Paper:
On the Optimality of Classifier Chain for Multi-label Classification
To capture the interdependencies between labels in multi-label classification problems, classifier chain (CC) tries to take the multiple labels of each instance into account under a deterministic high-order Markov Chain model. Since its performance is sensitive to the choice of label order, the key issue is how to determine the optimal label order for CC. In this work, we first generalize the CC model over a random label order. Then, we present a theoretical analysis of the generalization error for the proposed generalized model. Based on our results, we propose a dynamic programming based classifier chain (CC-DP) algorithm to search the globally optimal label order for CC and a greedy classifier chain (CC-Greedy) algorithm to find a locally optimal CC. Comprehensive experiments on a number of real-world multi-label data sets from various domains demonstrate that our proposed CC-DP algorithm outperforms state-of-the-art approaches and the CCGreedy algorithm achieves comparable prediction performance with CC-DP.

Review:
The paper deals with the construction of optimal classifier chains for multi-label classification. The first part of the paper provides a bound on the error of the classifer chain in terms of the margins over the labels. This result is used in the second part to derive a DP and greedy algorithm. The experimental section shows that that the DP approach has the best results in 5 out of 8 datasets and the greedy approach in 1.Quality: The bound on error involves interesting ideas. Hence the paper scores high on quality.Clarity: The exposition is clear. The authors should address the following questions.1. The greedy approach performs better than DP on 2 out of 8 datasets. Some explanation will be helpful. 2. Comparison of actual runtimes of greedy vs DP will help.The paper has some typos. For example, line 313 should read "\gamma^1_i represents ..."Orginality: HighSignificance: The techniques used in the paper have theoretical significance. I have not seen many people using multilabel classification in practice.