Campus Units

Statistics, Industrial and Manufacturing Systems Engineering

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

11-5-2019

Journal or Book Title

Information and Inference: A Journal of the IMA

DOI

10.1093/imaiai/iaz022

Abstract

A probability model exhibits instability if small changes in a data outcome result in large and, often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a given configuration of parameters. For correlated data structures found in several application areas, there is increasing interest in identifying such sensitivity in model probability structure. We consider the problem of quantifying instability for general probability models defined on sequences of observations, where each sequence of length N has a finite number of possible values that can be taken at each point. A sequence of probability models, indexed by N⁠, and an associated parameter sequence result to accommodate data of expanding dimension. Model instability is formally shown to occur when a certain log probability ratio under such models grows faster than N⁠. In this case, a one component change in the data sequence can shift probability by orders of magnitude. Also, as instability becomes more extreme, the resulting probability models are shown to tend to degeneracy, placing all their probability on potentially small portions of the sample space. These results on instability apply to large classes of models commonly used in random graphs, network analysis and machine learning contexts.

Comments

This is a pre-copyedited, author-produced version of an article accepted for publication in Information and Inference: A Journal of the IMA following peer review. The version of record: Kaplan, Andee, Daniel J. Nordman, and Stephen B. Vardeman. "On the S-instability and degeneracy of discrete deep learning models," Information and Inference: A Journal of the IMA is available online at DOI: 10.1093/imaiai/iaz022. Posted with permission.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

Available for download on Thursday, November 05, 2020

Published Version

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