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.

The EM-algorithm is a general procedure to get maximum likelihood estimates if part of the observations on the variables of a network are missing. In this paper a stochastic version of the algorithm is adapted to probabilistic neural networks describing the associative dependency of variables. These networks have a proba­ bility distribution, which is a special case of the distribution generated by proba­ bilistic inference networks. Hence both types of networks can be combined al­ lowing to integrate probabilistic rules as well as unspecified associations in a sound way. The resulting network may have a number of interesting features including cycles of probabilistic rules, hidden 'un­ observable' variables, and uncertain and contradictory evidence.
Integrating Probabilistic Rules into Neural Networks: A Stochastic EM Learning Algorithm

So-called combined approaches answer a conjunctive query over a description logic ontology in three steps: first, they materialise certain consequences of the ontology and the data; second, they evaluate the query over the data; and third, they filter the result of the second phase to eliminate unsound answers. Such approaches were developed for various members of the DL-Lite and the EL families of languages, but none of them can handle ontologies containing nominals. In our work, we bridge this gap and present a combined query answering approach for ELHO ⊥—a logic that contains all features of the OWL 2 EL standard apart from transitive roles and complex role inclusions. This extension is nontrivial because nominals require equality reasoning, which introduces complexity into the first and the third step. Our empirical evaluation suggests that our technique is suitable for practical application, and so it provides a practical basis for conjunctive query answering in a large fragment of OWL 2 EL.
Introducing Nominals to the Combined Query Answering Approaches for EL

The weighted Maximum Satisfiability problem (weighted MAX-SAT) is a NP-hard problem with numerous applications arising in artificial intelligence. As an efficient tool for heuristic design, the backbone has been applied to heuristics design for many NP-hard problems. In this paper, we investigated the computational complexity for retrieving the backbone in weighted MAX-SAT and developed a new algorithm for solving this problem. We showed that it is intractable to retrieve the full backbone under the assumption that NP P  . Moreover, it is intractable to retrieve a fixed fraction of the backbone as well. And then we presented a backbone guided local search (BGLS) with Walksat operator for weighted MAX-SAT. BGLS consists of two phases: the first phase samples the backbone information from local optima and the backbone phase conducts local search under the guideline of backbone. Extensive experimental results on the benchmark showed that BGLS outperforms the existing heuristics in both solution quality and runtime.

Approximating the Backbone in the Weighted Maximum Satisfiability Problem