Learning Weighted Automata

Language and Automata Theory and Applications

“…In recent years, the spectral method of Hsu et al [40] for learning hidden Markov models, which relies on the SVD of a Hankel matrix, has driven much follow-up research, see the survey [8]. Balle and Mohri combined spectral methods with constrained matrix completion algorithms to learn arbitrary weighted automata, [7].…”

Proceedings of the SIGFSM Workshop on Statistical NLP and Weighted Automata

“…In this section, we provide the definitions of weighted automata in (Balle and Mohri, 2015;Sakarovitch, 2009) and matrix-space models of language in (Rudolph and Giesbrecht, 2010).…”

“…Moreover, Balle and Mohri (2015) discuss modern learning methods (spectral methods) for an arbitrary WFA in different scenarios. They provide WFA reconstruction algorithms and standardization.…”

“…The problem of learning WFAs is finding a WFA closely estimating a target function, using for training a finite sample of strings labeled with their target values (Balle and Mohri, 2015). By learning WFAs, one obtains an automaton that is a tuple A = α, β, {A a } a∈Σ , and one can compute the target function f A (x).…”

“…Also, the vectors α A ∈ R Q A and β A ∈ R Q A are the start and final weights of the states in Q A , respectively. Then, Equation 1 can be equally expressed as follows in terms of matrices with entries in R (Balle and Mohri, 2015):…”