Symmetry Breaking for Answer Set Programming

In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry detection to a graph automorphism problem which allows to extract symmetries of a logic program from the symmetries of the constructed coloured graph. We also propose an encoding of symmetry-breaking constraints in terms of permutation cycles and use only generators in this process which implicitly represent symmetries and always with exponential compression. These ideas are formulated as preprocessing and implemented in a completely automated flow that first detects symmetries from a given answer set program, adds symmetry-breaking constraints, and can be applied to any existing answer set solver. We demonstrate computational impact on benchmarks versus direct application of the solver. Furthermore, we explore symmetry breaking for answer set programming in two domains: first, constraint answer set programming as a novel approach to represent and solve constraint satisfaction problems, and second, distributed nonmonotonic multi-context systems. In particular, we formulate a translation-based approach to constraint answer set solving which allows for the application of our symmetry detection and symmetry breaking methods. To compare their performance with a-priori symmetry breaking techniques, we also contribute a decomposition of the global value precedence constraint that enforces domain consistency on the original constraint via the unit-propagation of an answer set solver. We evaluate both options in an empirical analysis. In the context of distributed nonmonotonic multi-context system, we develop an algorithm for distributed symmetry detection and also carry over symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201

Reviewing Excess Liquidity Measures - A Comparison for Asset Markets

The conduct of US monetary policy is often accompanied by controversial debates on the adequacy of monetary conditions. These can result from different concepts of excess liquidity measures. The paper analyzes the theoretical and empirical information content of these concepts for asset markets. The analysis classifies, reviews and assesses measures of monetary conditions. For those that qualify as excess liquidity measures, the analysis continues with a comparison of the sources of imbalances and a discussion of the adequacy for asset markets. The theoretical results are cross-checked with empirical evidence. All excess liquidity measures are estimated and compared in the light of recent US asset bubbles. The analysis draws the following main conclusions. Firstly, not all measures of monetary conditions qualify as excess liquidity measure. Secondly, the increasing relevance of asset markets leads to growing distortions of excess liquidity measures. Thirdly, the choice of excess liquidity measure has influence on the assessment of monetary conditions in asset markets.monetary overhang, real money gap, nominal money gap, credit ratios, leverage ratios, price gap, natural interest rate gap, Taylor gap

Translation-based Constraint Answer Set Solving

We solve constraint satisfaction problems through translation to answer set programming (ASP). Our reformulations have the property that unit-propagation in the ASP solver achieves well defined local consistency properties like arc, bound and range consistency. Experiments demonstrate the computational value of this approach.Comment: Self-archived version for IJCAI'11 Best Paper Track submissio

Measuring Monetary Conditions in US Asset Markets - A Market Specific Approach

We analyze monetary conditions in US asset markets — corporate equity, real estate, Treasury bond and corporate & foreign bond — from a market specific perspective, proposing the concept of market leverage. Market leverage measures the average leverage of all asset holders in a particular asset market. The concept builds on an accounting based network that links balance sheet leverages of asset holders to their corresponding shares of ownership. Our empirical analysis yields the following results. Firstly, market specific monetary conditions can differ considerably among asset markets. Secondly, market specific monetary conditions are positively related to asset prices. Thirdly, US asset markets have experienced a loosening in market specific monetary conditions in the last decades. Fourthly, the loosening of market specific monetary conditions explains long-term increases in US asset prices. Fifthly, the recent convergence of market specific monetary conditions of real asset markets towards those of financial asset markets implies a rise in upside risk to future US asset price inflation.market leverage; monetary conditions; asset prices

Symmetry-breaking Answer Set Solving

In the context of Answer Set Programming, this paper investigates symmetry-breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We propose a reduction of disjunctive logic programs to a coloured digraph such that permutational symmetries can be constructed from graph automorphisms. Symmetries are then broken by introducing symmetry-breaking constraints. For this purpose, we formulate a preprocessor that integrates a graph automorphism system. Experiments demonstrate its computational impact.Comment: Proceedings of ICLP'10 Workshop on Answer Set Programming and Other Computing Paradig

Efficient calculation of probability metrics of the f-E-class

Throughout this thesis, we introduce the class of \fE-metrics, a parameterizable class of metrics for probability distributions, containing the Prokhorov and \winf{} metrics. Starting with the theoretical foundations, we show the similarities and differences between the latter two metrics and explore the two topologies the \fE-class induces. This provides a joint framework for the previously mostly independently considered metrics, highlighting their connections. Figuratively speaking, this is a way of comparing how much mass has to be transported how far to transform one distribution into the other. The \fE-metric is then attained at the balance of the distance and the $f$-weighted mass. In contrast to the Wasserstein-p metric, which averages all transported mass together with the distances, \fE-metrics are only considering a cutoff point. In Proposition 2.5.1 and Proposition 2.5.2, we provide two generally valid algorithms for the exact computation of the distance of finite support distributions of size $m \geq n$. Obtaining a worst case complexity of \Ocal \left( m n ^2 \log(m) \right) , the computation of the \fE-class is instantly on par with the well researched Wasserstein-p metric. We further introduce for the first time quasi-convex metrics, a concept linking metric and ordered spaces. This allows for sorting the supports of our probability distributions in corresponding metric spaces while keeping a strong link with the underlying metric. The theoretical foundation lies within Monge sequences, which we cover throughout this thesis. Combining these, we can significantly improve the general complexity to quasi-linearity for the Prokhorov and \winf{} metric. We proof correctness and worst case complexities for all algorithms, setting them on par with the Wasserstein-p metric. In detail, we obtain a general complexity of \Ocal \left( m n ^2 \log(m) \right) and refined for the quasi-convex case to a strongly quasi-linear \Ocal \left(m \log(m)\right) for the \winf{} metric in Corollary 4.2.18 and a weakly quasi-linear \Ocal \left(m \max\{\log(m), \frac{1}{acc_X}\}\right) depending on the support of the distributions for the Prokhorov metric in Theorem 4.1.12. We compare the \fE-class with existing metrics to embed it in the current tool set and show their relationships. We conclude with a numerical analysis of our algorithms to check correctness and complexity based on implementations in MATLAB. In total, we have newly developed a broad class of probability metrics, containing the well known Prokhorov and \winf{} metric, analyzed their theoretical properties and provided a comprehensive set of exact and efficient algorithms for their computation for finitely supported measures.In dieser Arbeit führen wir die Klasse der \fE-Metriken ein, eine parametrisierbare Klasse von Metriken für Wahrscheinlichkeitsverteilungen, die die Prokhorov und \winf{}-Metriken enthält. Beginnend mit den theoretischen Grundlagen zeigen wir die Gemeinsamkeiten und Unterschiede zwischen letzteren beiden Metriken und untersuchen die zwei induzierten Topologien, die die \fE-Klasse enthält. Damit wird ein gemeinsamer Rahmen für die bisher meist unabhängig voneinander betrachteten Metriken geschaffen und ihre Zusammenhänge verdeutlicht. Bildlich gesprochen wird hierbei verglichen, wie viel Masse wie weit transportiert werden muss, um eine Verteilung in die andere zu transformieren. Die \fE-Metrik ergibt sich dann aus dem Gleichgewicht zwischen der Entfernung und der mit f-gewichteten Masse. Im Gegensatz zur Wasserstein-$p$ Metrik, die die gesamte transportierte Masse zusammen mit den Entfernungen mittelt, wird bei der \fE-Metrik nur ein Trennpunkt betrachtet. In Proposition 2.5.1 und Proposition 2.5.2 stellen wir zwei allgemeingültige Algorithmen für die exakte Berechnung des Abstands von Wahrscheinlichkeitsverteilungen mit endlichen Trägern der Größen $m \geq n$ vor. Mit einer Worst-Case-Komplexität von \Ocal \left( m n ^2 \log(m) \right) ist die Berechnung der \fE-Klasse somit aus dem Stand gleichwertig mit der gut erforschten Wasserstein-p Metrik. Weiterhin führen wir als Erste quasikonvexe Metriken ein, ein Konzept, das metrische und geordnete Räume miteinander verbindet. Dies erlaubt es uns, die Träger unserer Wahrscheinlichkeitsverteilungen in entsprechenden metrischen Räumen zu ordnen und dabei eine starke Verbindung mit der zugrundeliegenden Metrik zu bewahren. Die theoretische Grundlage hierfür bieten Monge-Folgen, die wir ebenfalls in dieser Arbeit behandeln. Indem wir diese kombinieren, können wir die allgemeine Komplexität deutlich verbessern und erhalten Quasi-Linearität für die Prokhorov und \winf{} Metrik. Wir beweisen Korrektheit und Worst-Case-Komplexität für alle Algorithmen und erhalten die selben Komplexitäten wie für die Wasserstein-p Metrik. Im Detail erhalten wir eine allgemeine Komplexität von \Ocal \left( m n ^2 \log(m) \right) und verbessern diese für den quasi-konvexen Fall zu einem stark quasi-linearen \Ocal \left(m \log(m)\right) für die \winf{}-Metrik in Corollary 4.2.18 und einem schwach quasi-linearen \Ocal \left(m \max\{\log(m), \frac{1}{acc_X}\}\right) in Abhängigkeit vom Träger der Verteilungen für die Prokhorov Metrik in Theorem 4.1.12. Wir vergleichen die \fE-Klasse mit bestehenden Metriken und zeigen ihre Relation zu diesen. Wir schließen mit einer numerischen Analyse unserer Algorithmen zur Überprüfung der Korrektheit und Komplexität anhand von Implementierungen in MATLAB ab. Insgesamt haben wir in dieser Arbeit eine breite Klasse von Wahrscheinlichkeitsmetriken neu entwickelt, die die bekannten Prokhorov und \winf{} Metriken enthält, ihre theoretischen Eigenschaften analysiert und einen umfassenden Satz von exakten und effizienten Algorithmen für deren Berechnung für Wahrscheinlichkeitsverteilungen mit endlichem Träger vorgestellt

The Fed's TRAP: A Taylor-type Rule with Asset Prices

The paper examines if US monetary policy implicitly responds to asset prices. Using real-time data and a GMM framework we estimate a Taylor-type rule with an asset cycle variable, which refers to real estate prices. To analyze the Fed's responses we describe real estate price movements by means of an asset cycle dating procedure. This procedure reveals quasi real-time bull and bear markets. Our analysis yields two main findings. Firstly, the Fed does implicitly respond to real estate prices. Secondly, these responses are pro-cyclical and their intensity changes over time.Fed; Monetary Policy; Taylor Rule; Asset Price Cycles; Real Estate