Book of Abstracts of the Sixth SIAM Workshop on Combinatorial Scientific Computing

Book of Abstracts of CSC14 edited by Bora UçarInternational audienceThe Sixth SIAM Workshop on Combinatorial Scientific Computing, CSC14, was organized at the Ecole Normale Supérieure de Lyon, France on 21st to 23rd July, 2014. This two and a half day event marked the sixth in a series that started ten years ago in San Francisco, USA. The CSC14 Workshop's focus was on combinatorial mathematics and algorithms in high performance computing, broadly interpreted. The workshop featured three invited talks, 27 contributed talks and eight poster presentations. All three invited talks were focused on two interesting fields of research specifically: randomized algorithms for numerical linear algebra and network analysis. The contributed talks and the posters targeted modeling, analysis, bisection, clustering, and partitioning of graphs, applied in the context of networks, sparse matrix factorizations, iterative solvers, fast multi-pole methods, automatic differentiation, high-performance computing, and linear programming. The workshop was held at the premises of the LIP laboratory of ENS Lyon and was generously supported by the LABEX MILYON (ANR-10-LABX-0070, Université de Lyon, within the program ''Investissements d'Avenir'' ANR-11-IDEX-0007 operated by the French National Research Agency), and by SIAM

Probabilistic modelling of oil rig drilling operations for business decision support: a real world application of Bayesian networks and computational intelligence.

This work investigates the use of evolved Bayesian networks learning algorithms based on computational intelligence meta-heuristic algorithms. These algorithms are applied to a new domain provided by the exclusive data, available to this project from an industry partnership with ODS-Petrodata, a business intelligence company in Aberdeen, Scotland. This research proposes statistical models that serve as a foundation for building a novel operational tool for forecasting the performance of rig drilling operations. A prototype for a tool able to forecast the future performance of a drilling operation is created using the obtained data, the statistical model and the experts' domain knowledge. This work makes the following contributions: applying K2GA and Bayesian networks to a real-world industry problem; developing a well-performing and adaptive solution to forecast oil drilling rig performance; using the knowledge of industry experts to guide the creation of competitive models; creating models able to forecast oil drilling rig performance consistently with nearly 80% forecast accuracy, using either logistic regression or Bayesian network learning using genetic algorithms; introducing the node juxtaposition analysis graph, which allows the visualisation of the frequency of nodes links appearing in a set of orderings, thereby providing new insights when analysing node ordering landscapes; exploring the correlation factors between model score and model predictive accuracy, and showing that the model score does not correlate with the predictive accuracy of the model; exploring a method for feature selection using multiple algorithms and drastically reducing the modelling time by multiple factors; proposing new fixed structure Bayesian network learning algorithms for node ordering search-space exploration. Finally, this work proposes real-world applications for the models based on current industry needs, such as recommender systems, an oil drilling rig selection tool, a user-ready rig performance forecasting software and rig scheduling tools

Real-time algorithm configuration

This dissertation presents a number of contributions to the field of algorithm configur- ation. In particular, we present an extension to the algorithm configuration problem, real-time algorithm configuration, where configuration occurs online on a stream of instances, without the need for prior training, and problem solutions are returned in the shortest time possible. We propose a framework for solving the real-time algorithm configuration problem, ReACT. With ReACT we demonstrate that by using the parallel computing architectures, commonplace in many systems today, and a robust aggregate ranking system, configuration can occur without any impact on performance from the perspective of the user. This is achieved by means of a racing procedure. We show two concrete instantiations of the framework, and show them to be on a par with or even exceed the state-of-the-art in offline algorithm configuration using empirical evaluations on a range of combinatorial problems from the literature. We discuss, assess, and provide justification for each of the components used in our framework instantiations. Specifically, we show that the TrueSkill ranking system commonly used to rank players’ skill in multiplayer games can be used to accurately es- timate the quality of an algorithm’s configuration using only censored results from races between algorithm configurations. We confirm that the order that problem instances arrive in influences the configuration performance and that the optimal selection of configurations to participate in races is dependent on the distribution of the incoming in- stance stream. We outline how to maintain a pool of quality configurations by removing underperforming configurations, and techniques to generate replacement configurations with minimal computational overhead. Finally, we show that the configuration space can be reduced using feature selection techniques from the machine learning literature, and that doing so can provide a boost in configuration performance

Offline Learning for Sequence-based Selection Hyper-heuristics

This thesis is concerned with finding solutions to discrete NP-hard problems. Such problems occur in a wide range of real-world applications, such as bin packing, industrial flow shop problems, determining Boolean satisfiability, the traveling salesman and vehicle routing problems, course timetabling, personnel scheduling, and the optimisation of water distribution networks. They are typically represented as optimisation problems where the goal is to find a ``best'' solution from a given space of feasible solutions. As no known polynomial-time algorithmic solution exists for NP-hard problems, they are usually solved by applying heuristic methods. Selection hyper-heuristics are algorithms that organise and combine a number of individual low level heuristics into a higher level framework with the objective of improving optimisation performance. Many selection hyper-heuristics employ learning algorithms in order to enhance optimisation performance by improving the selection of single heuristics, and this learning may be classified as either online or offline. This thesis presents a novel statistical framework for the offline learning of subsequences of low level heuristics in order to improve the optimisation performance of sequenced-based selection hyper-heuristics. A selection hyper-heuristic is used to optimise the HyFlex set of discrete benchmark problems. The resulting sequences of low level heuristic selections and objective function values are used to generate an offline learning database of heuristic selections. The sequences in the database are broken down into subsequences and the mathematical concept of a logarithmic return is used to discriminate between ``effective'' subsequences, that tend to lead to improvements in optimisation performance, and ``disruptive'' subsequences that tend to lead to worsening performance. Effective subsequences are used to improve hyper-heuristics performance directly, by embedding them in a simple hyper-heuristic design, and indirectly as the inputs to an appropriate hyper-heuristic learning algorithm. Furthermore, by comparing effective subsequences across different problem domains it is possible to investigate the potential for cross-domain learning. The results presented here demonstrates that the use of well chosen subsequences of heuristics can lead to small, but statistically significant, improvements in optimisation performance

Reliable statistical modeling of weakly structured information

The statistical analysis of "real-world" data is often confronted with the fact that most standard statistical methods were developed under some kind of idealization of the data that is often not adequate in practical situations. This concerns among others i) the potentially deficient quality of the data that can arise for example due to measurement error, non-response in surveys or data processing errors and ii) the scale quality of the data, that is idealized as "the data have some clear scale of measurement that can be uniquely located within the scale hierarchy of Stevens (or that of Narens and Luce or Orth)". Modern statistical methods like, e.g., correction techniques for measurement error or robust methods cope with issue i). In the context of missing or coarsened data, imputation techniques and methods that explicitly model the missing/coarsening process are nowadays wellestablished tools of refined data analysis. Concerning ii) the typical statistical viewpoint is a more pragmatical one, in case of doubt one simply presumes the strongest scale of measurement that is clearly "justified". In more complex situations, like for example in the context of the analysis of ranking data, statisticians often simply do not worry about purely measurement theoretic reservations too much, but instead embed the data structure in an appropriate, easy to handle space, like e.g. a metric space and then use all statistical tools available for this space. Against this background, the present cumulative dissertation tries to contribute from different perspectives to the appropriate handling of data that challenge the above-mentioned idealizations. A focus here is on the one hand on analysis of interval-valued and set-valued data within the methodology of partial identification, and on the other hand on the analysis of data with values in a partially ordered set (poset-valued data). Further tools of statistical modeling treated in the dissertation are necessity measures in the context of possibility theory and concepts of stochastic dominance for poset-valued data. The present dissertation consists of 8 contributions, which will be detailedly discussed in the following sections: Contribution 1 analyzes different identification regions for partially identified linear models under interval-valued responses and develops a further kind of identification region (as well as a corresponding estimator). Estimates for the identifcation regions are compared to each other and also to classical statistical approaches for a data set on wine quality. Contribution 2 deals with logistic regression under coarsened responses, analyzes point-identifying assumptions and develops likelihood-based estimators for the identified set. The methods are illustrated with data of a wave of the panel study "Labor Market and Social Security" (PASS). Contribution 3 analyzes the combinatorial structure of the extreme points and the edges of a polytope (called credal set or core in the literature) that plays a crucial role in imprecise probability theory. Furthermore, an efficient algorithm for enumerating all extreme points is given and compared to existing standard methods. Contribution 4 develops a quantile concept for data or random variables with values in a complete lattice, which is applied in Contribution 5 to the case of ranking data in the context of a data set on the wisdom of the crowd phenomena. In Contribution 6 a framework for evaluating the quality of different aggregation functions of Social Choice Theory is developed, which enables analysis of quality in dependence of group specific homogeneity. In a simulation study, selected aggregation functions, including an aggregation function based on the concepts of Contribution 4 and Contribution 5, are analyzed. Contribution 7 supplies a linear program that allows for detecting stochastic dominance for poset-valued random variables, gives proposals for inference and regularization, and generalizes the approach to the general task of optimizing a linear function on a closure system. The generality of the developed methods is illustrated with data examples in the context of multivariate inequality analysis, item impact and differential item functioning in the context of item response theory, analyzing distributional differences in spatial statistics and guided regularization in the context of cognitive diagnosis models. Contribution 8 uses concepts of stochastic dominance to establish a descriptive approach for a relational analysis of person ability and item difficulty in the context of multidimensional item response theory. All developed methods have been implemented in the language R ([R Development Core Team, 2014]) and are available from the author upon request. The application examples corroborate the usefulness of weak types of statistical modeling examined in this thesis, which, beyond their flexibility to deal with many kinds of data deficiency, can still lead to informative substance matter conclusions that are then more reliable due to the weak modeling.Die statistische Analyse real erhobener Daten sieht sich oft mit der Tatsache konfrontiert, dass übliche statistische Standardmethoden unter einer starken Idealisierung der Datensituation entwickelt wurden, die in der Praxis jedoch oft nicht angemessen ist. Dies betrifft i) die möglicherweise defizitäre Qualität der Daten, die beispielsweise durch Vorhandensein von Messfehlern, durch systematischen Antwortausfall im Kontext sozialwissenschaftlicher Erhebungen oder auch durch Fehler während der Datenverarbeitung bedingt ist und ii) die Skalenqualität der Daten an sich: Viele Datensituationen lassen sich nicht in die einfachen Skalenhierarchien von Stevens (oder die von Narens und Luce oder Orth) einordnen. Modernere statistische Verfahren wie beispielsweise Messfehlerkorrekturverfahren oder robuste Methoden versuchen, der Idealisierung der Datenqualität im Nachhinein Rechnung zu tragen. Im Zusammenhang mit fehlenden bzw. intervallzensierten Daten haben sich Imputationsverfahren zur Vervollständigung fehlender Werte bzw. Verfahren, die den Entstehungprozess der vergröberten Daten explizit modellieren, durchgesetzt. In Bezug auf die Skalenqualität geht die Statistik meist eher pragmatisch vor, im Zweifelsfall wird das niedrigste Skalenniveau gewählt, das klar gerechtfertigt ist. In komplexeren multivariaten Situationen, wie beispielsweise der Analyse von Ranking-Daten, die kaum noch in das Stevensche "Korsett" gezwungen werden können, bedient man sich oft der einfachen Idee der Einbettung der Daten in einen geeigneten metrischen Raum, um dann anschließend alle Werkzeuge metrischer Modellierung nutzen zu können. Vor diesem Hintergrund hat die hier vorgelegte kumulative Dissertation deshalb zum Ziel, aus verschiedenen Blickwinkeln Beiträge zum adäquaten Umgang mit Daten, die jene Idealisierungen herausfordern, zu leisten. Dabei steht hier vor allem die Analyse intervallwertiger bzw. mengenwertiger Daten mittels partieller Identifikation auf der Seite defzitärer Datenqualität im Vordergrund, während bezüglich Skalenqualität der Fall von verbandswertigen Daten behandelt wird. Als weitere Werkzeuge statistischer Modellierung werden hier insbesondere Necessity-Maße im Rahmen der Imprecise Probabilities und Konzepte stochastischer Dominanz für Zufallsvariablen mit Werten in einer partiell geordneten Menge betrachtet. Die vorliegende Dissertation umfasst 8 Beiträge, die in den folgenden Kapiteln näher diskutiert werden: Beitrag 1 analysiert verschiedene Identifikationsregionen für partiell identifizierte lineare Modelle unter intervallwertig beobachteter Responsevariable und schlägt eine neue Identifikationsregion (inklusive Schätzer) vor. Für einen Datensatz, der die Qualität von verschiedenen Rotweinen, gegeben durch ExpertInnenurteile, in Abhängigkeit von verschiedenen physikochemischen Eigenschaften beschreibt, werden Schätzungen für die Identifikationsregionen analysiert. Die Ergebnisse werden ebenfalls mit den Ergebissen klassischer Methoden für Intervalldaten verglichen. Beitrag 2 behandelt logistische Regression unter vergröberter Responsevariable, analysiert punktidentifizierende Annahmen und entwickelt likelihoodbasierte Schätzer für die entsprechenden Identifikationsregionen. Die Methode wird mit Daten einer Welle der Panelstudie "Arbeitsmarkt und Soziale Sicherung" (PASS) illustriert. Beitrag 3 analysiert die kombinatorische Struktur der Extrempunkte und der Kanten eines Polytops (sogenannte Struktur bzw. Kern einer Intervallwahrscheinlichkeit bzw. einer nicht-additiven Mengenfunktion), das von wesentlicher Bedeutung in vielen Gebieten der Imprecise Probability Theory ist. Ein effizienter Algorithmus zur Enumeration aller Extrempunkte wird ebenfalls gegeben und mit existierenden Standardenumerationsmethoden verglichen. In Beitrag 4 wird ein Quantilkonzept für verbandswertige Daten bzw. Zufallsvariablen vorgestellt. Dieses Quantilkonzept wird in Beitrag 5 auf Ranking-Daten im Zusammenhang mit einem Datensatz, der das "Weisheit der Vielen"-Phänomen untersucht, angewendet. Beitrag 6 entwickelt eine Methode zur probabilistischen Analyse der "Qualität" verschiedener Aggregationsfunktionen der Social Choice Theory. Die Analyse wird hier in Abhäangigkeit der Homogenität der betrachteten Gruppen durchgeführt. In einer simulationsbasierten Studie werden exemplarisch verschiedene klassische Aggregationsfunktionen, sowie eine neue Aggregationsfunktion basierend auf den Beiträgen 4 und 5, verglichen. Beitrag 7 stellt einen Ansatz vor, um das Vorliegen stochastischer Dominanz zwischen zwei Zufallsvariablen zu überprüfen. Der Anstaz nutzt Techniken linearer Programmierung. Weiterhin werden Vorschläge für statistische Inferenz und Regularisierung gemacht. Die Methode wird anschließend auch auf den allgemeineren Fall des Optimierens einer linearen Funktion auf einem Hüllensystem ausgeweitet. Die flexible Anwendbarkeit wird durch verschiedene Anwendungsbeispiele illustriert. Beitrag 8 nutzt Ideen stochastischer Dominanz, um Datensätze der multidimensionalen Item Response Theory relational zu analysieren, indem Paare von sich gegenseitig empirisch stützenden Fähigkeitsrelationen der Personen und Schwierigkeitsrelationen der Aufgaben entwickelt werden. Alle entwickelten Methoden wurden in R ([R Development Core Team, 2014]) implementiert. Die Anwendungsbeispiele zeigen die Flexibilität der hier betrachteten Methoden relationaler bzw. "schwacher" Modellierung insbesondere zur Behandlung defizitärer Daten und unterstreichen die Tatsache, dass auch mit Methoden schwacher Modellierung oft immer noch nichttriviale substanzwissenschaftliche Rückschlüsse möglich sind, die aufgrund der inhaltlich vorsichtigeren Modellierung dann auch sehr viel stärker belastbar sind

Learning Bayesian network equivalence classes using ant colony optimisation

Bayesian networks have become an indispensable tool in the modelling of uncertain knowledge. Conceptually, they consist of two parts: a directed acyclic graph called the structure, and conditional probability distributions attached to each node known as the parameters. As a result of their expressiveness, understandability and rigorous mathematical basis, Bayesian networks have become one of the first methods investigated, when faced with an uncertain problem domain. However, a recurring problem persists in specifying a Bayesian network. Both the structure and parameters can be difficult for experts to conceive, especially if their knowledge is tacit.To counteract these problems, research has been ongoing, on learning both the structure and parameters of Bayesian networks from data. Whilst there are simple methods for learning the parameters, learning the structure has proved harder. Part ofthis stems from the NP-hardness of the problem and the super-exponential space of possible structures. To help solve this task, this thesis seeks to employ a relatively new technique, that has had much success in tackling NP-hard problems. This technique is called ant colony optimisation. Ant colony optimisation is a metaheuristic based on the behaviour of ants acting together in a colony. It uses the stochastic activity of artificial ants to find good solutions to combinatorial optimisation problems. In the current work, this method is applied to the problem of searching through the space of equivalence classes of Bayesian networks, in order to find a good match against a set of data. The system uses operators that evaluate potential modifications to a current state. Each of the modifications is scored and the results used to inform the search. In order to facilitate these steps, other techniques are also devised, to speed up the learning process. The techniques includeThe techniques are tested by sampling data from gold standard networks and learning structures from this sampled data. These structures are analysed using various goodnessof-fit measures to see how well the algorithms perform. The measures include structural similarity metrics and Bayesian scoring metrics. The results are compared in depth against systems that also use ant colony optimisation and other methods, including evolutionary programming and greedy heuristics. Also, comparisons are made to well known state-of-the-art algorithms and a study performed on a real-life data set. The results show favourable performance compared to the other methods and on modelling the real-life data

Learning Bayesian network equivalence classes with ant colony optimization

Bayesian networks are a useful tool in the representation of uncertain knowledge. This paper proposes a new algorithm called ACO-E, to learn the structure of a Bayesian network. It does this by conducting a search through the space of equivalence classes of Bayesian networks using Ant Colony Optimization (ACO). To this end, two novel extensions of traditional ACO techniques are proposed and implemented. Firstly, multiple types of moves are allowed. Secondly, moves can be given in terms of indices that are not based on construction graph nodes. The results of testing show that ACO-E performs better than a greedy search and other state-of-the-art and metaheuristic algorithms whilst searching in the space of equivalence classe

Neural function approximation on graphs: shape modelling, graph discrimination & compression

Graphs serve as a versatile mathematical abstraction of real-world phenomena in numerous scientific disciplines. This thesis is part of the Geometric Deep Learning subject area, a family of learning paradigms, that capitalise on the increasing volume of non-Euclidean data so as to solve real-world tasks in a data-driven manner. In particular, we focus on the topic of graph function approximation using neural networks, which lies at the heart of many relevant methods. In the first part of the thesis, we contribute to the understanding and design of Graph Neural Networks (GNNs). Initially, we investigate the problem of learning on signals supported on a fixed graph. We show that treating graph signals as general graph spaces is restrictive and conventional GNNs have limited expressivity. Instead, we expose a more enlightening perspective by drawing parallels between graph signals and signals on Euclidean grids, such as images and audio. Accordingly, we propose a permutation-sensitive GNN based on an operator analogous to shifts in grids and instantiate it on 3D meshes for shape modelling (Spiral Convolutions). Following, we focus on learning on general graph spaces and in particular on functions that are invariant to graph isomorphism. We identify a fundamental trade-off between invariance, expressivity and computational complexity, which we address with a symmetry-breaking mechanism based on substructure encodings (Graph Substructure Networks). Substructures are shown to be a powerful tool that provably improves expressivity while controlling computational complexity, and a useful inductive bias in network science and chemistry. In the second part of the thesis, we discuss the problem of graph compression, where we analyse the information-theoretic principles and the connections with graph generative models. We show that another inevitable trade-off surfaces, now between computational complexity and compression quality, due to graph isomorphism. We propose a substructure-based dictionary coder - Partition and Code (PnC) - with theoretical guarantees that can be adapted to different graph distributions by estimating its parameters from observations. Additionally, contrary to the majority of neural compressors, PnC is parameter and sample efficient and is therefore of wide practical relevance. Finally, within this framework, substructures are further illustrated as a decisive archetype for learning problems on graph spaces.Open Acces

Combining Monte-Carlo and hyper-heuristic methods for the multi-mode resource-constrained multi-project scheduling problem

Multi-mode resource and precedence-constrained project scheduling is a well-known challenging real-world optimisation problem. An important variant of the problem requires scheduling of activities for multiple projects considering availability of local and global resources while respecting a range of constraints. A critical aspect of the benchmarks addressed in this paper is that the primary objective is to minimise the sum of the project completion times, with the usual makespan minimisation as a secondary objective. We observe that this leads to an expected different overall structure of good solutions and discuss the effects this has on the algorithm design. This paper presents a carefully-designed hybrid of Monte-Carlo tree search, novel neighbourhood moves, memetic algorithms, and hyper-heuristic methods. The implementation is also engineered to increase the speed with which iterations are performed, and to exploit the computing power of multicore machines. Empirical evaluation shows that the resulting information-sharing multi-component algorithm significantly outperforms other solvers on a set of “hidden” instances, i.e. instances not available at the algorithm design phase