INTERPRETATION OF EXPERIMENTS IN PAUL TRAP

Chosen aspects of laser spectroscopy in a Paul trap have been discussed. On the example of interpretation of the experimental results for europium ion the advantages of the use of semiempirical atomicstructure calculations have been proved. For the calculations a computer package, prepared and adopted by ourselves to be used on vector computers, has been applied.Pozna

COMPUTATIONAL PACKAGE FOR ANALYSIS OF THE FINE STRUCTURE OF A FREE ATOM

This work describes some computer programs that are available in compiled form for users of the SGI Power Challenge machine at Poznań Supercomputing and Networking Center. These programs give apossibility to solve very complex problems in the structure of free atoms using experimental data. The procedure of determination of the Slater integrals, spin-orbit parameters and also the parameters representingthe effect of virtual excitations (many-body effects) is described. The program gives the propositions of the spectroscopic designations of energy levels. Moreover, the wavefunctions in intermediate coupling scheme in many-configurations approximation for the selected configuration system can be obtained.Pozna

Learning Interpretable Rules for Multi-label Classification

Multi-label classification (MLC) is a supervised learning problem in which, contrary to standard multiclass classification, an instance can be associated with several class labels simultaneously. In this chapter, we advocate a rule-based approach to multi-label classification. Rule learning algorithms are often employed when one is not only interested in accurate predictions, but also requires an interpretable theory that can be understood, analyzed, and qualitatively evaluated by domain experts. Ideally, by revealing patterns and regularities contained in the data, a rule-based theory yields new insights in the application domain. Recently, several authors have started to investigate how rule-based models can be used for modeling multi-label data. Discussing this task in detail, we highlight some of the problems that make rule learning considerably more challenging for MLC than for conventional classification. While mainly focusing on our own previous work, we also provide a short overview of related work in this area.Comment: Preprint version. To appear in: Explainable and Interpretable Models in Computer Vision and Machine Learning. The Springer Series on Challenges in Machine Learning. Springer (2018). See http://www.ke.tu-darmstadt.de/bibtex/publications/show/3077 for further informatio

Efficient Discovery of Expressive Multi-label Rules using Relaxed Pruning

Being able to model correlations between labels is considered crucial in multi-label classification. Rule-based models enable to expose such dependencies, e.g., implications, subsumptions, or exclusions, in an interpretable and human-comprehensible manner. Albeit the number of possible label combinations increases exponentially with the number of available labels, it has been shown that rules with multiple labels in their heads, which are a natural form to model local label dependencies, can be induced efficiently by exploiting certain properties of rule evaluation measures and pruning the label search space accordingly. However, experiments have revealed that multi-label heads are unlikely to be learned by existing methods due to their restrictiveness. To overcome this limitation, we propose a plug-in approach that relaxes the search space pruning used by existing methods in order to introduce a bias towards larger multi-label heads resulting in more expressive rules. We further demonstrate the effectiveness of our approach empirically and show that it does not come with drawbacks in terms of training time or predictive performance.Comment: Preprint version. To appear in Proceedings of the 22nd International Conference on Discovery Science, 201

Exploiting Anti-monotonicity of Multi-label Evaluation Measures for Inducing Multi-label Rules

Exploiting dependencies between labels is considered to be crucial for multi-label classification. Rules are able to expose label dependencies such as implications, subsumptions or exclusions in a human-comprehensible and interpretable manner. However, the induction of rules with multiple labels in the head is particularly challenging, as the number of label combinations which must be taken into account for each rule grows exponentially with the number of available labels. To overcome this limitation, algorithms for exhaustive rule mining typically use properties such as anti-monotonicity or decomposability in order to prune the search space. In the present paper, we examine whether commonly used multi-label evaluation metrics satisfy these properties and therefore are suited to prune the search space for multi-label heads.Comment: Preprint version. To appear in: Proceedings of the Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD) 2018. See http://www.ke.tu-darmstadt.de/bibtex/publications/show/3074 for further information. arXiv admin note: text overlap with arXiv:1812.0005

Multi-Target Prediction: A Unifying View on Problems and Methods

Multi-target prediction (MTP) is concerned with the simultaneous prediction of multiple target variables of diverse type. Due to its enormous application potential, it has developed into an active and rapidly expanding research field that combines several subfields of machine learning, including multivariate regression, multi-label classification, multi-task learning, dyadic prediction, zero-shot learning, network inference, and matrix completion. In this paper, we present a unifying view on MTP problems and methods. First, we formally discuss commonalities and differences between existing MTP problems. To this end, we introduce a general framework that covers the above subfields as special cases. As a second contribution, we provide a structured overview of MTP methods. This is accomplished by identifying a number of key properties, which distinguish such methods and determine their suitability for different types of problems. Finally, we also discuss a few challenges for future research

On Aggregation in Ensembles of Multilabel Classifiers

While a variety of ensemble methods for multilabel classification have been proposed in the literature, the question of how to aggregate the predictions of the individual members of the ensemble has received little attention so far. In this paper, we introduce a formal framework of ensemble multilabel classification, in which we distinguish two principal approaches: "predict then combine" (PTC), where the ensemble members first make loss minimizing predictions which are subsequently combined, and "combine then predict" (CTP), which first aggregates information such as marginal label probabilities from the individual ensemble members, and then derives a prediction from this aggregation. While both approaches generalize voting techniques commonly used for multilabel ensembles, they allow to explicitly take the target performance measure into account. Therefore, concrete instantiations of CTP and PTC can be tailored to concrete loss functions. Experimentally, we show that standard voting techniques are indeed outperformed by suitable instantiations of CTP and PTC, and provide some evidence that CTP performs well for decomposable loss functions, whereas PTC is the better choice for non-decomposable losses.Comment: 14 pages, 2 figure

On calibration of nested dichotomies

Nested dichotomies (NDs) are used as a method of transforming a multiclass classification problem into a series of binary problems. A tree structure is induced that recursively splits the set of classes into subsets, and a binary classification model learns to discriminate between the two subsets of classes at each node. In this paper, we demonstrate that these NDs typically exhibit poor probability calibration, even when the binary base models are well-calibrated. We also show that this problem is exacerbated when the binary models are poorly calibrated. We discuss the effectiveness of different calibration strategies and show that accuracy and log-loss can be significantly improved by calibrating both the internal base models and the full ND structure, especially when the number of classes is high