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.

Ex Input:
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).

Ex Output:
Parameterized Complexity Results for Exact Bayesian Network Structure Learning

Ex Input:
A currently successful approach to computational semantics is to represent words as embeddings in a machine-learned vector space. We present an ensemble method that combines embeddings produced by GloVe (Pennington et al., 2014) and word2vec (Mikolov et al., 2013) with structured knowledge from the semantic networks ConceptNet (Speer and Havasi, 2012) and PPDB (Ganitkevitch et al., 2013), merging their information into a common representation with a large, multilingual vocabulary. The embeddings it produces achieve state-of-the-art performance on many word-similarity evaluations. Its score of = .596 on an evaluation of rare words (Luong et al., 2013) is 16% higher than the previous best known system.

Ex Output:
An Ensemble Method to Produce High-Quality Word Embeddings

Ex Input:
In this paper, we propose and investigate a novel memory architecture for neural networks called Hierarchical Attentive Memory (HAM). It is based on a binary tree with leaves corresponding to memory cells. This allows HAM to perform memory access in (logn) complexity, which is a significant improvement over the standard attention mechanism that requires (n) operations, where n is the size of the memory. We show that an LSTM network augmented with HAM can learn algorithms for problems like merging, sorting or binary searching from pure input-output examples. In particular, it learns to sort n numbers in time (n logn) and generalizes well to input sequences much longer than the ones seen during the training. We also show that HAM can be trained to act like classic data structures: a stack, a FIFO queue and a priority queue.

Ex Output:
Learning Efficient Algorithms with Hierarchical Attentive Memory