Generalization Bounds for Weighted Automata
This work addresses generalization guarantees for learning weighted automata, which is incremental as it builds on existing theory with new bounds.
The paper tackles the problem of learning weighted automata from finite labeled training data by deriving new data-dependent generalization bounds based on Rademacher complexity for families defined by weight, function, or Hankel matrix norms, and provides upper bounds that reveal key data-dependent complexity terms.
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.