Integrity Constraints Revisited: From Exact to Approximate Implication

Integrity constraints such as functional dependencies (FD), and multi-valued dependencies (MVD) are fundamental in database schema design. Likewise, probabilistic conditional independences (CI) are crucial for reasoning about multivariate probability distributions. The implication problem studies whether a set of constraints (antecedents) implies another constraint (consequent), and has been investigated in both the database and the AI literature, under the assumption that all constraints hold exactly. However, many applications today consider constraints that hold only approximately. In this paper we define an approximate implication as a linear inequality between the degree of satisfaction of the antecedents and consequent, and we study the relaxation problem: when does an exact implication relax to an approximate implication? We use information theory to define the degree of satisfaction, and prove several results. First, we show that any implication from a set of data dependencies (MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most quadratic in the number of variables; when the consequent is an FD, the factor can be reduced to 1. Second, we prove that there exists an implication between CIs that does not admit any relaxation; however, we prove that every implication between CIs relaxes "in the limit". Finally, we show that the implication problem for differential constraints in market basket analysis also admits a relaxation with a factor equal to 1. Our results recover, and sometimes extend, several previously known results about the implication problem: implication of MVDs can be checked by considering only 2-tuple relations, and the implication of differential constraints for frequent item sets can be checked by considering only databases containing a single transaction

Probabilistic Team Semantics

Team semantics is a semantical framework for the study of dependence and independence concepts ubiquitous in many areas such as databases and statistics. In recent works team semantics has been generalised to accommodate also multisets and probabilistic dependencies. In this article we study a variant of probabilistic team semantics and relate this framework to a Tarskian two-sorted logic. We also show that very simple quantifier-free formulae of our logic give rise to backslashmathrm NP NP -hard model checking problems.Peer reviewe

Entropy characterization of commutative partitions.

Lo Ying Hang.Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.Includes bibliographical references (leaves 80-81).Abstracts in English and Chinese.Chapter Chapter 1 --- Introduction --- p.1Chapter Chapter 2 --- Background --- p.4Chapter Chapter 3 --- Commutative Partition Pair Analysis --- p.9Chapter Chapter 4 --- Entropy Inequalities for Partition Pair --- p.19Chapter Chapter 5 --- Entropy Characterization of Commutative Partition Pair --- p.32Chapter Chapter 6 --- Ordered Commutative Partitions --- p.43Chapter Chapter 7 --- Running Intersection Property for Partitions --- p.45Chapter Chapter 8 --- Entropy Characterization of Ordered Commutative Partitions --- p.53Chapter Chapter 9 --- Significance and Application --- p.72Chapter Chapter 10 --- Future Plan --- p.78Chapter Chapter 11 --- Conclusion --- p.79Bibliography --- p.8

Prototipo de tutor inteligente para el aprendizaje de la programación de computadores

Trabajo de InvestigaciónLa creciente necesidad de ingenieros, en especial desarrolladores de software, ha incrementado la importancia de la instrucción de estos profesionales. Las dificultades en el aprendizaje de programación resaltan la importancia de localizar los factores críticos que afectan el desempeño de los estudiantes y plantear estrategias que permitan mejorar las posibilidades de cada estudiante en su proceso de aprendizaje. Para esto, se usan métodos de clasificación automática para localizar patrones que relacionen características personales con el desempeño en programación de computadores. Además se sugiere el uso de un modelo para mejorar el proceso de enseñanza.INTRODUCCIÓN 1. GENERALIDADES 2. CARACTERIZACIÓN DE LA ENSEÑANZA DE LA PROGRAMACIÓN 4. TUTORES INTELIGENTES 5. ALGORITMOS PARA EL RECONOCIMIENTO DE PATRONES. 6. DISEÑO DEL MODELO DE DATOS PARA LAS CARACTERISTICAS 7. ANÁLISIS DE RESULTADOS 8. DISEÑO Y CONSTRUCCIÓN DEL TUTOR INTELIGENTE 9. CONCLUSIONES 10. RECOMENDACIONES BIBLIOGRAFÍAPregradoIngeniero de Sistema

On the Implication Problem for Probabilistic Conditional Independency

The implication problem is to test whether a given set of independencies logically implies another independency. This problem is crucial in the design of a probabilistic reasoning system. We advocate that Bayesian networks are a generalization of standard relational databases. On the contrary, it has been suggested that Bayesian networks are different from the relational databases because the implication problem of these two systems does not coincide for some classes of probabilistic independencies. This remark, however, does not take into consideration one important issue, namely, the solvability of the implication problem