In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact Bayesian network structure learning under graph theoretic restrictions on the (directed) super-structure. The super-structure is an undirected graph that contains as subgraphs the skeletons of solution networks. We introduce the directed super-structure as a natural generalization of its undirected counterpart. Our results apply to several variants of score-based Bayesian network structure learning where the score of a network decomposes into local scores of its nodes. Results: We show that exact Bayesian network structure learning can be carried out in non-uniform polynomial time if the super-structure has bounded treewidth, and in linear time if in addition the super-structure has bounded maximum degree. Furthermore, we show that if the directed super-structure is acyclic, then exact Bayesian network structure learning can be carried out in quadratic time. We complement these positive results with a number of hardness results. We show that both restrictions (treewidth and degree) are essential and cannot be dropped without loosing uniform polynomial time tractability (subject to a complexity-theoretic assumption). Similarly, exact Bayesian network structure learning remains NP-hard for “almost acyclic” directed super-structures. Furthermore, we show that the restrictions remain essential if we do not search for a globally optimal network but aim to improve a given network by means of at most k arc additions, arc deletions, or arc reversals (k-neighborhood local search).

A: Parameterized Complexity Results for Exact Bayesian Network Structure Learning
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Q: Due to imprecision and uncertainties in predicting real world problems, artificial neural network (ANN) techniques have become increasingly useful for modeling and optimization. This paper presents an artificial neural network approach for forecasting electric energy consumption. For effective planning and operation of power systems, optimal forecasting tools are needed for energy operators to maximize profit and also to provide maximum satisfaction to energy consumers. Monthly data for electric energy consumed in the Gaza strip was collected from year 1994 to 2013. Data was trained and the proposed model was validated using 2-Fold and K-Fold cross validation techniques. The model has been tested with actual energy consumption data and yields satisfactory performance.

A: Using Artificial Neural Network Techniques for Prediction of Electric Energy Consumption
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Q: The follow the leader (FTL) algorithm, perhaps the simplest of all online learning algorithms, is known to perform well when the loss functions it is used on are convex and positively curved. In this paper we ask whether there are other “lucky” settings when FTL achieves sublinear, “small” regret. In particular, we study the fundamental problem of linear prediction over a non-empty convex, compact domain. Amongst other results, we prove that the curvature of the boundary of the domain can act as if the losses were curved: In this case, we prove that as long as the mean of the loss vectors have positive lengths bounded away from zero, FTL enjoys a logarithmic growth rate of regret, while, e.g., for polytope domains and stochastic data it enjoys finite expected regret. Building on a previously known meta-algorithm, we also get an algorithm that simultaneously enjoys the worst-case guarantees and the bound available for FTL.

A:
Following the Leader and Fast Rates in Linear Prediction: Curved Constraint Sets and Other Regularities∗
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