On how complexity affects the stability of a predictor

Joel Ratsaby
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:161-167, 2018.

Abstract

Given a finite random sample from a Markov chain environment, we select a predictor that minimizes a criterion function and refer to it as being calibrated to its environment. If its prediction error is not bounded by its criterion value, we say that the criterion fails. We define the predictor’s complexity to be the amount of uncertainty in detecting that the criterion fails given that it fails. We define a predictor’s stability to be the discrepancy between the average number of prediction errors that it makes on two random samples. We show that complexity is inversely proportional to the level of adaptivity of the calibrated predictor to its random environment. The calibrated predictor becomes less stable as its complexity increases or as its level of adaptivity decreases.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-ratsaby18a, title = {On how complexity affects the stability of a predictor}, author = {Ratsaby, Joel}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {161--167}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/ratsaby18a/ratsaby18a.pdf}, url = {https://proceedings.mlr.press/v84/ratsaby18a.html}, abstract = {Given a finite random sample from a Markov chain environment, we select a predictor that minimizes a criterion function and refer to it as being calibrated to its environment. If its prediction error is not bounded by its criterion value, we say that the criterion fails. We define the predictor’s complexity to be the amount of uncertainty in detecting that the criterion fails given that it fails. We define a predictor’s stability to be the discrepancy between the average number of prediction errors that it makes on two random samples. We show that complexity is inversely proportional to the level of adaptivity of the calibrated predictor to its random environment. The calibrated predictor becomes less stable as its complexity increases or as its level of adaptivity decreases.} }
Endnote
%0 Conference Paper %T On how complexity affects the stability of a predictor %A Joel Ratsaby %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-ratsaby18a %I PMLR %P 161--167 %U https://proceedings.mlr.press/v84/ratsaby18a.html %V 84 %X Given a finite random sample from a Markov chain environment, we select a predictor that minimizes a criterion function and refer to it as being calibrated to its environment. If its prediction error is not bounded by its criterion value, we say that the criterion fails. We define the predictor’s complexity to be the amount of uncertainty in detecting that the criterion fails given that it fails. We define a predictor’s stability to be the discrepancy between the average number of prediction errors that it makes on two random samples. We show that complexity is inversely proportional to the level of adaptivity of the calibrated predictor to its random environment. The calibrated predictor becomes less stable as its complexity increases or as its level of adaptivity decreases.
APA
Ratsaby, J.. (2018). On how complexity affects the stability of a predictor. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:161-167 Available from https://proceedings.mlr.press/v84/ratsaby18a.html.

Related Material