Conditional Probability Tree Estimation Analysis and Algorithms

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 106 labels.

Authors

• Alina Beygelzimer
• John Langford 0001
• Yury Lifshits
• Gregory B. Sorkin
• Alexander L. Strehl

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