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Learning predictive models from small high-dimensional data sets is a keyproblem in high-dimensional statistics. Expert knowledge elicitation can help,and a strong line of work focuses on directly eliciting informative priordistributions for parameters. This either requires considerable statisticalexpertise or is laborious, as the emphasis has been on accuracy and not onefficiency of the process. Another line of work queries about importance offeatures one at a time, assuming them to be independent and hence missingcovariance information. In contrast, we propose eliciting expert knowledgeabout pairwise feature similarities, to borrow statistical strength in thepredictions, and using sequential decision making techniques to minimize theeffort of the expert. Empirical results demonstrate improvement in predictiveperformance on both simulated and real data, in high-dimensional linearregression tasks, where we learn the covariance structure with a Gaussianprocess, based on sequential elicitation.

Human-in-the-loop Active Covariance Learning for Improving Prediction in Small Data Sets