Learning Balls of Strings with Correction Queries

Abstract

Abstract. During the 80's, Angluin introduced an active learning paradigm, using an Oracle, capable of answering both membership and equivalence queries. However, practical evidence tends to show that if the former are often available, this is usually not the case of the latter. We propose new queries, called correction queries, which we study in the framework of Grammatical Inference. When a string is submitted to the Oracle, either she validates it if it belongs to the target language, or she proposes a correction, i.e., a string of the language close to the query with respect to the edit distance. We also introduce a non-standard class of languages: The topological balls of strings. We show that this class is not learnable in Angluin's Mat model, but is with a linear number of correction queries. We conduct several experiments with an Oracle simulating a human Expert, and show that our algorithm is resistant to approximate answers.

One-shot learners using negative counterexamples and nearest positive examples

“…[4,6,22,23] suggested a somewhat different approach, using corrections as extensions of queried strings. In [5], the authors use corrections at the shortest edit distance from the queried strings. However, as far as learning natural languages is concerned, whereas all such types of corrections are more or less natural from syntactical standpoint, they might be still semantically inadequate, as semantics of the correction would typically heavily depend on the context (for example, the incorrect English word ''milb'' could be ''mill'' or ''mild'' or ''mile'', depending on the context).…”

Towards a Bio-computational Model of Natural Language Learning

“…In [7] we proposed a new CQ based on edit distance. When the learner submits to the teacher a string that does not belong to the target language, the teacher returns a string of the language close to the query with respect to the edit distance (the edit distance is the minimum number of deletion, insertion or substitution operations needed to transform one string into another).…”

Bio-inspired Grammatical Inference

“…Since this idea was totally new in GI, we started by learning deterministic finite automata [8], in the framework of query learning (i.e., the learner is able to ask queries to the teacher, and the teacher has to answer correctly to these questions). Later, these results were extended to learn other classes with interesting properties, such as balls of strings (which are defined by using the edit distance) [7]. In both cases, when the learner asks for a string that does not belong to the target language, the teacher returns a correction (in the first case, such correction is based on the shortest extension of the queried string, and in the second case, such correction is based on the edit distance).…”