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Advances in Info-MetricsInformation and Information Processing across Disciplines$
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Min Chen, J. Michael Dunn, Amos Golan, and Aman Ullah

Print publication date: 2020

Print ISBN-13: 9780190636685

Published to Oxford Scholarship Online: December 2020

DOI: 10.1093/oso/9780190636685.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 17 June 2021

Reduced Perplexity

Reduced Perplexity

A Simplified Perspective on Assessing Probabilistic Forecasts

(p.325) 12 Reduced Perplexity
Advances in Info-Metrics

Kenric P. Nelson

Oxford University Press

This chapter introduces a simple, intuitive approach to the assessment of probabilistic inferences. The Shannon information metrics are translated to the probability domain. The translation shows that the negative logarithmic score and the geometric mean are equivalent measures of the accuracy of a probabilistic inference. The geometric mean of forecasted probabilities is thus a measure of forecast accuracy and represents the central tendency of the forecasts. The reciprocal of the geometric mean is referred to as the perplexity and defines the number of independent choices needed to resolve the uncertainty. The assessment method introduced in this chapter is intended to reduce the ‘qualitative’ perplexity relative to the potpourri of scoring rules currently used to evaluate machine learning and other probabilistic algorithms. Utilization of this assessment will provide insight into designing algorithms with reduced the ‘quantitative’ perplexity and thus improved the accuracy of probabilistic forecasts. The translation of information metrics to the probability domain is incorporating the generalized entropy functions developed Rényi and Tsallis. Both generalizations translate to the weighted generalized mean. The generalized mean of probabilistic forecasts forms a spectrum of performance metrics referred to as a Risk Profile. The arithmetic mean is used to measure the decisiveness, while the –2/3 mean is used to measure the robustness.

Keywords:   Probability, statistics, scoring rule, entropy, complex systems, risk, information

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