Non-enumerative Cross Validation for the Determination of Structural Parameters in Feature-Selective SVMs

The relational approach to dependency estimation entails the selection of a sufficiently compact \´relevance\´ subset of training-set objects with which any newly occurring object may be compared in order to estimate its hidden target characteristics. If several comparison modalities are available, a \´relevance\´ subset of these may additionally have to be chosen via an appropriate selection criterion. Typically, the level of selectivity will constitute a free parameter, and in traditional approaches, multiple training repetitions would be required to determine this value via cross-validation. To avoid this, we seek to algorithmically emulate the cross-validation process using conservative assumptions as to the nature of the unknown probability distribution that produced the training set. We term this approach \´non-enumerative cross-validation\´, and demonstrate that the classical Akaike Information Criterion is a specific case of it under naive assumptions. The application of this non-enumerative cross-validation strategy is demonstrated on the standard multikernel data set, "chicken-pieces", treated from the perspective of relational discriminant analysis.