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

## TL;DR

This paper introduces a human-in-the-loop method for efficiently eliciting expert knowledge about feature similarities to improve covariance estimation and prediction accuracy in small, high-dimensional datasets.

## Contribution

It proposes a novel sequential decision-making approach for eliciting pairwise feature similarities, enhancing covariance learning and predictive performance in small data settings.

## Key findings

- Improved predictive accuracy on simulated data
- Enhanced performance on real high-dimensional datasets
- Efficient elicitation process reduces expert effort

## Abstract

Learning predictive models from small high-dimensional data sets is a key problem in high-dimensional statistics. Expert knowledge elicitation can help, and a strong line of work focuses on directly eliciting informative prior distributions for parameters. This either requires considerable statistical expertise or is laborious, as the emphasis has been on accuracy and not on efficiency of the process. Another line of work queries about importance of features one at a time, assuming them to be independent and hence missing covariance information. In contrast, we propose eliciting expert knowledge about pairwise feature similarities, to borrow statistical strength in the predictions, and using sequential decision making techniques to minimize the effort of the expert. Empirical results demonstrate improvement in predictive performance on both simulated and real data, in high-dimensional linear regression tasks, where we learn the covariance structure with a Gaussian process, based on sequential elicitation.