Set-valued prediction in hierarchical classification with constrained representation complexity

Thomas Mortier, Krzysztof Dembczynski, Eyke Hüllermeier, Willem Waegeman

Keywords: set-valued prediction, hierarchical multi-class classification, top-k, uncertainty

TL;DR: A new framework for set-valued prediction in hierarchical multi-class classification that restricts the semantic complexity of predictions.

Abstract: Set-valued prediction is a well-known concept in multi-class classification. When a classifier is uncertain about the class label for a test instance, it can predict a set of classes instead of a single class. In this paper, we focus on hierarchical multi-class classification problems, where valid sets (typically) correspond to internal nodes of the hierarchy. We argue that this is a very strong restriction, and we propose a relaxation by introducing the notion of representation complexity for a predicted set. In combination with probabilistic classifiers, this leads to a challenging inference problem for which specific combinatorial optimization algorithms are needed. We propose three methods and evaluate them on benchmark datasets: a naïve approach that is based on matrix-vector multiplication, a reformulation as a knapsack problem with conflict graph, and a recursive tree search method. Experimental results demonstrate that the last method is computationally more efficient than the other two approaches, due to a hierarchical factorization of the conditional class distribution.