  We propose Preferential MoE, a novel human-ML mixture-of-experts model that
augments human expertise in decision making with a data-based classifier only
when necessary for predictive performance. Our model exhibits an interpretable
gating function that provides information on when human rules should be
followed or avoided. The gating function is maximized for using human-based
rules, and classification errors are minimized. We propose solving a coupled
multi-objective problem with convex subproblems. We develop approximate
algorithms and study their performance and convergence. Finally, we demonstrate
the utility of Preferential MoE on two clinical applications for the treatment
of Human Immunodeficiency Virus (HIV) and management of Major Depressive
Disorder (MDD).
