A Statistical Learning Theory Approach for the Analysis of the Trade-off Between Sample Size and Precision in Truncated Ordinary Least Squares

This chapter deals with linear regression problems for which one has the possibility of varying the supervision cost per example, by controlling the conditional variance of the output given the feature vector. For a fixed upper bound on the total available supervision cost, the trade-off between the number of training examples and their precision of supervision is investigated, using a nonasymptotic data-independent bound from the literature in statistical learning theory. This bound is related to the truncated output of the ordinary least squares regression algorithm. The results of the analysis are also compared theoretically with the ones obtained in a previous work, based on a large-sample approximation of the untruncated output of ordinary least squares. Advantages and disadvantages of the investigated approach are discussed.