PAC learning of Probabilistic Automaton based on the Method of Moments (Supplementary Material)
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چکیده
In this paper, we prove the following Theorem. Theorem 1. Let p be a distribution realized by a minimal PRFA of size d, B = (P,S) be a complete and residual basis, we denote by σd the d-th largest singular values of (pu(v))u∈R. LetD be a training set of words generated by p, we denote by n the number of time the least occurring prefix of P appears in D (n = minu∈P |{∃v ∈ Σ|uv ∈ D}|). For all 0 < δ < 1, there exists a constant K such that, for all t > 0, > 0, with probability 1− δ, if
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تاریخ انتشار 2016