Prediction-hardness of acyclic conjunctive queries

AbstractA conjunctive query problem is a problem to determine whether or not a tuple belongs to the answer of a conjunctive query over a database. In this paper, a tuple, a conjunctive query and a database in relational database theory are regarded as a ground atom, a nonrecursive function-free definite clause and a finite set of ground atoms, respectively, in inductive logic programming terminology. An acyclic conjunctive query problem is a conjunctive query problem with acyclicity. Concerned with the acyclic conjunctive query problem, in this paper, we present the hardness results of predicting acyclic conjunctive queries from an instance with a j-database of which predicate symbol is at most j-ary. Also we deal with two kinds of instances, a simple instance as a set of ground atoms and an extended instance as a set of pairs of a ground atom and a description. We mainly show that, from both a simple and an extended instances, acyclic conjunctive queries are not polynomial-time predictable with j-databases (j⩾3) under the cryptographic assumptions, and predicting acyclic conjunctive queries with 2-databases is as hard as predicting DNF formulas. Hence, the acyclic conjunctive queries become a natural example that the equivalence between subsumption-efficiency and efficient pac-learnability from both a simple and an extended instances collapses

Logical settings for concept learning from incomplete examples in First Order Logic

We investigate here concept learning from incomplete examples. Our first purpose is to discuss to what extent logical learning settings have to be modified in order to cope with data incompleteness. More precisely we are interested in extending the learning from interpretations setting introduced by L. De Raedt that extends to relational representations the classical propositional (or attribute-value) concept learning from examples framework. We are inspired here by ideas presented by H. Hirsh in a work extending the Version space inductive paradigm to incomplete data. H. Hirsh proposes to slightly modify the notion of solution when dealing with incomplete examples: a solution has to be a hypothesis compatible with all pieces of information concerning the examples. We identify two main classes of incompleteness. First, uncertainty deals with our state of knowledge concerning an example. Second, generalization (or abstraction) deals with what part of the description of the example is sufficient for the learning purpose. These two main sources of incompleteness can be mixed up when only part of the useful information is known. We discuss a general learning setting, referred to as "learning from possibilities" that formalizes these ideas, then we present a more specific learning setting, referred to as "assumption-based learning" that cope with examples which uncertainty can be reduced when considering contextual information outside of the proper description of the examples. Assumption-based learning is illustrated on a recent work concerning the prediction of a consensus secondary structure common to a set of RNA sequences

Learning Inequated Range Restricted Horn Expressions

A learning algorithm for the class of inequated range restricted Horn expressions is presented and proved correct. The main property of this class is that all the terms in the conclusion of a clause appear in the antecedent of the clause, possibly as subterms of more complex terms. And every clause includes in its antecedent all inequalities possible between all terms appearing in it. The algorithm works within the framework of learning from entailment, where the goal is to exactly identify some pre-fixed and unknown expression by making questions to membership and equivalence oracles

A New Algorithm for Learning Range Restricted Horn Expressions

A learning algorithm for the class of range restricted Horn expressions is presented and proved correct. The algorithm works within the framework of learning from entailment, where the goal is to exactly identify some pre-fixed and unknown expression by making questions to membership and equivalence oracles. This class has been shown to be learnable in previous work. The main contribution of this paper is in presenting a more direct algorithm for the problem which yields an improvement in terms of the number of queries made to the oracles. The algorithm is also adapted to the class of Horn expressions with inequalities on all syntactically distinct terms where further improvement in the number of queries is obtained

Representationally Robust and Scalable Learning over Relational Databases

Learning novel concepts from relational databases is an important problem with applications in several disciplines, such as data management, natural language processing, and bioinformatics. For a learning algorithm to be effective, the input data should be clean and in some desired representation. However, real-world data is usually heterogeneous – the same data may be represented under different representations. The current approach to effectively use learning algorithms is to find the desired representations for these algorithms, transform the data to these representations, and clean the data. These tasks are hard and time-consuming and are major obstacles for unlocking the value of data. This thesis demonstrates that it is possible to develop robust learning algorithms that learn in the presence of representational variations. We develop two systems called Castor and CastorX, which exploit data dependencies to be robust against different types of representational variations. Further, we propose several techniques that allow these systems to learn efficiently over large databases. The proposed systems learn over the original data, removing the need for transforming the data before applying learning algorithms. Our results show that Castor and CastorX learn accurately and efficiently over real-world databases. This work paves the way for new approaches that replace pre-processing tasks such as data wrangling with robust learning algorithms

Learning Function-Free Horn Expressions

The problem of learning universally quantified function free first order Horn expressions is studied. Several models of learning from equivalence and membership queries are considered, including the model where interpretations are examples (Learning from Interpretations), the model where clauses are examples (Learning from Entailment), models where extentional or intentional background knowledge is given to the learner (as done in Inductive Logic Programming), and the model where the reasoning performance of the learner rather than identification is of interest (Learning to Reason). We present learning algorithms for all these tasks for the class of universally quantified function free Horn expressions. The algorithms are polynomial in the number of predicate symbols in the language and the number of clauses in the target Horn expression but exponential in the arity of predicates and the number of universally quantified variables. We also provide lower bounds for these tasks by way of ..