Predicting with Proxies: Transfer Learning in High Dimension

Predictive analytics is increasingly used to guide decision making in many applications. However, in practice, we often have limited data on the true predictive task of interest and must instead rely on more abundant data on a closely related proxy predictive task. For example, e-commerce platforms use abundant customer click data (proxy) to make product recommendations rather than the relatively sparse customer purchase data (true outcome of interest); alternatively, hospitals often rely on medical risk scores trained on a different patient population (proxy) rather than their own patient population (true cohort of interest) to assign interventions. Yet, not accounting for the bias in the proxy can lead to suboptimal decisions. Using real data sets, we find that this bias can often be captured by a sparse function of the features. Thus, we propose a novel two-step estimator that uses techniques from high-dimensional statistics to efficiently combine a large amount of proxy data and a small amount of true data. We prove upper bounds on the error of our proposed estimator and lower bounds on several heuristics used by data scientists; in particular, our proposed estimator can achieve the same accuracy with exponentially less true data (in the number of features d ). Finally, we demonstrate the effectiveness of our approach on e-commerce and healthcare data sets; in both cases, we achieve significantly better predictive accuracy as well as managerial insights into the nature of the bias in the proxy data.