Conditional Probability Tree Estimation Analysis and Algorithms - Beygelzimer, Alina; Langford, John; Lifshits, Yuri; Sorkin, Gregory; Strehl, Alex (Twenty-Fifth Conference on Uncertainty in Artificial Intelligence, 2014)
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.
See related paper from June 2009