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.

Religion and Science in Abraham Ibn Ezra's Sefer ha-Olam

The thesis examines rabbi Abraham Ibn Ezra's (11096-1064) conceptions of the relationship between religion and science with special focus on his seventh astrological treatise Sefer ha-Olam (The Book of the World). The thesis includes an analysis of medieval arabic astrology and the concepts science and religion in the relevant period. The appendix holds a tentative english translation of the hebrew text.

Rhetoric and Representation : Exploring the Cultural Meaning of the Natural Sciences in Contemporary Popular Science Writing and Literature

Kirjallisuuden- ja kulttuurintutkimus on viimeisten kolmen vuosikymmenen aikana tullut yhä enenevässä määrin tietoiseksi tieteen ja taiteen suhteen monimutkaisesta luonteesta. Nykyään näiden kahden kulttuurin tutkimus muodostaa oman kenttänsä, jolla niiden suhdetta tarkastellaan ennen kaikkea dynaamisena vuorovaikutuksena, joka heijastaa kulttuurimme kieltä, arvoja ja ideologisia sisältöjä. Toisin kuin aiemmat näkemykset, jotka pitävät tiedettä ja taidetta toisilleen enemmän tai vähemmän vastakkaisina pyrkimyksinä, nykytutkimus lähtee oletuksesta, jonka mukaan ne ovat kulttuurillisesti rakentuneita diskursseja, jotka kohtaavat usein samankaltaisia todellisuuden mallintamiseen liittyviä ongelmia, vaikka niiden käyttämät metodit eroavatkin toisistaan. Väitöskirjani keskittyy yllä mainitun suhteen osa-alueista popularisoidun tietokirjallisuuden (muun muassa Paul Davies, James Gleick ja Richard Dawkins) käyttämän kielen ja luonnontieteistä ideoita ammentavan kaunokirjallisuuden (muun muassa Jeanette Winterson, Tom Stoppard ja Richard Powers) hyödyntämien keinojen tarkasteluun nojautuen yli 30 teoksen kattavaa aineistoa koskevaan tyylin ja teemojen tekstianalyysiin. Populaarin tietokirjallisuuden osalta tarkoituksenani on osoittaa, että sen käyttämä kieli rakentuu huomattavassa määrin sellaisille rakenteille, jotka tarjoavat mahdollisuuden esittää todellisuutta koskevia argumentteja mahdollisimman vakuuttavalla tavalla. Tässä tehtävässä monilla klassisen retoriikan määrittelemillä kuvioilla on tärkeä rooli, koska ne auttavat liittämään sanotun sisällön ja muodon tiukasti toisiinsa: retoristen kuvioiden käyttö ei näin ollen edusta pelkkää tyylikeinoa, vaan se myös usein kiteyttää argumenttien taustalla olevat tieteenfilosofiset olettamukset ja auttaa vakiinnuttamaan argumentoinnin logiikan. Koska monet aikaisemmin ilmestyneistä tutkimuksista ovat keskittyneet pelkästään metaforan rooliin tieteellisissä argumenteissa, tämä väitöskirja pyrkii laajentamaan tutkimuskenttää analysoimalla myös toisenlaisten kuvioiden käyttöä. Osoitan myös, että retoristen kuvioiden käyttö muodostaa yhtymäkohdan tieteellisiä ideoita hyödyntävään kaunokirjallisuuteen. Siinä missä popularisoitu tiede käyttää retoriikkaa vahvistaakseen sekä argumentatiivisia että kaunokirjallisia ominaisuuksiaan, kuvaa tällainen sanataide tiedettä tavoilla, jotka usein heijastelevat tietokirjallisuuden kielellisiä rakenteita. Toisaalta on myös mahdollista nähdä, miten kaunokirjallisuuden keinot heijastuvat popularisoidun tieteen kerrontatapoihin ja kieleen todistaen kahden kulttuurin dynaamisesta vuorovaikutuksesta. Nykyaikaisen populaaritieteen retoristen elementtien ja kaunokirjallisuuden keinojen vertailu näyttää lisäksi, kuinka tiede ja taide osallistuvat keskusteluun kulttuurimme tiettyjen peruskäsitteiden kuten identiteetin, tiedon ja ajan merkityksestä. Tällä tavoin on mahdollista nähdä, että molemmat ovat perustavanlaatuisia osia merkityksenantoprosessissa, jonka kautta niin tieteelliset ideat kuin ihmiselämän suuret kysymyksetkin saavat kulttuurillisesti rakentuneen merkityksensä.

Karl Popper's Philosophy of Science - And the Evolution of the Popperian Worlds

This doctoral thesis in theoretical philosophy is a systematic analysis of Karl Popper's philosophy of science and its relation to his theory of three worlds. The general aim is to study Popper's philosophy of science and to show that Popper's theory of three worlds was a restatement of his earlier positions. As a result, a new reading of Popper's philosophy and development is offered and the theory of three worlds is analysed in a new manner. It is suggested that the theory of three worlds is not purely an ontological theory, but has a profound epistemological motivation. In Part One, Popper's epistemology and philosophy of science is analysed. It is claimed that Popper's thinking was bifurcated: he held two profound positions without noticing the tension between them. Popper adopted the position called the theorist around 1930 and focused on the logical structure of scientific theories. In Logik der Forschung (1935), he attempted to build a logic of science on the grounds that scientific theories may be regarded as universal statements which are not verifiable but can be falsified. Later, Popper emphasized another position, called here the processionalist. Popper focused on the study of science as a process and held that a) philosophy of science should study the growth of knowledge and that b) all cognitive processes are constitutive. Moreover, the constitutive idea that we see the world in the searchlight of our theories was combined with the biological insight that knowledge grows by trial and error. In Part Two, the theory of three worlds is analysed systematically. The theory is discussed as a cluster of theories which originate from Popper's attempt to solve some internal problems in his thinking. Popper adhered to realism and wished to reconcile the theorist and the processionalist. He also stressed the real and active nature of the human mind, and the possibility of objective knowledge. Finally, he wished to create a scientific world view.

Logic as the Universal Science : Bertrand Russell's Early Conception of Logic and Its Philosophical Context

Bertrand Russell (1872 1970) introduced the English-speaking philosophical world to modern, mathematical logic and foundational study of mathematics. The present study concerns the conception of logic that underlies his early logicist philosophy of mathematics, formulated in The Principles of Mathematics (1903). In 1967, Jean van Heijenoort published a paper, Logic as Language and Logic as Calculus, in which he argued that the early development of modern logic (roughly the period 1879 1930) can be understood, when considered in the light of a distinction between two essentially different perspectives on logic. According to the view of logic as language, logic constitutes the general framework for all rational discourse, or meaningful use of language, whereas the conception of logic as calculus regards logic more as a symbolism which is subject to reinterpretation. The calculus-view paves the way for systematic metatheory, where logic itself becomes a subject of mathematical study (model-theory). Several scholars have interpreted Russell s views on logic with the help of the interpretative tool introduced by van Heijenoort,. They have commonly argued that Russell s is a clear-cut case of the view of logic as language. In the present study a detailed reconstruction of the view and its implications is provided, and it is argued that the interpretation is seriously misleading as to what he really thought about logic. I argue that Russell s conception is best understood by setting it in its proper philosophical context. This is constituted by Immanuel Kant s theory of mathematics. Kant had argued that purely conceptual thought basically, the logical forms recognised in Aristotelian logic cannot capture the content of mathematical judgments and reasonings. Mathematical cognition is not grounded in logic but in space and time as the pure forms of intuition. As against this view, Russell argued that once logic is developed into a proper tool which can be applied to mathematical theories, Kant s views turn out to be completely wrong. In the present work the view is defended that Russell s logicist philosophy of mathematics, or the view that mathematics is really only logic, is based on what I term the Bolzanian account of logic . According to this conception, (i) the distinction between form and content is not explanatory in logic; (ii) the propositions of logic have genuine content; (iii) this content is conferred upon them by special entities, logical constants . The Bolzanian account, it is argued, is both historically important and throws genuine light on Russell s conception of logic.

Scheffleriläinen rationaalisuus ja kasvatustodellisuuden monikerroksisuus : Jännitteitä ja ratkaisuja Israel Schefflerin kasvatusfilosofiassa

The study is a philosophical analysis of Israel Scheffler’s philosophy of education, focusing on three crucial conceptions in his philosophy: the conception of rationality, the conception of human nature, and the conception of reality. The interrelations of these three concepts as well as their relations to educational theorizing are analysed and elaborated. A conceptual problem concerning Scheffler’s ideal of rationality derives from Scheffler’s supposition of the strong analogy between science education and moral education in terms of the ideal of rationality. This analogy is argued to be conceptually problematic, since the interconnections of rationality, objectivity, and truth, appear to differ from each other in the realms of ethics and science, given the presuppositions of ontological realism and ethical naturalism, to which Scheffler explicitly subscribes. This study considers two philosophical alternatives for solving this problem. The first alternative relates the analogy to the normative concept of personhood deriving from the teleological understanding of human nature. Nevertheless, this position turns out to be problematic for Scheffler, since he rejects all teleological thinking in his philosophy. The problem can be solved, as it is argued, by limiting Scheffler’s rejection of teleology – in light of his philosophical outlook on the whole – in a manner that allows a modest version of a teleological conception of human nature. The second alternative, based especially on Scheffler’s later contributions, is to suggest that reality is actually more complex and manifold than it appears to be in light of a contemporary naturalist worldview. This idea of plurealism – Scheffler’s synthesis of pluralism and realism – is represented especially in Scheffler’s contributions related to his debate with Nelson Goodman dealing with both constructivism and realism. The idea of plurealism is not only related to the ethics-science-distinction, but is more widely related to the relationship between ontological realism and the incommensurable systems of description in diverse realms of human understanding. The Scheffler-Goodman debate is also analysed in relation to the contemporary constructivism-realism debate in educational philosophy. In terms of educational questions, Scheffler’s plurealism is argued as offering a fruitful perspective. Scheffler’s philosophy of education can be interpreted as searching for solutions to the problems deriving from the tension between the tradition of analytical philosophy and the complexity and multiplicity of educational reality. The complexity of reality combined with the supposition of the limitedness of human knowledge does not lead Scheffler to relativism or particularism, but, in contrast, Schefflerian formulations of rationality and objectivity preserve the possibility for critical inquiry in all realms of educational reality. In light of this study, Scheffler’s philosophy of education provides an exceptional example of combining ontological realism, epistemological fallibilism, and the defence of the ideal of rationality, combined with a wide-ranging understanding of educational reality.

Women, environmental changes and forestry-related development : Gender-affected roles of rural people in land degradation and environmental rehabilitation in a dry region of Sudan

The purpose of the present study was to increase understanding of the interaction of rural people and, specifically, women with the environment in a dry area in Sudan. The study that included both nomadic pastoralists and farmers aimed at answering two main research questions, namely: What kinds of roles have the local people, and the women in particular, had in land degradation in the study area and what kinds of issues would a gender-sensitive, forestry-related environmental rehabilitation intervention need to consider there? The study adopted the definition of land degradation as proposed by the United Nations Convention to Combat Desertification (UNCCD), which describes land degradation as reduction or loss the biological or economic productivity and complexity of land in arid, semi-arid and dry sub-humid areas. The Convention perceives desertification as land degradation. The dry study area in Sudan, South of the Sahara, has been the subject of land degradation or desertification discussions since the 1970s, and other studies have been also conducted to assess the degradation in the area. Nevertheless, the exact occurrence, scale and local significance of land degradation in the area is still unclear. This study explored how the rural population whose livelihood depended on the area, perceived environmental changes occurring there and compared their conceptions with other sources of information of the area such as research reports. The main fieldwork methods included interviews with open-ended questions and observation of people and the environment. The theoretical framework conceptualised the rural population as land users whose choices of environmental activities are affected by multiple factors in the social and biophysical contexts in which they live. It was emphasised that these factors have their own specific characteristics in different contexts, simultaneously recognising that there are also factors that generally affect environmental practices in various areas such as the land users' environmental literacy (conceptions of the environment), gender and livelihood needs. The people studied described that environmental changes, such as reduced vegetation cover and cropland production, had complicated the maintenance of their livelihoods in the study area. Some degraded sites were also identified through observations during the fieldwork. Whether a large-scale reduction of cropland productivity had occurred in the farmers' croplands remained, however, unclear. The study found that the environmental impact of the rural women's activities varied and was normally limited. The women's most significant environmental impact resulted from their cutting of trees, which was likely to contribute, at least in some places, to land degradation, affecting the environment together with climate and livestock. However, when a wider perspective is taken, it becomes questionable whether the women have really played roles in land degradation, since gender, poverty and the need to maintain livelihood had caused them to conduct environmentally harmful activities. The women have had, however, no power to change the causes of their activities. The findings further suggested that an inadequate availability of food was the most critical problem in the study area. Therefore, an environmental programme in the area was suggested to include technical measures to increase the productivity of croplands, opportunities for income generation and readiness to co-operate with other programmes to improve the local people's abilities to maintain their livelihoods. In order to protect the environment and alleviate the women's work burden, the introduction of fuel-saving stoves was also suggested. Furthermore, it was suggested that increased planting of trees on homesteads would be supported by an easy availability of tree seedlings. Planting trees on common property land was, however, perceived as extremely demanding in the study area, due to scarcity of such land. In addition, it became apparent that the local land users, and women in particular, needed to allocate their labour to maintain the immediate livelihood of their families and were not motivated to allocate their labour solely for environmental rehabilitation. Nonetheless, from the point of view of the existing social structures, women's active participation in a community-based environmental programme would be rather natural, particularly among the farmer women who had already formed a women's group and participated in communal decision making. Forming of a women group or groups was suggested to further support both the farmer women's and pastoral women's active participation within an environmental programme and their general empowerment. An Environmental programme would need to acknowledge that improving rural people's well-being and maintaining their livelihood in the study area requires development and co-operation with various sectors in Sudan.