# Statistical learning theory

• ### VC dimension, Rademacher complexity, and growth function

Nathanaël Fijalkow

• ### Angluin's style learning for weighted automata

Nathanaël Fijalkow

We show that weighted automata over the reals can be learned efficiently in Angluin's supervised scenario.This post uses all the notations of the previous post,and the result presented here was proved in this paper.The scenario is Angluin’s style ...

• ### Minimising weighted tree automata and context-free grammars

Nathanaël Fijalkow

We discuss an extension of Fliess' theorem for minimising weighted tree automata.This post is somehow a follow-up of this one, but it can be read independently.Minimising weighted tree automataWe consider tree formal series (here over the reals), ...

• ### PAC-learning and compression schemes

Nathanaël Fijalkow

We state and prove the equivalence between PAC-learnability, finite VC dimension, and the existence of compression schemes.Many thanks to Borja Balle, Pascale Gourdeau, and Pierre Ohlmann, for discussions on compression schemes and for the joint e...

• ### Weighted automata and matrix factorisations

Nathanaël Fijalkow

We discuss extensions of Fliess' theorem which says that the smallest weighted automaton for a function is exactly the rank of its Hankel matrix.The goal is to extend this theorem to subclasses of weighted automata such as probabilistic automata.M...