's variance; it is because the zero distance of an observation with itself (the diagonal in a matrix of pairs) conveys no information.

Information theory: A unified mathematical theory of communication, created by Claude Shannon, which expresses messages as sequences of 0s and 1s and, based on the inverse relationship of information and probability, prescribes the optimal redundancy of symbols to manage the speed and accuracy of transmission.

Circumstance: A set of attribute values that collectively describes an observation.