Learning with Partially Ordered Representations

Abstract

This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one unary relation. We consider unconventional string models where positions can have multiple, shared properties, which are arguably useful in many applications. We show the structures given by these models are partially ordered, and present a learning algorithm that exploits this ordering relation to effectively prune the hypothesis space. We prove this learning algorithm, which takes positive examples as input, finds the most general grammar which covers the data.

Categorical Account of Gradient Acceptability of Word-Initial Polish Onsets

“…Finally, we would also be interested in categorical model that can generalize constraints over featural representations as the HWPL does. The Bottom Up Factor Inference Algorithm (BUFIA) is a promising candidate in this regard (Chandlee et al, 2019;Rawski, 2021). Figure 2 shows these six possibilities with the learning model in bold the ones that we examined in this paper.…”

“…Examples of categorical learning models include the ones introduced by Gorman (2013) and Durvasula (2020). Chandlee et al (2019) also present a general method for finding inviolable constraints using any representational scheme in a data sample. As mentioned, HWPL (Hayes & Wilson, 2008) uses the principle of Maximum Entropy to return weighted constraints over featural representations which are used to assign probabilities to forms.…”

Learning Nonlocal Phonotactics in a Strictly Piecewise Probabilistic Phonotactic Model

“…[+F, +G]. This issue might also be resolved by enriching the representation with natural classes, which is not treated in the current paper (see Chandlee et al (2019) for a solution based on partially ordered structure of feature system).…”

“…Besides learning and grammar, the current study also has different representational assumption comparing to the natural classbased representation in Hayes & Wilson (2008). Chandlee et al (2019) has shown some promising result of learning natural classbased representation based on Model Theory (Libkin, 2013), while incorporating natural classbased representation to SP phonotactic model is left to future studies. However, these proposals also simultaneously assumes tierbased local ngrams (or tierbased strictly local language; TSL (Heinz et al, 2011)) as the hypothesis space, which predicts blocking effect in nonlocal phonotactics (Heinz, 2010).…”