Measuring the VC-dimension using optimized experimental design

VC-dimension is the measure of model complexity (capacity) used in VC-theor y. The knowledge of the VC-dimension of an estimator is necessary for rigor ous complexity control using analytic VC generalization bounds. Unfortunate ly, it is not possible to obtain the analytic estimates of the VC-dimension in most cases. Hence, a recent proposal is to measure the VC-dimension of an estimator experimentally by fitting the theoretical formula to a set of experimental measurements of the frequency of errors on artificially genera ted data sets of varying sizes (Vapnik, Levin, & Le Cun, 1994). However, it may be difficult to obtain an accurate estimate of the VC-dimension due to the variability of random samples in the experimental procedure proposed b y Vapnik et al. (1994). We address this problem by proposing an improved de sign procedure for specifying the measurement points (i.e., the sample size and the number of repeated experiments at a given sample size). Our approa ch leads to a nonuniform design structure as opposed to the uniform design structure used in the original article (Vapnik et al., 1994). Our simulatio n results show that the proposed optimized design structure leads to a more accurate estimation of the VC-dimension using the experimental procedure. The results also show that a more accurate estimation of VC-dimension leads to improved complexity control using analytic VC-generalization bounds and , hence, better prediction accuracy.