Conditional probability tree estimation analysis and algorithms

  • Authors:
  • Alina Beygelzimer;John Langford;Yuri Lifshits;Gregory Sorkin;Alex Strehl

  • Affiliations:
  • IBM Research;Yahoo! Research;Yahoo! Research;IBM Research;Yahoo! Research

  • Venue:
  • UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
  • Year:
  • 2009

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Abstract

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.