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We consider multi-label classification where the goal is to annotate eachdata point with the most relevant $\textit{subset}$ of labels from an extremelylarge label set. Efficient annotation can be achieved with balanced treepredictors, i.e. trees with logarithmic-depth in the label complexity, whoseleaves correspond to labels. Designing prediction mechanism with such trees forreal data applications is non-trivial as it needs to accommodate sendingexamples to multiple leaves while at the same time sustain high predictionaccuracy. In this paper we develop the LdSM algorithm for the construction andtraining of multi-label decision trees, where in every node of the tree weoptimize a novel objective function that favors balanced splits, maintains highclass purity of children nodes, and allows sending examples to multipledirections but with a penalty that prevents tree over-growth. Each node of thetree is trained once the previous node is completed leading to a streamingapproach for training. We analyze the proposed objective theoretically and showthat minimizing it leads to pure and balanced data splits. Furthermore, we showa boosting theorem that captures its connection to the multi-labelclassification error. Experimental results on benchmark data sets demonstratethat our approach achieves high prediction accuracy and low prediction time andposition LdSM as a competitive tool among existing state-of-the-art approaches.

LdSM: Logarithm-depth Streaming Multi-label Decision Trees