Shapley Chains: Extending Shapley Values to Classifier Chains

In spite of increased attention on explainable machine learning models, explaining multi-output predictions has not yet been extensively addressed. Methods that use Shapley values to attribute feature contributions to the decision making are one of the most popular approaches to explain local individual and global predictions. By considering each output separately in multi-output tasks, these methods fail to provide complete feature explanations. We propose Shapley Chains to overcome this issue by including label interdependencies in the explanation design process. Shapley Chains assign Shapley values as feature importance scores in multi-output classification using classifier chains, by separating the direct and indirect influence of these feature scores. Compared to existing methods, this approach allows to attribute a more complete feature contribution to the predictions of multi-output classification tasks. We provide a mechanism to distribute the hidden contributions of the outputs with respect to a given chaining order of these outputs. Moreover, we show how our approach can reveal indirect feature contributions missed by existing approaches. Shapley Chains help to emphasize the real learning factors in multi-output applications and allows a better understanding of the flow of information through output interdependencies in synthetic and real-world datasets.