Regression Under Human Assistance

Decisions are increasingly taken by both humans and machine learning models. However, machine learning models are currently trained for full automation-they are not aware that some of the decisions may still be taken by humans. In this paper, we take a first step towards making machine learning models aware of the presence of human decision-makers. More specifically, we first introduce the problem of ridge regression under human assistance and show that it is NP-hard. Then, we derive an alternative representation of the corresponding objective function as a difference of nondecreasing submodular functions. Building on this representation, we further show that the objective is nondecreasing and satisfies \xi-submodularity, a recently introduced notion of approximate submodularity. These properties allow simple and efficient greedy algorithm to enjoy approximation guarantees at solving the problem. Experiments on synthetic and real-world data from two important applications-medical diagnoses and content moderation-demonstrate that the greedy algorithm beats several competitive baselines.