November 24, 2021: Francesca Zaffora Blando: Wald randomness and learning-theoretic randomness
Luci Lunch Seminars - Autumn 2021 Series - by the LUCI (Logic, Computation and Information) Group
Francesca Zaffora Blando (Carnegie Mellon University)
Wald randomness and learning-theoretic randomness
November 24, 2021: Zoom, H. 13:00-15:00.
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The theory of algorithmic randomness has its roots in Richard von Mises’ work on the foundations of probability. Von Mises was a fervent proponent of the frequency interpretation of probability, which he supplemented with a (more or less) formal definition of randomness for infinite sequences of experimental outcomes. In a nutshell, according to von Mises’ account, the probability of an event is to be identified with its limiting relative frequency within a random sequence. Abraham Wald’s most well-known contribution to the heated debate that immediately followed von Mises’ proposal is his proof of the consistency of von Mises’ definition of randomness. In this talk, I will focus on a lesser known contribution by Wald: a definition of randomness that he put forth to rescue von Mises’ original definition from the objection that is often regarded as having dealt the death blow to his entire approach (namely, the objection based on Ville’s Theorem). We will see that, when reframed in computability-theoretic terms, Wald’s definition of randomness coincides with a well-known algorithmic randomness notion and that his overall approach is very close, both formally and conceptually, to a recent framework for modeling algorithmic randomness that rests on learning-theoretic tools and intuitions.
The meeting will be held in English.
Participation is strongly recommended to students of the Doctoral School in Philosophy and Human Sciences and to students of the Doctoral School of Mind, Brain, and Reasoning.
Everyone interested is welcome to attend.
The Logic Group, Department of Philosophy, University of Milan - luci.unimi.it