2,285 research outputs found

    Learning and reasoning with graph data

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    Reasoning about graphs, and learning from graph data is a field of artificial intelligence that has recently received much attention in the machine learning areas of graph representation learning and graph neural networks. Graphs are also the underlying structures of interest in a wide range of more traditional fields ranging from logic-oriented knowledge representation and reasoning to graph kernels and statistical relational learning. In this review we outline a broad map and inventory of the field of learning and reasoning with graphs that spans the spectrum from reasoning in the form of logical deduction to learning node embeddings. To obtain a unified perspective on such a diverse landscape we introduce a simple and general semantic concept of a model that covers logic knowledge bases, graph neural networks, kernel support vector machines, and many other types of frameworks. Still at a high semantic level, we survey common strategies for model specification using probabilistic factorization and standard feature construction techniques. Based on this semantic foundation we introduce a taxonomy of reasoning tasks that casts problems ranging from transductive link prediction to asymptotic analysis of random graph models as queries of different complexities for a given model. Similarly, we express learning in different frameworks and settings in terms of a common statistical maximum likelihood principle. Overall, this review aims to provide a coherent conceptual framework that provides a basis for further theoretical analyses of respective strengths and limitations of different approaches to handling graph data, and that facilitates combination and integration of different modeling paradigms

    High-order renormalization of scalar quantum fields

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    Thema dieser Dissertation ist die Renormierung von perturbativer skalarer Quantenfeldtheorie bei großer Schleifenzahl. Der Hauptteil der Arbeit ist dem Einfluss von Renormierungsbedingungen auf renormierte Greenfunktionen gewidmet. Zunächst studieren wir Dyson-Schwinger-Gleichungen und die Renormierungsgruppe, inklusive der Gegenterme in dimensionaler Regularisierung. Anhand zahlreicher Beispiele illustrieren wir die verschiedenen Größen. Alsdann diskutieren wir, welche Freiheitsgrade ein Renormierungsschema hat und wie diese mit den Gegentermen und den renormierten Greenfunktionen zusammenhängen. Für ungekoppelte Dyson-Schwinger-Gleichungen stellen wir fest, dass alle Renormierungsschemata bis auf eine Verschiebung des Renormierungspunktes äquivalent sind. Die Verschiebung zwischen kinematischer Renormierung und Minimaler Subtraktion ist eine Funktion der Kopplung und des Regularisierungsparameters. Wir leiten eine neuartige Formel für den Fall einer linearen Dyson-Schwinger Gleichung vom Propagatortyp her, um die Verschiebung direkt aus der Mellintransformation des Integrationskerns zu berechnen. Schließlich berechnen wir obige Verschiebung störungstheoretisch für drei beispielhafte nichtlineare Dyson-Schwinger-Gleichungen und untersuchen das asymptotische Verhalten der Reihenkoeffizienten. Ein zweites Thema der vorliegenden Arbeit sind Diffeomorphismen der Feldvariable in einer Quantenfeldtheorie. Wir präsentieren eine Störungstheorie des Diffeomorphismusfeldes im Impulsraum und verifizieren, dass der Diffeomorphismus keinen Einfluss auf messbare Größen hat. Weiterhin untersuchen wir die Divergenzen des Diffeomorphismusfeldes und stellen fest, dass die Divergenzen Wardidentitäten erfüllen, die die Abwesenheit dieser Terme von der S-Matrix ausdrücken. Trotz der Wardidentitäten bleiben unendlich viele Divergenzen unbestimmt. Den Abschluss bildet ein Kommentar über die numerische Quadratur von Periodenintegralen.This thesis concerns the renormalization of perturbative quantum field theory. More precisely, we examine scalar quantum fields at high loop order. The bulk of the thesis is devoted to the influence of renormalization conditions on the renormalized Green functions. Firstly, we perform a detailed review of Dyson-Schwinger equations and the renormalization group, including the counterterms in dimensional regularization. Using numerous examples, we illustrate how the various quantities are computable in a concrete case and which relations they satisfy. Secondly, we discuss which degrees of freedom are present in a renormalization scheme, and how they are related to counterterms and renormalized Green functions. We establish that, in the case of an un-coupled Dyson-Schwinger equation, all renormalization schemes are equivalent up to a shift in the renormalization point. The shift between kinematic renormalization and Minimal Subtraction is a function of the coupling and the regularization parameter. We derive a novel formula for the case of a linear propagator-type Dyson-Schwinger equation to compute the shift directly from the Mellin transform of the kernel. Thirdly, we compute the shift perturbatively for three examples of non-linear Dyson-Schwinger equations and examine the asymptotic growth of series coefficients. A second, smaller topic of the present thesis are diffeomorphisms of the field variable in a quantum field theory. We present the perturbation theory of the diffeomorphism field in momentum space and find that the diffeomorphism has no influence on measurable quantities. Moreover, we study the divergences in the diffeomorphism field and establish that they satisfy Ward identities, which ensure their absence from the S-matrix. Nevertheless, the Ward identities leave infinitely many divergences unspecified and the diffeomorphism theory is perturbatively unrenormalizable. Finally, we remark on a third topic, the numerical quadrature of Feynman periods

    The Sample Complexity of Approximate Rejection Sampling with Applications to Smoothed Online Learning

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    Suppose we are given access to nn independent samples from distribution μ\mu and we wish to output one of them with the goal of making the output distributed as close as possible to a target distribution ν\nu. In this work we show that the optimal total variation distance as a function of nn is given by Θ~(Df′(n))\tilde\Theta(\frac{D}{f'(n)}) over the class of all pairs ν,μ\nu,\mu with a bounded ff-divergence Df(ν∥μ)≤DD_f(\nu\|\mu)\leq D. Previously, this question was studied only for the case when the Radon-Nikodym derivative of ν\nu with respect to μ\mu is uniformly bounded. We then consider an application in the seemingly very different field of smoothed online learning, where we show that recent results on the minimax regret and the regret of oracle-efficient algorithms still hold even under relaxed constraints on the adversary (to have bounded ff-divergence, as opposed to bounded Radon-Nikodym derivative). Finally, we also study efficacy of importance sampling for mean estimates uniform over a function class and compare importance sampling with rejection sampling

    A distributional investigation of German verbs

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    Diese Dissertation bietet eine empirische Untersuchung deutscher Verben auf der Grundlage statistischer Beschreibungen, die aus einem großen deutschen Textkorpus gewonnen wurden. In einem kurzen Überblick über linguistische Theorien zur lexikalischen Semantik von Verben skizziere ich die Idee, dass die Verbbedeutung wesentlich von seiner Argumentstruktur (der Anzahl und Art der Argumente, die zusammen mit dem Verb auftreten) und seiner Aspektstruktur (Eigenschaften, die den zeitlichen Ablauf des vom Verb denotierten Ereignisses bestimmen) abhängt. Anschließend erstelle ich statistische Beschreibungen von Verben, die auf diesen beiden unterschiedlichen Bedeutungsfacetten basieren. Insbesondere untersuche ich verbale Subkategorisierung, Selektionspräferenzen und Aspekt. Alle diese Modellierungsstrategien werden anhand einer gemeinsamen Aufgabe, der Verbklassifikation, bewertet. Ich zeige, dass im Rahmen von maschinellem Lernen erworbene Merkmale, die verbale lexikalische Aspekte erfassen, für eine Anwendung von Vorteil sind, die Argumentstrukturen betrifft, nämlich semantische Rollenkennzeichnung. Darüber hinaus zeige ich, dass Merkmale, die die verbale Argumentstruktur erfassen, bei der Aufgabe, ein Verb nach seiner Aspektklasse zu klassifizieren, gut funktionieren. Diese Ergebnisse bestätigen, dass diese beiden Facetten der Verbbedeutung auf grundsätzliche Weise zusammenhängen.This dissertation provides an empirical investigation of German verbs conducted on the basis of statistical descriptions acquired from a large corpus of German text. In a brief overview of the linguistic theory pertaining to the lexical semantics of verbs, I outline the idea that verb meaning is composed of argument structure (the number and types of arguments that co-occur with a verb) and aspectual structure (properties describing the temporal progression of an event referenced by the verb). I then produce statistical descriptions of verbs according to these two distinct facets of meaning: In particular, I examine verbal subcategorisation, selectional preferences, and aspectual type. All three of these modelling strategies are evaluated on a common task, automatic verb classification. I demonstrate that automatically acquired features capturing verbal lexical aspect are beneficial for an application that concerns argument structure, namely semantic role labelling. Furthermore, I demonstrate that features capturing verbal argument structure perform well on the task of classifying a verb for its aspectual type. These findings suggest that these two facets of verb meaning are related in an underlying way

    KI-Realitäten: Modelle, Praktiken und Topologien maschinellen Lernens

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    Maschinelles Lernen stellt zunehmend einen wichtigen Faktor soziotechnischen Wandels dar. Zugleich ist es selbst Produkt der Realitäten, an deren Reproduktion es in Form praktischer Anwendungen wie auch als Spekulationsobjekt beteiligt ist. Die Beiträge des Bandes verhandeln gegenwärtige Manifestationen maschinellen Lernens als Phänomene, die für epistemische Verunsicherungen sorgen und die Bedingungen von Sozialität rekonfigurieren. Sie begegnen dieser Herausforderung, indem sie konkrete Verfahren in ihrer gesellschaftlichen Einbettung analysieren sowie bestehende theoretische Charakterisierungen sogenannter Künstlicher Intelligenz kritisch reflektieren

    Màster universitari en estadística i investigació operativa

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    Computational Stylistics in Poetry, Prose, and Drama

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    The contributions in this edited volume approach poetry, narrative, and drama from the perspective of Computational Stylistics. They exemplify methods of computational textual analysis and explore the possibility of computational generation of literary texts. The volume presents a range of computational and Natural Language Processing applications to literary studies, such as motif detection, network analysis, machine learning, and deep learning

    Selected Topics in Gravity, Field Theory and Quantum Mechanics

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    Quantum field theory has achieved some extraordinary successes over the past sixty years; however, it retains a set of challenging problems. It is not yet able to describe gravity in a mathematically consistent manner. CP violation remains unexplained. Grand unified theories have been eliminated by experiment, and a viable unification model has yet to replace them. Even the highly successful quantum chromodynamics, despite significant computational achievements, struggles to provide theoretical insight into the low-energy regime of quark physics, where the nature and structure of hadrons are determined. The only proposal for resolving the fine-tuning problem, low-energy supersymmetry, has been eliminated by results from the LHC. Since mathematics is the true and proper language for quantitative physical models, we expect new mathematical constructions to provide insight into physical phenomena and fresh approaches for building physical theories

    University of Windsor Undergraduate Calendar 2023 Spring

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    https://scholar.uwindsor.ca/universitywindsorundergraduatecalendars/1023/thumbnail.jp
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