Year: 2020
Type: preprint
Abstract: We study the problem of sequentially predicting properties of a probabilistic model and its next outcome over an infinite horizon, with the goal of ensuring that the predictions incur only finitely many errors with probability 1. We introduce a general framework that models such prediction problems, provide general characterizations for the existence of successful prediction rules, and demonstrate the application of these characterizations through several concrete problem setups, including hypothesis testing, online learning, and risk domination. In particular, our characterizations allow us to recover the findings of Dembo and Peres (1994) with simple and elementary proofs, and offer a partial resolution to an open problem posed therein.
Source: arXiv (Cornell University)
Authors: Wu, Changlong, Santhanam, Narayana
Institution: University of Hawaiʻi at Mānoa
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2999680803