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Artificial intelligence (AI) and machine learning models are being increasingly deployed in real-world applications. In many of these applications, there is strong motivation to develop hybrid systems in which humans and AI algorithms can work together, leveraging their complementary strengths and weaknesses. We develop a Bayesian framework for combining the predictions and different types of confidence scores from humans and machines. The framework allows us to investigate the factors that influence complementarity, where a hybrid combination of human and machine predictions leads to better performance than combinations of human or machine predictions alone. We apply this framework to a large-scale dataset where humans and a variety of convolutional neural networks perform the same challenging image classification task. We show empirically and theoretically that complementarity can be achieved even if the human and machine classifiers perform at different accuracy levels as long as these accuracy differences fall within a bound determined by the latent correlation between human and machine classifier confidence scores. In addition, we demonstrate that hybrid human–machine performance can be improved by differentiating between the errors that humans and machine classifiers make across different class labels. Finally, our results show that eliciting and including human confidence ratings improve hybrid performance in the Bayesian combination model. Our approach is applicable to a wide variety of classification problems involving human and machine algorithms. 

An increasingly common use case for machine learning models is augmenting the abilities of human decision makers. For classification tasks where neither the human nor model are perfectly accurate, a key step in obtaining high performance is combining their individual predictions in a manner that leverages their relative strengths. In this work, we develop a set of algorithms that combine the probabilistic output of a model with the class-level output of a human. We show theoretically that the accuracy of our combination model is driven not only by the individual human and model accuracies, but also by the model's confidence. Empirical results on image classification with CIFAR-10 and a subset of ImageNet demonstrate that such human-model combinations consistently have higher accuracies than the model or human alone, and that the parameters of the combination method can be estimated effectively with as few as ten labeled datapoints.