Francesca Zaffora Blando’s Seminar

We are all very looking forward to this week’s invited talk! On Wednesday 24 we will host Francesca Zaffora Blando (Carnegie Mellon University) who will give a talk on Wald randomness and learning-theoretic randomness. Remember that our talks usually start at 1PM (CET) and typically last 1 hour. At the end we will have room for Q&A and an informal discussion of Francesca’s talk. Don’t forget to take a look at our youtube channel and twitter feed for our videos and news!

Title: Wald randomness and learning-theoretic randomness

Abstract: 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.

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