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Methods for Discovering and Analysis of Regularities Systems - Approach based on Optimal Partitioning of Explanatory Variables Space

The goal of discussed Optimal valid partitioning (OVP) method is discovering of regularities describing effect of explanatory variables on outcome value. OVP method is based on searching partitions of explanatory variables space with best possible separation of objects with different levels of outcome variable. Optimal partitions are searched inside several previously defined families by empirical (training) datasets. Random permutation tests are used for assessment of statistical validity and optimization of used models complexity. Additional mathematical tools that are aimed at improving performance of OVP approach are discussed. They include methods for evaluating structure of found regularities systems and estimating importance of explanatory variables. Paper also represents variant of OVP technique that allows to compare effects of explanatory variables on outcome in different groups of objects.