Learning of Structurally Unambiguous Probabilistic Grammars
This work addresses a foundational gap in grammar learning for computational linguistics and bioinformatics, though it is incremental as it focuses on a restricted class of grammars.
The authors tackled the problem of learning both the topology and probabilistic weights of structurally unambiguous probabilistic context-free grammars (SUPCFGs), which had been largely ignored due to hardness results, by developing a polynomial-time query learning algorithm that converts co-linear multiplicity tree automata into probabilistic grammars, demonstrating its application on genomic data.
The problem of identifying a probabilistic context free grammar has two aspects: the first is determining the grammar's topology (the rules of the grammar) and the second is estimating probabilistic weights for each rule. Given the hardness results for learning context-free grammars in general, and probabilistic grammars in particular, most of the literature has concentrated on the second problem. In this work we address the first problem. We restrict attention to structurally unambiguous weighted context-free grammars (SUWCFG) and provide a query learning algorithm for structurally unambiguous probabilistic context-free grammars (SUPCFG). We show that SUWCFG can be represented using co-linear multiplicity tree automata (CMTA), and provide a polynomial learning algorithm that learns CMTAs. We show that the learned CMTA can be converted into a probabilistic grammar, thus providing a complete algorithm for learning a structurally unambiguous probabilistic context free grammar (both the grammar topology and the probabilistic weights) using structured membership queries and structured equivalence queries. We demonstrate the usefulness of our algorithm in learning PCFGs over genomic data.