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Forecasting using incomplete models (2018) (arxiv.org)
2 points by headalgorithm on Feb 15, 2019 | hide | past | pdf | discuss on HN

In plain words: Instead of an exact rule, the forecaster knows only that the truth lies in one of several sets of rules, and blends forecasts to stay near them. When the real process fits one set, the forecasts settle into it, weaker than Bayesian convergence.

Abstract · Forecasting using incomplete models

We consider the task of forecasting an infinite sequence of future observations based on some number of past observations, where the probability measure generating the observations is "suspected" to satisfy one or more of a set of incomplete models, i.e. convex sets in the space of probability measures. This setting is in some sense intermediate between the realizable setting where the probability measure comes from some known set of probability measures (which can be addressed using e.g. Bayesian inference) and the unrealizable setting where the probability measure is completely arbitrary. We demonstrate a method of forecasting which guarantees that, whenever the true probability measure satisfies an incomplete model in a given countable set, the forecast converges to the same incomplete model in the (appropriately normalized) Kantorovich-Rubinstein metric. This is analogous to merging of opinions for Bayesian inference, except that convergence in the Kantorovich-Rubinstein metric is weaker than convergence in total variation.

Vanessa Kosoy
arXiv:1705.04630 · cs.LG · submitted May 12, 2017 · updated May 16, 2019
abstract · pdf · html · 29 pages

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