The Topology of Statistical Verifiability
Abstract
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2], statistics [6, 7] and modal logic [17, 4]. In those applications, open sets are typically interpreted as hypotheses deductively verifiable by true propositional information that rules out relevant possibilities. However, in statistical data analysis, one routinely receives random samples logically compatible with every statistical hypothesis. We bridge the gap between propositional and statistical data by solving for the unique topology on probability measures in which the open sets are exactly the statistically verifiable hypotheses. Furthermore, we extend that result to a topological characterization of learnability in the limit from statistical data.
 Publication:

arXiv eprints
 Pub Date:
 July 2017
 DOI:
 10.48550/arXiv.1707.09378
 arXiv:
 arXiv:1707.09378
 Bibcode:
 2017arXiv170709378G
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Artificial Intelligence;
 Mathematics  Probability
 EPrint:
 In Proceedings TARK 2017, arXiv:1707.08250