Regression with n → 1 by expert knowledge elicitation

We consider regression under the "extremely small n large p" condition, where the number of samples n is so small compared to the dimensionality p that predictors cannot be estimated without prior knowledge. This setup occurs in personalized medicine, for instance, when predicting treatment outcomes for an individual patient based on noisy high-dimensional genomics data. A remaining source of information is expert knowledge, which has received relatively little attention in recent years. We formulate the inference problem of asking expert feedback on features on a budget, propose an elicitation strategy for a simple "small n" setting, and derive conditions under which the elicitation strategy is optimal. Experiments on simulated experts, both on synthetic and genomics data, demonstrate that the proposed strategy can drastically improve prediction accuracy.