Efficient search for statistically significant dependency rules in binary data

Analyzing statistical dependencies is a fundamental problem in all empirical science. Dependencies help us understand causes and effects, create new scientific theories, and invent cures to problems. Nowadays, large amounts of data is available, but efficient computational tools for analyzing the data are missing. In this research, we develop efficient algorithms for a commonly occurring search problem - searching for the statistically most significant dependency rules in binary data. We consider dependency rules of the form X->A or X->not A, where X is a set of positive-valued attributes and A is a single attribute. Such rules describe which factors either increase or decrease the probability of the consequent A. A classical example are genetic and environmental factors, which can either cause or prevent a disease. The emphasis in this research is that the discovered dependencies should be genuine - i.e. they should also hold in future data. This is an important distinction from the traditional association rules, which - in spite of their name and a similar appearance to dependency rules - do not necessarily represent statistical dependencies at all or represent only spurious connections, which occur by chance. Therefore, the principal objective is to search for the rules with statistical significance measures. Another important objective is to search for only non-redundant rules, which express the real causes of dependence, without any occasional extra factors. The extra factors do not add any new information on the dependence, but can only blur it and make it less accurate in future data. The problem is computationally very demanding, because the number of all possible rules increases exponentially with the number of attributes. In addition, neither the statistical dependency nor the statistical significance are monotonic properties, which means that the traditional pruning techniques do not work. As a solution, we first derive the mathematical basis for pruning the search space with any well-behaving statistical significance measures. The mathematical theory is complemented by a new algorithmic invention, which enables an efficient search without any heuristic restrictions. The resulting algorithm can be used to search for both positive and negative dependencies with any commonly used statistical measures, like Fisher's exact test, the chi-squared measure, mutual information, and z scores. According to our experiments, the algorithm is well-scalable, especially with Fisher's exact test. It can easily handle even the densest data sets with 10000-20000 attributes. Still, the results are globally optimal, which is a remarkable improvement over the existing solutions. In practice, this means that the user does not have to worry whether the dependencies hold in future data or if the data still contains better, but undiscovered dependencies.

Contributions to the Theory of Finite-State Based Grammars

This dissertation is a theoretical study of finite-state based grammars used in natural language processing. The study is concerned with certain varieties of finite-state intersection grammars (FSIG) whose parsers define regular relations between surface strings and annotated surface strings. The study focuses on the following three aspects of FSIGs: (i) Computational complexity of grammars under limiting parameters In the study, the computational complexity in practical natural language processing is approached through performance-motivated parameters on structural complexity. Each parameter splits some grammars in the Chomsky hierarchy into an infinite set of subset approximations. When the approximations are regular, they seem to fall into the logarithmic-time hierarchyand the dot-depth hierarchy of star-free regular languages. This theoretical result is important and possibly relevant to grammar induction. (ii) Linguistically applicable structural representations Related to the linguistically applicable representations of syntactic entities, the study contains new bracketing schemes that cope with dependency links, left- and right branching, crossing dependencies and spurious ambiguity. New grammar representations that resemble the Chomsky-Schützenberger representation of context-free languages are presented in the study, and they include, in particular, representations for mildly context-sensitive non-projective dependency grammars whose performance-motivated approximations are linear time parseable. (iii) Compilation and simplification of linguistic constraints Efficient compilation methods for certain regular operations such as generalized restriction are presented. These include an elegant algorithm that has already been adopted as the approach in a proprietary finite-state tool. In addition to the compilation methods, an approach to on-the-fly simplifications of finite-state representations for parse forests is sketched. These findings are tightly coupled with each other under the theme of locality. I argue that the findings help us to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing. Avainsanat: syntactic parsing, finite-state automata, dependency grammar, first-order logic, linguistic performance, star-free regular approximations, mildly context-sensitive grammars