Zoom link: https://huji.zoom.us/j/81233462094?pwd=3R7at2COMiDrSYrwJTbtRQ7OCDDlUT.1
Meeting ID: 812 3346 2094
Passcode: 070504
Title: Learnability: A Model-Theoretic Perspective
Abstract: This talk aims at developing a learnability framework within a model-theoretic
context, thereby building a bridge between Model Theory and Statistical Learning
Theory. Specifically, relations between the notions PAC learning, VC dimension,
NIP and o-minimality are studied, with a particular emphasis on measurability
aspects.
In the context of Statistical Learning Theory, the formal model of (agnostic) PAC
learning is introduced. Further, the Fundamental Theorem of Statistical Learning
is presented, which states that a class of indicator functions is PAC learnable if and
only if its VC dimension is finite. The learning model as well as the theorem are
scrutinized from a measure-theoretic perspective, in order to extract the minimal
measurability requirements needed for rigorous reasoning.
Then it is explained how we can establish learnability results within a model-
theoretic context, focusing on o-minimal expansions of the reals. In particular, we
discuss when the above-mentioned measurability requirements are partly or fully
satisfied.
I report on [L. S. Krapp and L. Wirth, ’Measurability in the Fundamental Theo-
rem of Statistical Learning’, Preprint, 2024, arXiv:2410.10243], which is submitted
for publication and is part of my doctoral research project supervised by Professor
Salma Kuhlmann and Dr. Lothar Sebastian Krapp at University of Konstanz.