Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov regularisation parameter from noisy data. In this work, we improve their results and extend the analysis to the elastic net regularisation, providing explicit error bounds on the accuracy of the approximated parameter and the corresponding regularisation solution in a simplified case. Furthermore, in the general case we design a data-driven, automated algorithm for the computation of an approximate regularisation parameter. Our analysis combines statistical learning theory with insights from regularisation theory. We compare our approach with state-of-the-art parameter selection criteria and illustrate its superiority in terms of accuracy and computational time on simulated and real data sets.

Inspired by recent interests of developing machine learning and data mining algorithms on hypergraphs, we investigate in this paper the semi-supervised learning algorithm of propagating "soft labels" (e.g. Furthermore, in a PAC learning framework, we provide generalization error bounds for propagating one-dimensional distributions on graphs and hypergraphs using 2-Wasserstein distance, by establishing the algorithmic stability of the proposed semi-supervised learning algorithm. These theoretical results also shed new lights upon deeper understandings of the Wasserstein propagation on graphs. Recent decades have witnessed a growing interest in developing machine learning and data mining algorithms on hypergraphs [ZHS07], [JM18], [BP09], [LR15], [LM17], [HSJR13], [HZY15]. As a natural generalization of graphs, a hypergraph is a combinatorial structure consisting of vertices and hyperedges, where each hyperedge is allowed to connect any number of vertices.

Exponential and concentration inequalities are corner stones of machine learning theory. The first distribution-free bounds on the Empirical Risk Minimiser (ERM), proven by Vapnik and Cervnonenkis in the early 70s, are based on Hoeffding's inequality, see Vapnik (1998). Model selection techniques rely heavily on concentration inequalities (Massart (2007)). We defer the reader to Boucheron et al. (2013) for an overview on concentration inequalities. However, all the results in these references are in the case of i.i.d random variables. Many extensions of Hoeffding and Bernstein's inequalities were proposed for dependent observations: see Catoni (2003); Bertail and Clémençon (2010); Joulin and Ollivier (2010); Dedecker and Fan (2015); Fan et al. (2018) under

Learning of user preferences, as represented by, for example, Conditional Preference Networks (CP-nets), has become a core issue in AI research. Recent studies investigate learning of CP-nets from randomly chosen examples or from membership and equivalence queries. To assess the optimality of learning algorithms as well as to better understand the combinatorial structure of classes of CP-nets, it is helpful to calculate certain learning-theoretic information complexity parameters. This article focuses on the frequently studied case of learning from so-called swap examples, which express preferences among objects that differ in only one attribute. It presents bounds on or exact values of some well-studied information complexity parameters, namely the VC dimension, the teaching dimension, and the recursive teaching dimension, for classes of acyclic CP-nets. We further provide algorithms that learn tree-structured and general acyclic CP-nets from membership queries. Using our results on complexity parameters, we assess the optimality of our algorithms as well as that of another query learning algorithm for acyclic CP-nets presented in the literature. Our algorithms are near-optimal, and can, under certain assumptions, be adapted to the case when the membership oracle is faulty.

Machine learning is a field of computer science that gives computers the ability to learn without being explicitly programmed. Arthur Samuel, an American pioneer in the field of computer gaming and artificial intelligence, coined the term "Machine Learning" in 1959 while at IBM. Evolved from the study of pattern recognition and computational learning theory in artificial intelligence, machine learning explores the study and construction of algorithms that can learn from and make predictions on data. Machine learning is a type of artificial intelligence (AI) that allows software applications to become more accurate in predicting outcomes without being explicitly programmed. The basic premise of machine learning is to build algorithms that can receive input data and use statistical analysis to predict an output value within an acceptable range. Machine learning has given us self-driving cars, practical speech recognition, effective web search, and a vastly improved understanding of the human genome.

Machine learning is already here and have been applied by businesses already. Computers are used by machine learning to run predictive models which fetch details from existing data in order to detect fraud, demand forecasting or ad targeting. Machine learning offers lots of benefits to business which includes rapid processing, analysis, predictions, etc. It provides with the capability to deliver new products and services by lowering the cost of existing products. Our globally recognized experts have an advanced thinking in machine learning theory and hence these approaches make us the choice of all corporate big data requirements.

The problem of attempting to learn the mapping between data and labels is the crux of any machine learning task. It is, therefore, of interest to the machine learning community on practical as well as theoretical counts to consider the existence of a test or criterion for deciding the feasibility of attempting to learn. We investigate the existence of such a criterion in the setting of PAC-learning, basing the feasibility solely on whether the mapping to be learnt lends itself to approximation by a given class of hypothesis functions. We show that no such criterion exists, exposing a fundamental limitation in the decidability of learning. In other words, we prove that testing for PAC-learnability is undecidable in the Turing sense. We also briefly discuss some of the probable implications of this result to the current practice of machine learning.

Was it a chance encounter when you met that special someone or was there some deeper reason for it? What about that strange dream last night--was that just the random ramblings of the synapses of your brain or did it reveal something deep about your unconscious? Perhaps the dream was trying to tell you something about your future. Did the fact that a close relative developed a virulent form of cancer have profound meaning or was it simply a consequence of a random mutation of his DNA? We live our lives thinking about the patterns of events that happen around us.

For the published version of the article, see: Heck, D. W., Moshagen, M., & Erdfelder, E. (2014). Correspondence concerning this article should be addressed to Daniel W. Heck, Department of Psychology, School of Social Sciences, University of Mannheim, Schloss EO 254, D-68131 Mannheim, Germany. FISHER INFORMATION APPROXIMATION 2 Abstract The Fisher information approximation (FIA) is an implementation of the minimum description length principle for model selection. Unlike information criteria such as AIC or BIC, it has the advantage of taking the functional form of a model into account. Unfortunately, FIA can be misleading in finite samples, resulting in an inversion of the correct rank order of complexity terms for competing models in the worst case.

Original and learnt clauses in Conflict-Driven Clause Learning (CDCL) SAT solvers often contain redundant literals. This may have a negative impact on performance because redundant literals may deteriorate both the effectiveness of Boolean constraint propagation and the quality of subsequent learnt clauses. To overcome this drawback, we propose a clause vivification approach that eliminates redundant literals by applying unit propagation. The proposed clause vivification is activated before the SAT solver triggers some selected restarts, and only affects a subset of original and learnt clauses, which are considered to be more relevant according to metrics like the literal block distance (LBD). Moreover, we conducted an empirical investigation with instances coming from the hard combinatorial and application categories of recent SAT competitions. The results show that a remarkable number of additional instances are solved when the proposed approach is incorporated into five of the best performing CDCL SAT solvers (Glucose, TC_Glucose, COMiniSatPS, MapleCOMSPS and MapleCOMSPS_LRB). More importantly, the empirical investigation includes an in-depth analysis of the effectiveness of clause vivification. It is worth mentioning that one of the SAT solvers described here was ranked first in the main track of SAT Competition 2017 thanks to the incorporation of the proposed clause vivification. That solver was further improved in this paper and won the bronze medal in the main track of SAT Competition 2018.