Universal Algorithmic Intelligence

Professor Francesca Zaffora Blando will present her work on weak merging of opinions at the regular research meeting tomorrow, Monday April 27th, at 3 pm EDT.

Francesca Zaffora Blando is an Assistant Professor in the Department of Philosophy at Carnegie Mellon University specializing in logic, formal epistemology, and the philosophy of science – particularly the philosophy of probability and induction.

Title: Algorithmic randomness and the weak merging of computable probability measures

Abstract: I will present a general framework for studying “merging randomness”: namely, notions of algorithmic randomness defined via suitably effectivized notions of merging of opinions. The most well-known merging-of-opinions theorem is the Blackwell-Dubins Theorem (Blackwell and Dubins, 1962), which is concerned with predictions about infinite-horizon events, and where the distance between probabilistic forecasts is given in terms of the total variation distance. In this talk, I will instead focus on a weaker notion of merging between probability measures, studied extensively by Kalai and Lehrer (1994), which is concerned with one-step-ahead predictions. However, rather than merely focusing on the total variation distance, I will also consider notions of merging randomness defined in terms of the Hellinger distance and the Kullback-Leibler divergence. The main results I will present are novel characterizations of Martin-Löf randomness and Schnorr randomness—two canonical algorithmic randomness notions—in terms of weak merging of opinions and the Kullback-Leibler divergence. These results are joint work with Simon Huttegger (UC Irvine) and Sean Walsh (UCLA).