Definition: 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.
Input: 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