Conditional probability tree estimation analysis and algorithms
A Beygelzimer, J Langford, Y Lifshits, G Sorkin…�- arXiv preprint arXiv�…, 2014 - arxiv.org
A Beygelzimer, J Langford, Y Lifshits, G Sorkin, AL Strehl
arXiv preprint arXiv:1408.2031, 2014•arxiv.orgWe 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�…
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�…
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.
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