On Mean Squared Error of Hierarchical Estimator

Stanisław Brodowski


In this paper a new theorem about components of the mean squared error of Hierarchical Estimator is presented. Hierarchical Estimator is a machine learning meta-algorithm that attempts to build, in an incremental and hierarchical manner, a tree of relatively simple function estimators and combine their results to achieve better accuracy than any of the individual ones. The components of the error of a node of such a tree are: weighted mean of the error of the estimator in a node and the errors of children, a non-positive term that descreases below 0 if children responses on any example dier and a term representing relative quality of an internal weighting function, which can be conservatively kept at 0 if needed. Guidelines for achieving good results based on the theorem are brie discussed.

Słowa kluczowe: Hierarchial Estimator, hierarchical model, regression, function approximation, error, theorem

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