10 papers
Recursively Enumerably Representable Classes and Computable Versions of the Fundamental Theorem of Statistical Learning
David Kattermann, Lothar Sebastian Krapp
We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions. It had been previously observed that the Fundamental The…
Decomposing the automorphism group of the surreal numbers
Elliot Kaplan, Lothar Sebastian Krapp, Michele Serra
We study the automorphism group of the field of surreal numbers. Our main structure theorem presents a decomposition of this group into a product of five significant factors. Using…
Ordered henselian valued fields: definability and Borel sets
Lothar Sebastian Krapp, Floris Vermeulen
We firstly show that due to their resplendency ordered henselian valued fields admit relative field quantifier elimination in the Denef--Pas language expanded by linear orders in t…
Definable ranks
Lothar Sebastian Krapp, Salma Kuhlmann, Lasse Vogel
We introduce the notion of the definable rank of an ordered field, ordered abelian group and ordered set, respectively. We study the relation between the definable rank of an order…
Time-series Random Process Complexity Ranking Using a Bound on Conditional Differential Entropy
Jacob Ayers, Richard Hahnloser, Julia Ulrich +5
Conditional differential entropy provides an intuitive measure for relatively ranking time-series complexity by quantifying uncertainty in future observations given past context. H…
Measurability in the Fundamental Theorem of Statistical Learning
Lothar Sebastian Krapp, Laura Wirth
The Fundamental Theorem of Statistical Learning states that a hypothesis space is PAC learnable if and only if its VC dimension is finite. For the agnostic model of PAC learning, t…