Logarithmic Time Online Multiclass prediction Logarithmic Time Online Multiclass prediction
Paper summary This paper proposes a novel online algorithm for constructing a multiclass classifier that enjoys a time complexity logarithmic in the number of classes k. This is done by constructing online a decision tree which locally maximizes an appropriate novel objective function, which measures the quality of a tree according to a combined "balancedness" and "purity" score. A theoretical analysis (of a probably intractable algorithm) is provided via a boosting argument (assuming weak learnability), essentially extending the work of Kearns and Mansour (1996) \cite{conf/stoc/KearnsM96} to the multiclass setup. A concrete algorithm is given to a relaxed problem (but see below) without any guarantees, but quite simple, natural and interesting.

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