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Conditional probability tree estimation analysis and algorithms

By Alina Beygelzimer, John Langford, Yuri Lifshits, Gregory B. Sorkin and Alex Strehl

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 $10^6$ labels

Topics: QA75 Electronic computers. Computer science
Year: 2009
OAI identifier: oai:eprints.lse.ac.uk:35637
Provided by: LSE Research Online
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