Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

Matrix Decomposition Methods for Data Mining : Computational Complexity and Algorithms

Matrix decompositions, where a given matrix is represented as a product of two other matrices, are regularly used in data mining. Most matrix decompositions have their roots in linear algebra, but the needs of data mining are not always those of linear algebra. In data mining one needs to have results that are interpretable -- and what is considered interpretable in data mining can be very different to what is considered interpretable in linear algebra. --- The purpose of this thesis is to study matrix decompositions that directly address the issue of interpretability. An example is a decomposition of binary matrices where the factor matrices are assumed to be binary and the matrix multiplication is Boolean. The restriction to binary factor matrices increases interpretability -- factor matrices are of the same type as the original matrix -- and allows the use of Boolean matrix multiplication, which is often more intuitive than normal matrix multiplication with binary matrices. Also several other decomposition methods are described, and the computational complexity of computing them is studied together with the hardness of approximating the related optimization problems. Based on these studies, algorithms for constructing the decompositions are proposed. Constructing the decompositions turns out to be computationally hard, and the proposed algorithms are mostly based on various heuristics. Nevertheless, the algorithms are shown to be capable of finding good results in empirical experiments conducted with both synthetic and real-world data.

Linguistic grammars with very low complexity

We have presented an overview of the FSIG approach and related FSIG gram- mars to issues of very low complexity and parsing strategy. We ended up with serious optimism according to which most FSIG grammars could be decom- posed in a reasonable way and then processed efficiently.

Tax Reform and Payout Policy:Do Shareholder Clienteles or Payout Policy Adjust?

Changes in taxation of corporate dividends offer excellent opportunities to study dividend clientele effects. We explore payout policies and ownership structures around a major tax reform that took place in Finland in 2004. Consistent with dividend clienteles affecting firms’ dividend policy decisions, we find that Finnish firms altered their dividend policies based on the changed tax incentives of their largest shareholders. While firms adjust their payout policies, our results also indicate that ownership structures of Finnish firms also changed around the 2004 reform, consistent with shareholder clienteles adjusting to the new tax system.

Tax havens and their impacts on the non-haven countries

Tax havens have attracted increasing attention from the authorities of non-haven countries. The financial crisis exacerbates the negative attitude to tax havens. Offshore zones are now under strong pressure from the international, both financial and political institutions. Thus, the thesis will focus on the current problem of the modern economy, namely tax havens and their impact on the non-haven countries. This thesis will be based on the several articles, in particular “Tax Competition With Parasitic Tax Havens” by Joel Slemrod and John D. Wilson (University of Michigan, 2009) and “Do Havens Divert Economic Activity” by James R. Hines Jr., C. Fritz Foley and Mihir A. Desai (Ross School of Business, 2005). This paper provides two completely different and contradictory viewpoints on the problem of coexisting tax havens and non-haven countries. There are two models, examined in this work, present two important researches. The first one will be concentrated on the positive effect from tax havens whereas the last model will be focused on the completely negative effect from offshore jurisdictions. The first model gives us a good explanation and proof of its statement why tax havens can positively influence on nearby high-tax countries. It describes that the existence of offshore jurisdictions can stimulate the growth of operations and facilitates economic activity in non-haven countries. In contrast to above mentioned, the model with quite opposite view was presented. This economic model and its analysis confirms the undesirability of the existence of offshore areas. Taking into consideration, that the jurisdictions choose their optimal policy, the elimination of offshores will have positive impact on the rest of countries. The model proofs the statement that full or partial elimination of tax havens raises the equilibrium level of the public good and increases country welfare. According to the following study, it can be concluded that both of the models provide telling arguments to prove their assertions. Thereby both of these points of view have their right to exist. Nevertheless, the ongoing debate concerning this issue still will raise a lot of questions.

Language universals and linguistic complexity : Three case studies in core argument marking

In this dissertation I study language complexity from a typological perspective. Since the structuralist era, it has been assumed that local complexity differences in languages are balanced out in cross-linguistic comparisons and that complexity is not affected by the geopolitical or sociocultural aspects of the speech community. However, these assumptions have seldom been studied systematically from a typological point of view. My objective is to define complexity so that it is possible to compare it across languages and to approach its variation with the methods of quantitative typology. My main empirical research questions are: i) does language complexity vary in any systematic way in local domains, and ii) can language complexity be affected by the geographical or social environment? These questions are studied in three articles, whose findings are summarized in the introduction to the dissertation. In order to enable cross-language comparison, I measure complexity as the description length of the regularities in an entity; I separate it from difficulty, focus on local instead of global complexity, and break it up into different types. This approach helps avoid the problems that plagued earlier metrics of language complexity. My approach to grammar is functional-typological in nature, and the theoretical framework is basic linguistic theory. I delimit the empirical research functionally to the marking of core arguments (the basic participants in the sentence). I assess the distributions of complexity in this domain with multifactorial statistical methods and use different sampling strategies, implementing, for instance, the Greenbergian view of universals as diachronic laws of type preference. My data come from large and balanced samples (up to approximately 850 languages), drawn mainly from reference grammars. The results suggest that various significant trends occur in the marking of core arguments in regard to complexity and that complexity in this domain correlates with population size. These results provide evidence that linguistic patterns interact among themselves in terms of complexity, that language structure adapts to the social environment, and that there may be cognitive mechanisms that limit complexity locally. My approach to complexity and language universals can therefore be successfully applied to empirical data and may serve as a model for further research in these areas.