Synthetic Model Combination: An Instance-wise Approach to Unsupervised Ensemble Learning
Authors: Alex Chan, Mihaela van der Schaar

Consider making a prediction over new test data without any opportunity to learn from a training set of labelled data - instead given access to a set of expert models and their predictions alongside some limited information about the dataset used to train them. In scenarios from finance to the medical sciences, and even consumer practice, stakeholders have developed models on private data they either cannot, or do not want to, share. Given the value and legislation surrounding personal information, it is not surprising that only the models, and not the data, will be released - the pertinent question becoming: how best to use these models? Previous work has focused on global model selection or ensembling, with the result of a single final model across the feature space. Machine learning models perform notoriously poorly on data outside their training domain however, and so we argue that when ensembling models the weightings for individual instances must reflect their respective domains - in other words models that are more likely to have seen information on that instance should have more attention paid to them. We introduce a method for such an instance-wise ensembling of models, including a novel representation learning step for handling sparse high-dimensional domains. Finally, we demonstrate the need and generalisability of our method on classical machine learning tasks as well as highlighting a real world use case in the pharmacological setting of vancomycin precision dosing.