Gaussian Process Conjoint Analysis for Adaptive Marginal Effect Estimation

Choice-based conjoint analysis is an essential tool for learning the marginal effects of multidimensional explanatory features on preferences. However, existing marginal effect models rely on either non-parametric estimators that generalize poorly to individualized effects, or linear latent utility that completely ignores possible high-order interactions. We introduce Gaussian process conjoint analysis (GPCA) for learning marginal effects from observed choices as the first-order derivatives of the unknown systems. We also propose Gaussian mixture approximation for the predictive distributions of marginal effects that facilitates downstream tasks such as adaptive experimentation. Through synthetic data, we show GPCA could achieve more precise estimation of marginal effects and higher efficiency of effect estimation using adaptive experimentation.