Abstract:
We investigate ways to support interactive mining sessions, in the setting of association rule mining. In such sessions, users specify conditions (queries) on the associations to be generated. Our approach is a combination of the integration of querying conditions inside the mining phase, and the incremental querying of already generated associations. We present several concrete algorithms and compare their performance.

Abstract:
New applications of data mining, such as in biology, bioinformatics, or sociology, are faced with large datasetsstructured as graphs. We introduce a novel class of tree-shapedpatterns called tree queries, and present algorithms for miningtree queries and tree-query associations in a large data graph. Novel about our class of patterns is that they can containconstants, and can contain existential nodes which are not counted when determining the number of occurrences of the patternin the data graph. Our algorithms have a number of provableoptimality properties, which are based on the theory of conjunctive database queries. We propose a practical, database-oriented implementation in SQL, and show that the approach works in practice through experiments on data about food webs, protein interactions, and citation analysis.

Abstract:
Reinforcement learning is a formal framework for modeling agents that learn to solve tasks. For example, one important task for animals is to navigate in an environment to find food or to return to their nest. In such tasks, the agent has to learn a path through the environment from start states to goal states, by visiting a sequence of intermediate states. The agent receives reward on a goal state. Concretely, we need to learn a policy that maps each encountered state to an immediate action that leads to a next state, eventually leading to a goal state. We say that a learning process has converged if eventually the policy will no longer change, i.e., the policy stabilizes. The intuition of paths and navigation policies can be applied generally. Indeed, in this article, we study navigation tasks formalized as a graph structure that, for each application of an action to a state, describes the possible successor states that could result from that application. In contrast to standard reinforcement learning, we essentially simplify numeric reward signals to boolean flags on the transitions in the graph. The resulting framework enables a clear theoretical study of how properties of the graph structure can cause convergence of the learning process. In particular, we formally study a learning process that detects revisits to states in the graph, i.e., we detect cycles, and the process keeps adjusting the policy until no more cycles are made. So, eventually, the agent goes straight to reward from each start state. We identify reducibility of the task graph as a sufficient condition for this learning process to converge. We also syntactically characterize the form of the final policy, which can be used to detect convergence in a simulation.

Abstract:
We study the expressive power of positive neural networks. The model uses positive connection weights and multiple input neurons. Different behaviors can be expressed by varying the connection weights. We show that in discrete time, and in absence of noise, the class of positive neural networks captures the so-called monotone-regular behaviors, that are based on regular languages. A finer picture emerges if one takes into account the delay by which a monotone-regular behavior is implemented. Each monotone-regular behavior can be implemented by a positive neural network with a delay of one time unit. Some monotone-regular behaviors can be implemented with zero delay. And, interestingly, some simple monotone-regular behaviors can not be implemented with zero delay.

Abstract:
In recent years, the problem of association rule mining in transactional data has been well studied. We propose to extend the discovery of classical association rules to the discovery of association rules of conjunctive queries in arbitrary relational data, inspired by the WARMR algorithm, developed by Dehaspe and Toivonen, that discovers association rules over a limited set of conjunctive queries. Conjunctive query evaluation in relational databases is well understood, but still poses some great challenges when approached from a discovery viewpoint in which patterns are generated and evaluated with respect to some well defined search space and pruning operators.

Abstract:
The satisfiability problem for SPARQL patterns is undecidable in general, since the expressive power of SPARQL 1.0 is comparable with that of the relational algebra. The goal of this paper is to delineate the boundary of decidability of satisfiability in terms of the constraints allowed in filter conditions. The classes of constraints considered are bound-constraints, negated bound-constraints, equalities, nonequalities, constant-equalities, and constant-nonequalities. The main result of the paper can be summarized by saying that, as soon as inconsistent filter conditions can be formed, satisfiability is undecidable. The key insight in each case is to find a way to emulate the set difference operation. Undecidability can then be obtained from a known undecidability result for the algebra of binary relations with union, composition, and set difference. When no inconsistent filter conditions can be formed, satisfiability is efficiently decidable by simple checks on bound variables and on the use of literals. The paper also points out that satisfiability for the so-called `well-designed' patterns can be decided by a check on bound variables and a check for inconsistent filter conditions.

Abstract:
We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given expression. The principal type of an expression is a formula that specifies, in a clear and concise manner, all assignments of types (sets of attributes) to relation names, under which a given relational algebra expression is well-typed, as well as the output type that expression will have under each of these assignments. Topics discussed include complexity and polymorphic expressive power.

Abstract:
Enumerating all solutions of a relational algebra equation is a natural and powerful operation which, when added as a query language primitive to the nested relational algebra, yields a query language for nested relational databases, equivalent to the well-known powerset algebra. We study \emph{sparse} equations, which are equations with at most polynomially many solutions. We look at their complexity, and compare their expressive power with that of similar notions in the powerset algebra.

Abstract:
Two natural decision problems regarding the XML query language XQuery are well-definedness and semantic type-checking. We study these problems in the setting of a relational fragment of XQuery. We show that well-definedness and semantic type-checking are undecidable, even in the positive-existential case. Nevertheless, for a ``pure'' variant of XQuery, in which no identification is made between an item and the singleton containing that item, the problems become decidable. We also consider the analogous problems in the setting of the nested relational calculus.