DFORD: Directional Feedback based Online Ordinal Regression Learning
This addresses a weakly supervised learning problem for ordinal regression tasks, offering an incremental improvement over existing methods.
The paper tackles ordinal regression with weak supervision by introducing directional feedback, where the learner only receives left/right hints about the true label, and proposes an online algorithm achieving O(log T) expected regret while performing comparably to full-information methods.
In this paper, we introduce directional feedback in the ordinal regression setting, in which the learner receives feedback on whether the predicted label is on the left or the right side of the actual label. This is a weak supervision setting for ordinal regression compared to the full information setting, where the learner can access the labels. We propose an online algorithm for ordinal regression using directional feedback. The proposed algorithm uses an exploration-exploitation scheme to learn from directional feedback efficiently. Furthermore, we introduce its kernel-based variant to learn non-linear ordinal regression models in an online setting. We use a truncation trick to make the kernel implementation more memory efficient. The proposed algorithm maintains the ordering of the thresholds in the expected sense. Moreover, it achieves the expected regret of $\mathcal{O}(\log T)$. We compare our approach with a full information and a weakly supervised algorithm for ordinal regression on synthetic and real-world datasets. The proposed approach, which learns using directional feedback, performs comparably (sometimes better) to its full information counterpart.