Two new results about quantum exact learning

We present two new results about exact learning by quantum computers. First, we show how to exactly learn a k-Fourier-sparse n-bit Boolean function from O(k1.5(log⁡k)2) uniform quantum examples for that function. This improves over the bound of Θ~(kn) uniformly random classical examples (Haviv and Regev, CCC'15). Additionally, we provide a possible direction to improve our O~(k1.5) upper bound by proving an improvement of Chang's lemma for k-Fourier-sparse Boolean functions. Second, we show that if a concept class C can be exactly learned using Q quantum membership queries, then it can also be learned using O(Q2log⁡Qlog⁡|C|)classical membership queries. This improves the previous-best simulation result (Servedio and Gortler, SICOMP'04) by a log⁡Q-factor.

Compositional learning of mutually recursive procedural systems

This paper presents a compositional approach to active automata learning of Systems of Procedural Automata (SPAs), an extension of Deterministic Finite Automata (DFAs) to systems of DFAs that can mutually call each other. SPAs are of high practical relevance, as they allow one to efficiently learn intuitive recursive models of recursive programs after an easy instrumentation that makes calls and returns observable. Key to our approach is the simultaneous inference of individual DFAs for each of the involved procedures via expansion and projection: membership queries for the individual DFAs are expanded to membership queries of the entire SPA, and global counterexample traces are transformed into counterexamples for the DFAs of concerned procedures. This reduces the inference of SPAs to a simultaneous inference of the DFAs for the involved procedures for which we can utilize various existing regular learning algorithms. The inferred models are easy to understand and allow for an intuitive display of the procedural system under learning that reveals its recursive structure. We implemented the algorithm within the LearnLib framework in order to provide a ready-to-use tool for practical application which is publicly available on GitHub for experimentation.

Actively Learning Concepts and Conjunctive Queries under ELr-Ontologies

We consider the problem to learn a concept or a query in the presence of an ontology formulated in the description logic ELr, in Angluin's framework of active learning that allows the learning algorithm to interactively query an oracle (such as a domain expert). We show that the following can be learned in polynomial time: (1) EL-concepts, (2) symmetry-free ELI-concepts, and (3) conjunctive queries (CQs) that are chordal, symmetry-free, and of bounded arity. In all cases, the learner can pose to the oracle membership queries based on ABoxes and equivalence queries that ask whether a given concept/query from the considered class is equivalent to the target. The restriction to bounded arity in (3) can be removed when we admit unrestricted CQs in equivalence queries. We also show that EL-concepts are not polynomial query learnable in the presence of ELI-ontologies.

Attribute-efficient learning of Boolean functions from Post closed classes

We consider exact attribute-efficient learning of functions from Post closed classes using membership queries and obtain bounds on learning complexity.

Textual Membership Queries

Human labeling of data can be very time-consuming and expensive, yet, in many cases it is critical for the success of the learning process. In order to minimize human labeling efforts, we propose a novel active learning solution that does not rely on existing sources of unlabeled data. It uses a small amount of labeled data as the core set for the synthesis of useful membership queries (MQs) — unlabeled instances generated by an algorithm for human labeling. Our solution uses modification operators, functions that modify instances to some extent. We apply the operators on a small set of instances (core set), creating a set of new membership queries. Using this framework, we look at the instance space as a search space and apply search algorithms in order to generate new examples highly relevant to the learner. We implement this framework in the textual domain and test it on several text classification tasks and show improved classifier performance as more MQs are labeled and incorporated into the training set. To the best of our knowledge, this is the first work on membership queries in the textual domain.

On the Learnability of Possibilistic Theories

We investigate learnability of possibilistic theories from entailments in light of Angluin’s exact learning model. We consider cases in which only membership, only equivalence, and both kinds of queries can be posed by the learner. We then show that, for a large class of problems, polynomial time learnability results for classical logic can be transferred to the respective possibilistic extension. In particular, it follows from our results that the possibilistic extension of propositional Horn theories is exactly learnable in polynomial time. As polynomial time learnability in the exact model is transferable to the classical probably approximately correct (PAC) model extended with membership queries, our work also establishes such results in this model.