Learning Schemas for Unordered XML

TL;DR

This paper investigates the problem of learning unordered XML schemas, specifically disjunctive and disjunction-free multiplicity schemas, from positive and negative examples, providing algorithms with proven learnability and minimality guarantees.

Contribution

It introduces efficient algorithms for learning disjunctive and disjunction-free multiplicity schemas from examples, with formal proofs of learnability and minimality.

Findings

DMS are learnable from positive examples only.

MS are learnable from both positive and negative examples.

Algorithms produce minimal schemas consistent with the data.

Abstract

We consider unordered XML, where the relative order among siblings is ignored, and we investigate the problem of learning schemas from examples given by the user. We focus on the schema formalisms proposed in [10]: disjunctive multiplicity schemas (DMS) and its restriction, disjunction-free multiplicity schemas (MS). A learning algorithm takes as input a set of XML documents which must satisfy the schema (i.e., positive examples) and a set of XML documents which must not satisfy the schema (i.e., negative examples), and returns a schema consistent with the examples. We investigate a learning framework inspired by Gold [18], where a learning algorithm should be sound i.e., always return a schema consistent with the examples given by the user, and complete i.e., able to produce every schema with a sufficiently rich set of examples. Additionally, the algorithm should be efficient i.e., polynomial in the size of the input. We prove that the DMS are learnable from positive examples only, but they are not learnable when we also allow negative examples. Moreover, we show that the MS are learnable in the presence of positive examples only, and also in the presence of both positive and negative examples. Furthermore, for the learnable cases, the proposed learning algorithms return minimal schemas consistent with the examples.