Learning of Structurally Unambiguous Probabilistic Grammars

TL;DR

This paper presents a polynomial-time algorithm for learning structurally unambiguous probabilistic context-free grammars by representing them with co-linear multiplicity tree automata, addressing both topology and weights.

Contribution

It introduces a novel query learning algorithm for SUPCFG by leveraging CMTAs, enabling complete grammar and weight learning for structurally unambiguous grammars.

Findings

Polynomial learning algorithm for CMTAs

Complete grammar and weight recovery for SUPCFG

Representation of SUWCFG using CMTAs

Abstract

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 \emph{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. A summarized version of this work was published at AAAI 21.