Ranking

A multi-label classifier assigns a set of labels to each data object. A natural requirement in many end-use applications is that the classifier also provides a well-calibrated confidence (probability) to indicate the likelihood of the predicted set being correct; for example, an application may automate high-confidence predictions while manually verifying low-confidence predictions. The simplest multi-label classifier, called Binary Relevance (BR), applies one binary classifier to each label independently and takes the product of the individual label probabilities as the overall label-set probability (confidence). Despite its many known drawbacks, such as generating suboptimal predictions and poorly calibrated confidence scores, BR is widely used in practice due to its speed and simplicity. We seek in this work to improve both BR's confidence estimation and prediction through a post calibration and reranking procedure. We take the BR predicted set of labels and its product score as features, extract more features from the prediction itself to capture label constraints, and apply Gradient Boosted Trees (GB) as a calibrator to map these features into a calibrated confidence score. GB not only produces well-calibrated scores (aligned with accuracy and sharp), but also models label interactions, correcting a critical flaw in BR. We further show that reranking label sets by the new calibrated confidence makes accurate set predictions on par with state-of-the-art multi-label classifiers - yet calibrated, simpler, and faster.

Label ranking considers the problem of learning a mapping from instances to strict total orders over a predefined set of labels. In this paper, we present a framework for label ranking using a decomposition into a set of multiclass problems. Conceptually, our approach can be seen as a generalization of pairwise preference learning. In contrast to the latter, it allows for controlling the granularity of the decomposition, varying between binary preferences and complete rankings as extreme cases. It is specifically motivated by limitations of pairwise learning with regard to the minimization of certain loss functions. We discuss theoretical properties of the proposed method in terms of accuracy, error correction, and computational complexity. Experimental results are promising and indicate that improvements upon the special case of pairwise preference decomposition are indeed possible.