In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

We study the problem of multiclass classification with an extremely large number<lb>of classes, with the goal of obtaining train and test time complexity logarithmic<lb>in the number of classes. We develop top-down tree construction approaches for<lb>constructing logarithmic depth trees. On the theoretical front, we formulate a new<lb>objective function, which is optimized at each node of the tree and creates dy-<lb>namic partitions of the data which are both pure (in terms of class labels) and<lb>balanced. We demonstrate that under favorable conditions, we can construct loga-<lb>rithmic depth trees that have leaves with low label entropy. However, the objective<lb>function at the nodes is challenging to optimize computationally. We address the<lb>empirical problem with a new online decision tree construction procedure. Exper-<lb>iments demonstrate that this online algorithm quickly achieves small error rates<lb>relative to more common O(k) approaches and simultaneously achieves signif-<lb>icant improvement in test error compared to other logarithmic training time ap-<lb>proaches.
Logarithmic Time Online Multiclass prediction