構造化データに対する予測手法：グラフ，順序，時系列

京都大学新制・課程博士博士(情報学)甲第23439号情博第769号新制||情||131(附属図書館)京都大学大学院情報学研究科知能情報学専攻(主査)教授 鹿島 久嗣, 教授 山本 章博, 教授 阿久津 達也学位規則第4条第1項該当Doctor of InformaticsKyoto UniversityDFA

Projective Market Model Approach to AHP Decision-Making

In this paper we describe market in projective geometry language and give definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the Analytic Hierarchy Process (AHP). We use these observations to extend the AHP model to projective geometry formalism and generalise it to intransitive case. We give financial interpretations of such generalised model and propose its simplification. The unification of the AHP model and projective aspect of portfolio theory suggests a wide spectrum of new applications such extended model.Comment: APFA 6 - Applications of Physics in Financial Analysis 6th International Conference, 4-7 July 2007, Lisbon, Portuga

Intransitivity in Theory and in the Real World

This work considers reasons for and implications of discarding the assumption of transitivity, which (transitivity) is the fundamental postulate in the utility theory of Von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity are drawn from different fields, such as law, biology, game theory, economics and competitive evolutionary dynamic. This work is intended as a common platform that allows us to discuss intransitivity in the context of different disciplines. The basic concepts and terms that are needed for consistent treatment of intransitivity in various applications are presented and analysed in a unified manner. The analysis points out conditions that necessitate appearance of intransitivity, such as multiplicity of preference criteria and imperfect (i.e. approximate) discrimination of different cases. The present work observes that with increasing presence and strength of intransitivity, thermodynamics gradually fades away leaving space for more general kinetic considerations. Intransitivity in competitive systems is linked to complex phenomena that would be difficult or impossible to explain on the basis of transitive assumptions. Human preferences that seem irrational from the perspective of the conventional utility theory, become perfectly logical in the intransitive and relativistic framework suggested here. The example of competitive simulations for the risk/benefit dilemma demonstrates the significance of intransitivity in cyclic behaviour and abrupt changes in the system. The evolutionary intransitivity parameter, which is introduced in the Appendix, is a general measure of intransitivity, which is particularly useful in evolving competitive systems. Quantum preferences are also considered in the Appendix.Comment: 44 pages, 14 figures, 47 references, 6 appendice

A computational voting model

Social choice models usually assume that choice is among exogenously given and non decomposable alternatives. Often, on the contrary, choice is among objects that are constructed by individuals or institutions as complex bundles made of many interdependent components. In this paper we present a model of object construction in majority voting and show that, in general, by appropriate changes of such bundles, different social outcomes may be obtained, depending upon initial conditions and agenda, intransitive cycles and median voter dominance may be made appear or disappear, and that, finally, decidability may be ensured by increasing manipulability or viceversa.Social choice; object construction power; agenda power; intransitive cycles; median voter theorem.

Competitive interactions change the pattern of species co-occurrences under neutral dispersal

Non-random patterns of species segregation and aggregation within ecological communities are often interpreted as evidence for interspecific interactions. However, it is unclear whether theoretical models can predict such patterns and how environmental factors may modify the effects of species interactions on species co-occurrence. Here we extend a spatially explicit neutral model by including competitive effects on birth and death probabilities to assess whether competition alone is able to produce non-random patterns of species co-occurrence. We show that transitive and intransitive competitive hierarchies alone (in the absence of environmental heterogeneity) are indeed able to generate non-random patterns with commonly used metrics and null models. Moreover, even weak levels of intransitive competition can increase local species richness. However, there is no simple rule or consistent directional change towards aggregation or segregation caused by competitive interactions. Instead, the spatial pattern depends on both the type of species interaction and the strength of dispersal. We conclude that co-occurrence analysis alone may not able to identify the underlying processes that generate the patterns

The ghost of ecology in chaos, combining intransitive and higher order effects

Historically, musings about the structure of ecological communities has revolved around the structure of pairwise interactions, competition, predation, mutualism, etc. . . Recently a growing literature acknowledges that the baseline assumption that the pair of species is not necessarily the metaphorical molecule of community ecology, and that certain structures containing three or more species may not be usefully divisible into pairwise components. Two examples are intransitive competition (species A dominates species B dominates species C dominates species A), and nonlinear higher-order effects. While these two processes have been discussed extensively, the explicit analysis of how the two of them behave when simultaneously part of the same dynamic system has not yet appeared in the literature. A concrete situation exists on coffee farms in Puerto Rico in which three ant species, at least on some farms, form an intransitive competitive triplet, and that triplet is strongly influenced, nonlinearly, by a fly parasitoid that modifies the competitive ability of one of the species in the triplet. Using this arrangement as a template we explore the dynamical consequences with a simple ODE model. Results are complicated and include include alternative periodic and chaotic attractors. The qualitative structures of those complications, however, may be retrieved easily from a reflection on the basic natural history of the system.Comment: 29 pages, 15 figure

Testing Transitivity of Preferences on Two-Alternative Forced Choice Data

As Duncan Luce and other prominent scholars have pointed out on several occasions, testing algebraic models against empirical data raises difficult conceptual, mathematical, and statistical challenges. Empirical data often result from statistical sampling processes, whereas algebraic theories are nonprobabilistic. Many probabilistic specifications lead to statistical boundary problems and are subject to nontrivial order constrained statistical inference. The present paper discusses Luce's challenge for a particularly prominent axiom: Transitivity. The axiom of transitivity is a central component in many algebraic theories of preference and choice. We offer the currently most complete solution to the challenge in the case of transitivity of binary preference on the theory side and two-alternative forced choice on the empirical side, explicitly for up to five, and implicitly for up to seven, choice alternatives. We also discuss the relationship between our proposed solution and weak stochastic transitivity. We recommend to abandon the latter as a model of transitive individual preferences

Party competition in a heterogeneous electorate – the role of dominant-issue-voters

This paper provides a theoretical model of party competition in a heterogeneous electorate. The latter consists of numerous groups of dominant-issue-voters who base their voting decision primarily on one issue of the political agenda. Parties follow a lexicographic objective function, aiming to gain power at minimum programmatic concessions. The emerging pattern of movement in policy platforms is fundamentally different to the concept of convergence proposed by the spatial theory of voting. Rather than the centre of the scale of policy preference, its extreme ends, occupied by dominant-issue-voters, attract the policy platforms. The difference in policy platforms is not reduced. The conclusions are found to be compatible with some major empirical findings of the Manifesto Research Group. --voters,incomplete information,political parties,convergence

Modelling intransitivity in pairwise comparisons with application to baseball data

In most commonly used ranking systems, some level of underlying transitivity is assumed. If transitivity exists in a system then information about pairwise comparisons can be translated to other linked pairs. For example, if typically A beats B and B beats C, this could inform us about the expected outcome between A and C. We show that in the seminal Bradley-Terry model knowing the probabilities of A beating B and B beating C completely defines the probability of A beating C, with these probabilities determined by individual skill levels of A, B and C. Users of this model tend not to investigate the validity of this transitive assumption, nor that some skill levels may not be statistically significantly different from each other; the latter leading to false conclusions about rankings. We provide a novel extension to the Bradley-Terry model, which accounts for both of these features: the intransitive relationships between pairs of objects are dealt with through interaction terms that are specific to each pair; and by partitioning the $n$ skills into $A+1\leq n$ distinct clusters, any differences in the objects' skills become significant, given appropriate $A$. With $n$ competitors there are $n(n-1)/2$ interactions, so even in multiple round robin competitions this gives too many parameters to efficiently estimate. Therefore we separately cluster the $n(n-1)/2$ values of intransitivity into $K$ clusters, giving $(A,K)$ estimatable values respectively, typically with $A+K<n$. Using a Bayesian hierarchical model, $(A,K)$ are treated as unknown, and inference is conducted via a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. The model is shown to have an improved fit out of sample in both simulated data and when applied to American League baseball data.Comment: 26 pages, 7 figures, 2 tables in the main text. 17 pages in the supplementary materia