We present several exact and highly scalable local pattern sampling algorithms. They can be used as an alternative to exhaustive local pattern discovery methods (e.g, frequent set mining or optimistic-estimator-based subgroup discovery) and can substantially improve efficiency as well as controllability of pattern discovery processes. While previous sampling approaches mainly rely on theMarkov chainMonte Carlo method, our procedures are direct, i.e., non processsimulating, sampling algorithms. The advantages of these direct methods are an almost optimal time complexity per pattern as well as an exactly controlled distribution of the produced patterns. Namely, the proposed algorithms can sample (item-)sets according to frequency, area, squared frequency, and a class discriminativity measure. Experiments demonstrate that these procedures can improve the accuracy of pattern-based models similar to frequent sets and often also lead to substantial gains in terms of scalability. Copyright 2011 ACM

We study the problem of listing all closed sets of a closure operator a that is a partial function on the power set of some finite ground set E, i.e., sigma : F -> F with F subset of P(E). A very simple divide-and-conquer algorithm is analyzed that correctly solves this problem if and only if the domain of the closure operator is a strongly accessible set system. Strong accessibility is a strict relaxation of greedoids as well as of independence systems. This algorithm turns out to have delay O (vertical bar E vertical bar (T-F + T-sigma + vertical bar E vertical bar)) and space O (vertical bar E vertical bar + S-F + S-sigma), where T-F, S-F, T-sigma, and S-sigma are the time and space complexities of checking membership in F and computing a, respectively. In contrast, we show that the problem becomes intractable for accessible set systems. We relate our results to the data mining problem of listing all support-closed patterns of a dataset and show that there is a corresponding closure operator for all datasets if and only if the set system satisfies a certain confluence property

Mining patterns from multi-relational data is a problem attracting increasing interest within the data mining community. Traditional data mining approaches are typically developed for single-table databases, and are not directly applicable to multi-relational data. Nevertheless, multi-relational data is a more truthful and therefore often also a more powerful representation of reality. Mining patterns of a suitably expressive syntax directly from this representation, is thus a research problem of great importance. In this paper we introduce a novel approach to mining patterns in multi-relational data. We propose a new syntax for multi-relational patterns as complete connected subsets of database entities. We show how this pattern syntax is generally applicable to multi-relational data, while it reduces to well-known tiles " Geerts et al. (Proceedings of Discovery Science, pp 278-289, 2004)" when the data is a simple binary or attribute-value table. We propose RMiner, a simple yet practically efficient divide and conquer algorithm to mine such patterns which is an instantiation of an algorithmic framework for efficiently enumerating all fixed points of a suitable closure operator "Boley et al. (Theor Comput Sci 411(3):691-700, 2010)". We show how the interestingness of patterns of the proposed syntax can conveniently be quantified using a general framework for quantifying subjective interestingness of patterns "De Bie (Data Min Knowl Discov 23(3):407-446, 2011b)". Finally, we illustrate the usefulness and the general applicability of our approach by discussing results on real-world and synthetic databases

Subgroup discovery (SGD) is presented here as a data-mining approach to help find interpretable local patterns, correlations, and descriptors of a target property in materials-science data. Specifically, we will be concerned with data generated by density-functional theory calculations. At first, we demonstrate that SGD can identify physically meaningful models that classify the crystal structures of 82 octet binary (OB) semiconductors as either rocksalt or zincblende. SGD identifies an interpretable two-dimensional model derived from only the atomic radii of valence s and p orbitals that properly classifies the crystal structures for 79 of the 82 OB semiconductors. The SGD framework is subsequently applied to 24 400 configurations of neutral gas-phase gold clusters with 5-14 atoms to discern general patterns between geometrical and physicochemical properties. For example, SGD helps find that van der Waals interactions within gold clusters are linearly correlated with their radius of gyration and are weaker for planar clusters than for nonplanar clusters. Also, a descriptor that predicts a local linear correlation between the chemical hardness and the cluster isomer stability is found for the even-sized gold clusters.

In recent years, we have been witnessing a paradigm shift in computational materials science. In fact, traditional methods, mostly developed in the second half of the XXth century, are being complemented, extended, and sometimes even completely replaced by faster, simpler, and often more accurate approaches. The new approaches, that we collectively label by machine learning, have their origins in the fields of informatics and artificial intelligence, but are making rapid inroads in all other branches of science. With this in mind, this Roadmap article, consisting of multiple contributions from experts across the field, discusses the use of machine learning in materials science, and share perspectives on current and future challenges in problems as diverse as the prediction of materials properties, the construction of force-fields, the development of exchange correlation functionals for density-functional theory, the solution of the many-body problem, and more. In spite of the already numerous and exciting success stories, we are just at the beginning of a long path that will reshape materials science for the many challenges of the XXIth century.

Given a database and a target attribute of interest, how can we tell whether there exists a functional, or approximately functional dependence of the target on any set of other attributes in the data? How can we reliably, without bias to sample size or dimensionality, measure the strength of such a dependence? And, how can we efficiently discover the optimal or $\alpha$-approximate top-$k$ dependencies? These are exactly the questions we answer in this paper. As we want to be agnostic on the form of the dependence, we adopt an information-theoretic approach, and construct a reliable, bias correcting score that can be efficiently computed. Moreover, we give an effective optimistic estimator of this score, by which for the first time we can mine the approximate functional dependencies from data with guarantees of optimality. Empirical evaluation shows that the derived score achieves a good bias for variance trade-off, can be used within an efficient discovery algorithm, and indeed discovers meaningful dependencies. Most important, it remains reliable in the face of data sparsity.Comment: Accepted: In Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD), August 13-17, 2017, Halifax, NS, Canad

Although machine learning (ML) models promise to substantially accelerate the discovery of novel materials, their performance is often still insufficient to draw reliable conclusions. Improved ML models are therefore actively researched, but their design is currently guided mainly by monitoring the average model test error. This can render different models indistinguishable although their performance differs substantially across materials, or it can make a model appear generally insufficient while it actually works well in specific sub-domains. Here, we present a method, based on subgroup discovery, for detecting domains of applicability (DA) of models within a materials class. The utility of this approach is demonstrated by analyzing three state-of-the-art ML models for predicting the formation energy of transparent conducting oxides. We find that, despite having a mutually indistinguishable and unsatisfactory average error, the models have DAs with distinctive features and notably improved performance.

This paper shows how coupling from the past (CFTP) can be used to avoid time and memory bottlenecks in direct local pattern sampling procedures. Such procedures draw controlled amounts of suitably biased samples directly from the pattern space of a given dataset in polynomial time. Previous direct pattern sampling methods can produce patterns in rapid succession after some initial preprocessing phase. This preprocessing phase, however, turns out to be prohibitive in terms of time and memory for many datasets. We show how CFTP can be used to avoid any super-linear preprocessing and memory requirements. This allows to simulate more complex distributions, which previously were intractable. We show for a large number of public real-world datasets that these new algorithms are fast to execute and their pattern collections outperform previous approaches both in unsupervised as well as supervised contexts