Learning Tree Pattern Transformations

TL;DR

This paper investigates how to learn small sets of rules that explain structural differences between pairs of trees, using a pattern-based language, complexity analysis, and SAT solvers, with applications in data and education.

Contribution

It introduces a pattern-based language for tree transformations, analyzes the computational complexity, and proposes solving methods using SAT solvers for data explanation.

Findings

NP-hardness for restricted variants of the problem

A pattern-based specification language for tree transformations

Use of SAT solvers to find explanations in educational data

Abstract

Explaining why and how a tree $t$ structurally differs from another tree $t^\star$ is a question that is encountered throughout computer science, including in understanding tree-structured data such as XML or JSON data. In this article, we explore how to learn explanations for structural differences between pairs of trees from sample data: suppose we are given a set $\{(t_1, t_1^\star),\dots, (t_n, t_n^\star)\}$ of pairs of labelled, ordered trees; is there a small set of rules that explains the structural differences between all pairs $(t_i, t_i^\star)$? This raises two research questions: (i) what is a good notion of "rule" in this context?; and (ii) how can sets of rules explaining a data set be learned algorithmically? We explore these questions from the perspective of database theory by (1) introducing a pattern-based specification language for tree transformations; (2) exploring the computational complexity of variants of the above algorithmic problem, e.g. showing NP-hardness for very restricted variants; and (3) discussing how to solve the problem for data from CS education research using SAT solvers.