Calculate Joint Probability Distribution of Steady Directed Cyclic Graph with Local Data and Domain Casual Knowledge

It is desired to obtain the joint probability distribution(JPD) over a set of random variables with local data, so as to avoid the hard work to collect statistical data in the scale of all variables. A lot of work has been done when all variables are in a known directed acyclic graph(DAG). However, steady directed cyclic graphs(DCGs) may be involved when we simply combine modules containing local data together, where a module is composed of a child variable and its parent variables. So far, the physical and statistical meaning of steady DCGs remain unclear and unsolved. This paper illustrates the physical and statistical meaning of steady DCGs, and presents a method to calculate the JPD with local data, given that all variables are in a known single-valued Dynamic Uncertain Causality Graph(S-DUCG), and thus defines a new Bayesian Network with steady DCGs. The so-called single-valued means that only the causes of the true state of a variable are specified, while the false state is the complement of the true state.

Measuring air traffic complexity based on small samples

Air traffic complexity is an objective metric for evaluating the operational condition of the airspace. It has several applications, such as airspace design and traffic flow management.Therefore, identifying a reliable method to accurately measure traffic complexity is important. Considering that many factors correlate with traffic complexity in complicated nonlinear ways,researchers have proposed several complexity evaluation methods based on machine learning models which were trained with large samples. However, the high cost of sample collection usually results in limited training set. In this paper, an ensemble learning model is proposed for measuring air traffic complexity within a sector based on small samples. To exploit the classification information within each factor, multiple diverse factor subsets（FSSs） are generated under guidance from factor noise and independence analysis. Then, a base complexity evaluator is built corresponding to each FSS. The final complexity evaluation result is obtained by integrating all results from the base evaluators. Experimental studies using real-world air traffic operation data demonstrate the advantages of our model for small-sample-based traffic complexity evaluation over other stateof-the-art methods.