Weighted model counting has recently been extended to weighted model integration, which can be used to solve hybrid probabilistic reasoning problems. Such problems involve both discrete and continuous probability distributions. We show how standard knowledge compilation techniques (to SDDs and d-DNNFs) apply to weighted model integration, and use it in two novel solvers, one exact and one approximate solver. Furthermore, we extend the class of employable weight functions to actual probability density functions instead of mere polynomial weight functions.

We study ontology-mediated querying over probabilistic data for the case when the ontology is formulated in EL(hdr), an expressive member of the EL family of description logics. We leverage techniques that have been developed (i) for classical ontology-mediated querying and (ii) for probabilistic logic programming and provide an implementation based on our findings. We include both theoretical considerations and an experimental evaluation of our approach.

Answer Set Programming (ASP) is a powerful modeling formalism for combinatorial problems. However, writing ASP models can be hard. We propose a novel method, called Sketched Answer Set Programming (SkASP), aimed at facilitating this. In SkASP, the user writes partial ASP programs, in which uncertain parts are left open and marked with question marks. In addition, the user provides a number of positive and negative examples of the desired program behaviour. SkASP then synthesises a complete ASP program. This is realized by rewriting the SkASP program into another ASP program, which can then be solved by traditional ASP solvers. We evaluate our approach on 21 well known puzzles and combinatorial problems inspired by Karp's 21 NP-complete problems and on publicly available ASP encodings.

The ability to solve probability word problems such as those found in introductory discrete mathematics textbooks, is an important cognitive and intellectual skill. In this paper, we develop a two-step end-to-end fully automated approach for solving such questions that is able to automatically provide answers to exercises about probability formulated in natural language.In the first step, a question formulated in natural language is analysed and transformed into a high-level model specified in a declarative language. In the second step, a solution to the high-level model is computed using a probabilistic programming system. On a dataset of 2160 probability problems, our solver is able to correctly answer 97.5% of the questions given a correct model. On the end-to-end evaluation, we are able to answer 12.5% of the questions (or 31.1% if we exclude examples not supported by design).

Finding small sets of interesting patterns is an important challenge in pattern mining. In this paper, we argue that several well-known approaches that address this challenge are based on performing pair wise comparisons between patterns. Examples include finding closed patterns, free patterns, relevant subgroups and skyline patterns. Although progress has been made on each of these individual problems, a generic approach for solving these problems (and more) is still lacking. This paper tackles this challenge. It proposes a novel, generic approach for handling pattern mining problems that involve pair wise comparisons between patterns. Our key contributions are the following. First, we propose a novel algebra for programming pattern mining problems. This algebra extends relational algebras in a novel way towards pattern mining. It allows for the generic combination of constraints on individual patterns with dominance relations between patterns. Second, we introduce a modified generic constraint satisfaction system to evaluate these algebraic expressions. Experiments show that this generic approach can indeed effectively identify patterns expressed in the algebra.

In recent years many algorithms have been developed for finding patterns in graphs and networks. A disadvantage of these algorithms is that they use subgraph isomorphism to determine the support of a graph pattern; subgraph isomorphism is a well-known NP complete problem. In this paper, we propose an alternative approach which mines tree patterns in networks by using subgraph homomorphism. The advantage of homomorphism is that it can be computed in polynomial time, which allows us to develop an algorithm that mines tree patterns in arbitrary graphs in incremental polynomial time. Homomorphism however entails two problems not found when using isomorphism: (1) two patterns of different size can be equivalent; (2) patterns of unbounded size can be frequent. In this paper we formalize these problems and study solutions that easily fit within our algorithm.

We adapt Mitchell's version space algorithm for mining k-CNF formulas. Advantages of this algorithm are that it runs in a single pass over the data, is conceptually simple, can be used for missing value prediction, and has interesting theoretical properties, while an empirical evaluation on classification tasks yields competitive predictive results.

With more and more large networks becoming available, mining and querying such networks are increasingly important tasks which are not being supported by database models and querying languages. This paper wants to alleviate this situation by proposing a data model and a query language for facilitating the analysis of networks. Key features include support for executing external tools on the networks, flexible contexts on the network each resulting in a different graph, primitives for querying subgraphs (including paths) and transforming graphs.

An established method to detect concept drift in data streams is to perform statistical hypothesis testing on the multivariate data in the stream. Statistical decision theory offers rank-based statistics for this task. However, these statistics depend on a fixed set of characteristics of the underlying distribution. Thus, they work well whenever the change in the underlying distribution affects these properties measured by the statistic, but they perform not very well, if the drift influences the characteristics caught by the test statistic only to a small degree. To address this problem, we present three novel drift detection tests, whose test statistics are dynamically adapted to match the actual data at hand. The first one is based on a rank statistic on density estimates for a binary representation of the data, the second compares average margins of a linear classifier induced by the 1-norm support vector machine (SVM), and the last one is based on the average zero-one or sigmoid error rate of an SVM classifier. Experiments show that the margin- and error-based tests outperform the multivariate Wald-Wolfowitz test for concept drift detection. We also show that the tests work even if the drift is gradual in nature and that the new methods are faster than the Wald-Wolfowitz test.