Related papers: Conjunctive Queries: Unique Characterizations and …
Algorithms for learning database queries from examples and unique characterisations of queries by examples are prominent starting points for developing automated support for query construction and explanation. We investigate how far recent…
This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating…
A fitting algorithm for conjunctive queries (CQs) produces, given a set of positively and negatively labeled data examples, a CQ that fits these examples. In general, there may be many non-equivalent fitting CQs and thus the algorithm has…
The fitting problem for conjunctive queries (CQs) is the problem to construct a CQ that fits a given set of labeled data examples. When a fitting CQ exists, it is in general not unique. This leads us to proposing natural refinements of the…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
We study the complexity and expressive power of conjunctive queries over unranked labeled trees represented using a variety of structure relations such as ``child'', ``descendant'', and ``following'' as well as unary relations for node…
Three events in a probability space form a conjunctive fork if they satisfy specific constraints on conditional independence and covariances. Patterns of conjunctive forks within collections of events are characterized by means of systems…
This report presents an elementary theory of unification for positive conjunctive queries. A positive conjunctive query is a formula constructed from propositional constants, equations and atoms using the conjunction $\wedge$ and the…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
We introduce new combinatorial quantities for concept classes, and prove lower and upper bounds for learning complexity in several models of query learning in terms of various combinatorial quantities. Our approach is flexible and powerful…
We study learning of indexed families from positive data where a learner can freely choose a hypothesis space (with uniformly decidable membership) comprising at least the languages to be learned. This abstracts a very universal learning…
In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
Labeled examples (i.e., positive and negative examples) are an attractive medium for communicating complex concepts. They are useful for deriving concept expressions (such as in concept learning, interactive concept specification, and…
Counting the number of answers to conjunctive queries is a fundamental problem in databases that, under standard assumptions, does not have an efficient solution. The issue is inherently #P-hard, extending even to classes of acyclic…
Existential positive formulas form a fragment of first-order logic that includes and is semantically equivalent to unions of conjunctive queries, one of the most important and well-studied classes of queries in database theory. We consider…
In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…
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…
A major problem in computational learning theory is whether the class of formulas in conjunctive normal form (CNF) is efficiently learnable. Although it is known that this class cannot be polynomially learned using either membership or…