Learning conditional probability tables of large Bayesian Networks (BNs) with hidden nodes using the Expectation Maximization algorithm is heavily computationally intensive. There are at least two bottlenecks, namely the potentially huge data set size and the requirement for computation and memory resources. This work applies the distributed computing framework MapReduce to Bayesian parameter learning from complete and incomplete data. We formulate both traditional parameter learning (complete data) and the classical Expectation Maximization algorithm (incomplete data) within the MapReduce framework. Analytically and experimentally we analyze the speed-up that can be obtained by means of MapReduce. We present the details of our Hadoop implementation, report speed-ups versus the sequential case, and compare various Hadoop configurations for experiments with Bayesian networks of different sizes and structures. For Bayesian networks with large junction trees, we surprisingly find that MapReduce can give a speed-up compared to the sequential Expectation Maximization algorithm for learning from 20 cases or fewer. The benefit of MapReduce for learning various Bayesian networks is investigated on data sets with up to 1,000,000 records.

Ant colony optimization (ACO) has been proved to be one of the best performing algorithms for NP-hard problems as TSP. The volatility rate of pheromone trail is one of the main parameters in ACO algorithms. It is usually set experimentally in the literatures for the application of ACO. The present paper first proposes an adaptive strategy for the volatility rate of pheromone trail according to the quality of the solutions found by artificial ants. Second, the strategy is combined with the setting of other parameters to form a new ACO method. Then, the proposed algorithm can be proved to converge to the global optimal solution. Finally, the experimental results of computing traveling salesman problems and film-copy deliverer problems also indicate that the proposed ACO approach is more effective than other ant methods and non-ant methods

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