We introduce a new approach to model selection that performs better than the standard complexitypenalization and hold-out error estimation techniques in many cases. The basic idea is to exploit the intrinsic metric structure of a hypothesis space, as determined by the natural distribution of unlabeled training patterns, and use this metric as a reference to detect whether the empirical error estimates derived from a small (labeled) training sample can be trusted in the region around an empirically optimal hypothesis. Using simple metric intuitions we develop new geometric strategies for detecting overfitting and performing robust yet responsive model selection in spaces of candidate functions. These new metric-based strategies dramatically outperform previous approaches in experimental studies of classical polynomial curve fitting. Moreover, the technique is simple, efficient, and can be applied to most function learning tasks. The only requirement is access to an auxiliary collection ...

: We investigate the structure of model selection problems via the bias/variance decomposition. In particular, we characterize the essential structure of a model selection task by the bias and variance profiles it generates over the sequence of hypothesis classes. This leads to a new understanding of complexity-penalization methods: First, the penalty terms in effect postulate a particular profile for the variances as a function of model complexity--- if the postulated and true profiles do not match, then systematic under-fitting or over-fitting results, depending on whether the penalty terms are too large or too small. Second, it is usually best to penalize according to the true variances of the task, and therefore no fixed penalization strategy is optimal across all problems. We then use this bias/variance characterization to identify the notion of easy and hard model selection problems. In particular, we show that if the variance profile grows too rapidly in relation to the biases t...

We discuss the implications of Holte's recentlypublished article, which demonstrated that on the most commonly used data very simple classification rules are almost as accurate as decision trees produced by Quinlan's C4.5. We consider, in particular, what is the significance of Holte's results for the future of top-down induction of decision trees. To an extent, Holte questioned the sense of further research on multilevel decision tree learning. We go in detail through all the parts of Holte's study. We try to put the results into perspective. We argue that the (in absolute terms) small difference in accuracy between 1R and C4.5 that was witnessed by Holte is still significant. We claim that C4.5 possesses additional accuracy-related advantages over 1R. In addition we discuss the representativeness of the databases used by Holte. We compare empirically the optimal accuracies of multilevel and one-level decision trees and observe some significant differences. We point out several defici...

Post pruning of decision trees has been a successful approach in many real-world experiments, but over all possible concepts it does not bring any inherent improvement to an algorithm's performance. This work explores how a PAC-proven decision tree learning algorithm fares in comparison with two variants of the normal top-down induction of decision trees. The algorithm does not prune its hypothesis per se, but it can be understood to do pre-pruning of the evolving tree. We study a backtracking search algorithm, called Rank, for learning rank-minimal decision trees. Our experiments follow closely those performed by Schaffer [20]. They confirm the main findings of Schaffer: in learning concepts with simple description pruning works, for concepts with a complex description and when all concepts are equally likely pruning is injurious, rather than beneficial, to the average performance of the greedy topdown induction of decision trees. Pre-pruning, as a gentler technique, settles in the ...