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.

Positive unlabeled (PU) learning is useful in various practical situations, where there is a need to learn a classifier for a class of interest from an unlabeled data set, which may contain anomalies as well as samples from unknown classes. The learning task can be formulated as an optimization problem under the framework of statistical learning theory. Recent studies have theoretically analyzed its properties and generalization performance, nevertheless, little effort has been made to consider the problem of scalability, especially when large sets of unlabeled data are available. In this work we propose a novel scalable PU learning algorithm that is theoretically proven to provide the optimal solution, while showing superior computational and memory performance. Experimental evaluation confirms the theoretical evidence and shows that the proposed method can be successfully applied to a large variety of real-world problems involving PU learning.
Efficient Training for Positive Unlabeled Learning

Minimum vertex cover problem is an NP-Hard problem with the aim of finding minimum number of vertices to cover graph. In this paper, a learning automaton based algorithm is proposed to find minimum vertex cover in graph. In the proposed algorithm, each vertex of graph is equipped with a learning automaton that has two actions in the candidate or noncandidate of the corresponding vertex cover set. Due to characteristics of learning automata, this algorithm significantly reduces the number of covering vertices of graph. The proposed algorithm based on learning automata iteratively minimize the candidate vertex cover through the update its action probability. As the proposed algorithm proceeds, a candidate solution nears to optimal solution of the minimum vertex cover problem. In order to evaluate the proposed algorithm, several experiments conducted on DIMACS dataset which compared to conventional methods. Experimental results show the major superiority of the proposed algorithm over the other methods. Keywords— Minimum Vertex Cover; NP-Hard problems; Learning Automata; Distributed learning automata.
Solving Minimum Vertex Cover Problem Using Learning Automata

We present a new theoretical framework for analyzing and learning artificial neural networks. Our approach simultaneously and adaptively learns both the structure of the network as well as its weights. The methodology is based upon and accompanied by strong data-dependent theoretical learning guarantees, so that the final network architecture provably adapts to the complexity of any given problem.

AdaNet: Adaptive Structural Learning of Artificial Neural Networks