Abstract

We design ecient on-line algorithms that predict nearly as well as the best pruning of a planar decision graph. We assume that the graph has no cycles. As in the previous work on decision trees, we implicitly maintain one weight for each of the prunings (exponentially many). The method works for a large class of algorithms that update its weights multiplicatively. It can also be used to design algorithms that predict nearly as well as the best convex combination of prunings. 1 Introduction Decision trees are widely used in Machine Learning. Frequently a large tree is produced initially and then this tree is pruned for the purpose of obtaining a better predictor. A pruning is produced by deleting some nodes and with them all their successors. Although there are exponentially many prunings, a recent method developed in coding theory [WST95] and machine learning [Bun92] makes it possible to (implicitly) maintain one weight per pruning. In particular Helmbold and Schapire [HS97] use this m...

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