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• Mutual Constrained Independence (MCI) is a novel notion in probability theory. • MCI allows to objectively estimate frequencies of itemsets given certain constraints. • The mathematical results for the existence and characterization of MCI are proven. • A link between MCI models and Maximum Entropy models is established. • A method for computing MCI models based on algebraic geometry is presented. Dealing with redundancy is one of the main challenges in frequency based data mining and itemset mining in particular. To tackle this issue in the most objective possible way, we introduce the theoretical bases of a new probabilistic concept: Mutual constrained independence (MCI). Thanks to this notion, we describe a MCI model for the frequencies of all itemsets which is the least binding in terms of model hypotheses defined by the knowledge of the frequencies of some of the itemsets. We provide a method for computing MCI models based on algebraic geometry. We establish the link between MCI models and a class of MaxEnt models which has already known to be used in pattern mining. As such, our research presents further insight on the nature of such models and an entirely novel approach for computing them. [ABSTRACT FROM AUTHOR]

Purpose – The paper attempts to establish a two-dimension frame to analyze dynamic supplier risks of large-scale and complex equipment and study the probability distribution of the occurring risks. Design/methodology/approach – Starting from the dynamic and correlated supplier risks of large-scale and complex equipment, a two-dimension frame to analyze these risks is established. A maximum entropy model is also built to research the probability distribution of the risks; then, K-T conditions are proved to solve the model. A real case is also studied in the last part of the paper. Findings – The results are convincing: in order to analyze the supplier risk dynamically of large-scale and complex equipment development project, a two-dimension analysis frame is established and a maximum entropy model is worked out. The case study shows that they are valuable. Practical implications – The two-dimension frame gives a new viewpoint for risk management, but also the maximum entropy model supplies a valuable method for risk management. Originality/value – The paper succeeds in creating a dynamic analysis frame to study risks and building a new method to research the disciplines of the dynamic risks. [ABSTRACT FROM AUTHOR]