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Non-Enumerative Cross Validation for the Choice of Structural Parameters in Feature-Selective Support Vector Machines

The relational approach to dependence estimation inevitably entails the necessity of choosing, at least, a sufficiently small relevance subset of training-set objects with which any newly occurring object will have to be compared for estimating its hidden target characteristic. If several comparison modalities are tentatively supposed by the observer, a relevance subset of them is to be additionally chosen. To avoid multiple training repetitions concerned with the traditional explicit cross-validation when adjusting the appropriate selectivity level, we consider a principle of mentally emulating the cross-validation process on the basis of quite lenient assumptions on the nature’s unknown probability distribution having produced the training set. We call this principle the hypothetical non-enumerative cross-validation, and show that the classical Akaike Information Criterion is a particular case of it under some especially naïve assumptions. The effectiveness of the non-enumerative cross-validation is demonstrated on the wellknown chicken-pieces data set treated from the viewpoint of relational discriminant analysis. Keywords—relational dependence estimation; relevance vector machine; support vector machine; feature selection; selectivity adjustment; Akaike information criterion; hypothetical crossvalidation; non-enumerative model verification