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Prof. Dr.

# Wrobel, Stefan

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Publication

#### Decision Snippet Features

2021-05-05
,
Welke, Pascal
,
Alkhoury, Fouad
,
Bauckhage, Christian
,
Wrobel, Stefan

Decision trees excel at interpretability of their prediction results. To achieve required prediction accuracies, however, often large ensembles of decision trees random forests are considered, reducing interpretability due to large size. Additionally, their size slows down inference on modern hardware and restricts their applicability in low-memory embedded devices. We introduce Decision Snippet Features, which are obtained from small subtrees that appear frequently in trained random forests. We subsequently show that linear models on top of these features achieve comparable and sometimes even better predictive performance than the original random forest, while reducing the model size by up to two orders of magnitude.

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Publication

#### Visual Analytics for Data Scientists

2020
,
Andrienko, Natalia
,
Andrienko, Gennady
,
Fuchs, Georg
,
Slingsby, Aidan
,
Turkay, Cagatay
,
Wrobel, Stefan

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Publication

#### HOPS: Probabilistic Subtree Mining for Small and Large Graphs

2020
,
Welke, Pascal
,
Seiffahrt, Florian
,
Kamp, Michael
,
Wrobel, Stefan

Frequent subgraph mining, i.e., the identification of relevant patterns in graph databases, is a well-known data mining problem with high practical relevance, since next to summarizing the data, the resulting patterns can also be used to define powerful domain-specific similarity functions for prediction. In recent years, significant progress has been made towards subgraph mining algorithms that scale to complex graphs by focusing on tree patterns and probabilistically allowing a small amount of incompleteness in the result. Nonetheless, the complexity of the pattern matching component used for deciding subtree isomorphism on arbitrary graphs has significantly limited the scalability of existing approaches. In this paper, we adapt sampling techniques from mathematical combinatorics to the problem of probabilistic subtree mining in arbitrary databases of many small to medium-size graphs or a single large graph. By restricting on tree patterns, we provide an algorithm tha t approximately counts or decides subtree isomorphism for arbitrary transaction graphs in sub-linear time with one-sided error. Our empirical evaluation on a range of benchmark graph datasets shows that the novel algorithm substantially outperforms state-of-the-art approaches both in the task of approximate counting of embeddings in single large graphs and in probabilistic frequent subtree mining in large databases of small to medium sized graphs.

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Publication

#### Maximal Closed Set and Half-Space Separations in Finite Closure Systems

2020
,
Seiffarth, Florian
,
Horvath, Tamas
,
Wrobel, Stefan

Motivated by various binary classification problems in structured data (e.g., graphs or other relational and algebraic structures), we investigate some algorithmic properties of closed set and half-space separation in abstract closure systems. Assuming that the underlying closure system is finite and given by the corresponding closure operator, we formulate some negative and positive complexity results for these two separation problems. In particular, we prove that deciding half-space separability in abstract closure systems is NP-complete in general. On the other hand, for the relaxed problem of maximal closed set separation we propose a simple greedy algorithm and show that it is efficient and has the best possible lower bound on the number of closure operator calls. As a second direction to overcome the negative result above, we consider Kakutani closure systems and show first that our greedy algorithm provides an algorithmic characterization of this kind of set systems. As one of the major potential application fields, we then focus on Kakutani closure systems over graphs and generalize a fundamental characterization result based on the Pasch axiom to graph structure partitioning of finite sets. Though the primary focus of this work is on the generality of the results obtained, we experimentally demonstrate the practical usefulness of our approach on vertex classification in different graph datasets.

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Publication

#### Maximum Margin Separations in Finite Closure Systems

2021
,
Seiffahrt, Florian
,
Horvath, Tamas
,
Wrobel, Stefan

Monotone linkage functions provide a measure for proximities between elements and subsets of a ground set. Combining this notion with Vapniks idea of support vector machines, we extend the concepts of maximal closed set and half-space separation in finite closure systems to those with maximum margin. In particular, we define the notion of margin for finite closure systems by means of monotone linkage functions and give a greedy algorithm computing a maximum margin closed set separation for two sets efficiently. The output closed sets are maximum margin half-spaces, i.e., form a partitioning of the ground set if the closure system is Kakutani. We have empirically evaluated our approach on different synthetic datasets. In addition to binary classification of finite subsets of the Euclidean space, we considered also the problem of vertex classification in graphs. Our experimental results provide clear evidence that maximal closed set separation with maximum margin results in a much better predictive performance than that with arbitrary maximal closed sets.

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Publication

#### Zertifizierung von KI-Systemen. Kompass fÃ¼r die Entwicklung und Anwendung vertrauenswÃ¼rdiger KI-Systeme

2020
,
Heesen, Jessica
,
MÃ¼ller-Quade, JÃ¶rn
,
Wrobel, Stefan
,
Poretschkin, Maximilian

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Publication

#### Adiabatic Quantum Computing for Max-Sum Diversification

2020
,
Bauckhage, Christian
,
Sifa, Rafet
,
Wrobel, Stefan

The combinatorial problem of max-sum diversification asks for a maximally diverse subset of a given set of data. Here, we show that it can be expressed as an Ising energy minimization problem. Given this result, max-sum diversification can be solved on adiabatic quantum computers and we present proof of concept simulations which support this claim. This, in turn, suggests that quantum computing might play a role in data mining. We therefore discuss quantum computing in a tutorial like manner and elaborate on its current strengths and weaknesses for data analysis.

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Publication

#### Constructing Spaces and Times for Tactical Analysis in Football

2021
,
Andrienko, Gennady
,
Andrienko, Natalia
,
Anzer, Gabriel
,
Bauer, Pascal
,
Budziak, Guido
,
Fuchs, Georg
,
Hecker, Dirk
,
Weber, Hendrik
,
Wrobel, Stefan

A possible objective in analyzing trajectories of multiple simultaneously moving objects, such as football players during a game, is to extract and understand the general patterns of coordinated movement in different classes of situations as they develop. For achieving this objective, we propose an approach that includes a combination of query techniques for flexible selection of episodes of situation development, a method for dynamic aggregation of data from selected groups of episodes, and a data structure for representing the aggregates that enables their exploration and use in further analysis. The aggregation, which is meant to abstract general movement patterns, involves construction of new time-homomorphic reference systems owing to iterative application of aggregation operators to a sequence of data selections. As similar patterns may occur at different spatial locations, we also propose constructing new spatial reference systems for aligning and matching movements irrespective of their absolute locations. The approach was tested in application to tracking data from two Bundesliga games of the 2018/2019 season. It enabled detection of interesting and meaningful general patterns of team behaviors in three classes of situations defined by football experts. The experts found the approach and the underlying concepts worth implementing in tools for football analysts.

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Publication

#### Zertifizierung von KI-Systemen

2020
,
Heesen, Jessica
,
MÃ¼ller-Quade, JÃ¶rn
,
Wrobel, Stefan
,
Poretschkin, Maximilian

Die Zertifizierung von KÃ¼nstlicher Intelligenz (KI) gilt als eine mÃ¶gliche SchlÃ¼sselvoraussetzung, um den Einsatz von KI-Systemen in verschiedenen Wirtschafts- und Lebensbereichen voranzutreiben. FÃ¼r eine Vielzahl von KI-Systemen kann eine Zertifizierung dazu beitragen, das gesellschaftliche Nutzenpotential sicher und gemeinwohlorientiert auszuschÃ¶pfen. Eine gelungene Zertifizierung von KI-Systemen ermÃ¶glicht die ErfÃ¼llung wichtiger gesellschaftlicher und Ã¶konomischer Prinzipien, wie etwa Rechtssicherheit (z. B. Haftung und EntschÃ¤digung), InteroperabilitÃ¤t, IT-Sicherheit oder Datenschutz. Zudem kann sie bei BÃ¼rgerinnen und BÃ¼rgern Vertrauen schaffen, zu besseren Produkten fÃ¼hren und die nationale und internationale Marktdynamik beeinflussen. Damit sich Zertifizierungsverfahren aber nicht als Innovationshemmnis erweisen, gilt es, bestimmte Standards von KI-Systemen zu garantieren, Ãœberregulierung zu vermeiden, Innovation zu ermÃ¶glichen und bestenfalls neue Entwicklungen fÃ¼r einen europÃ¤ischen Weg in der KI-Anwendung auslÃ¶sen zu kÃ¶nnen. Das Spannungsfeld aus Potentialen und Herausforderungen bei der Zertifizierung von KI-Systemen haben Expertinnen und Experten der Plattform Lernende Systeme in vorliegendem Impulspapier systematisiert. Das Papier, das unter der Leitung der Arbeitsgruppe IT-Sicherheit, Privacy, Recht und Ethik sowie der Arbeitsgruppe Technologische Wegbereiter und Data Science entstand, beleuchtet verschiedene technische, juristische und ethische Herausforderungen und gibt zudem einen Ãœberblick Ã¼ber bestehende Initiativen zur Zertifizierung von KI-Systemen in Deutschland.

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Publication

#### Effective approximation of parametrized closure systems over transactional data streams

2020
,
Trabold, Daniel
,
Horvath, Tamas
,
Wrobel, Stefan

Strongly closed itemsets, defined by a parameterized closure operator, are a generalization of ordinary closed itemsets. Depending on the strength of closedness, the family of strongly closed itemsets typically forms a tiny subfamily of ordinary closed itemsets that is stable against changes in the input. In this paper we consider the problem of mining strongly closed itemsets from transactional data streams. Utilizing their algebraic and algorithmic properties, we propose an algorithm based on reservoir sampling for approximating this type of itemsets in the landmark streaming setting, prove its correctness, and show empirically that it yields a considerable speed-up over a straightforward naive algorithm without any significant loss in precision and recall. We motivate the problem setting considered by two practical applications. In particular, we first experimentally demonstrate that the above properties, i.e., compactness and stability, make strongly closed itemsets an excellent indicator of certain types of concept drifts in transactional data streams. As a second application we consider computer-aided product configuration, a real-world problem raised by an industrial project. For this problem, which is essentially exact concept identification, we propose a learning algorithm based on a certain type of subset queries formed by strongly closed itemsets and show on real-world datasets that it requires significantly less query evaluations than a naive algorithm based on membership queries.