Generalization Bounds for Weighted Automata

TL;DR

This paper provides new data-dependent generalization bounds for learning weighted automata, relating their complexity to Rademacher complexity and various norm-based measures, advancing theoretical understanding in automata learning.

Contribution

It introduces novel data-dependent generalization guarantees for weighted automata based on Rademacher complexity and provides upper bounds involving key complexity measures.

Findings

New data-dependent generalization bounds for weighted automata

Upper bounds on Rademacher complexities involving automaton norms

Insights into the complexity of learning weighted automata

Abstract

This paper studies the problem of learning weighted automata from a finite labeled training sample. We consider several general families of weighted automata defined in terms of three different measures: the norm of an automaton's weights, the norm of the function computed by an automaton, or the norm of the corresponding Hankel matrix. We present new data-dependent generalization guarantees for learning weighted automata expressed in terms of the Rademacher complexity of these families. We further present upper bounds on these Rademacher complexities, which reveal key new data-dependent terms related to the complexity of learning weighted automata.