We consider the problem of estimating the conditional probability of a label in time O(log n), where n is the number of possible labels. We analyze a natural reduction of this problem to a set of binary regression problems organized in a tree structure, proving a regret bound that scales with the depth of the tree. Motivated by this analysis, we propose the first online algorithm which provably constructs a logarithmic depth tree on the set of labels to solve this problem. We test the algorithm empirically, showing that it works succesfully on a dataset with roughly 10 6 labels.
The filter tree and the conditional probability tree REF for example are consistent reduction of multiclass problems to binary that learn a tree of classifiers.
Conditional Probability Tree Estimation Analysis and Algorithms
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Computer Science Mathematics