Learning of Structurally Unambiguous Probabilistic Grammars

The problem of identifying a probabilistic context free grammar has twoaspects: the first is determining the grammar's topology (the rules of thegrammar) and the second is estimating probabilistic weights for each rule.Given the hardness results for learning context-free grammars in general, andprobabilistic grammars in particular, most of the literature has concentratedon the second problem. In this work we address the first problem. We restrictattention to structurally unambiguous weighted context-free grammars (SUWCFG)and provide a query learning algorithm for \structurally unambiguousprobabilistic context-free grammars (SUPCFG). We show that SUWCFG can berepresented using \emph{co-linear multiplicity tree automata} (CMTA), andprovide a polynomial learning algorithm that learns CMTAs. We show that thelearned CMTA can be converted into a probabilistic grammar, thus providing acomplete algorithm for learning a structurally unambiguous probabilisticcontext free grammar (both the grammar topology and the probabilistic weights)using structured membership queries and structured equivalence queries. Asummarized version of this work was published at AAAI 21.Comment: arXiv admin note: substantial text overlap with arXiv:2011.0747