Response Time Improves Choice Prediction and Function Estimation for
  Gaussian Process Models of Perception and Preferences
Michael Shvartsman Benjamin Letham Stephen Keeley
Models for human choice prediction in preference learning and psychophysics
often consider only binary response data, requiring many samples to accurately
learn preferences or perceptual detection thresholds. The response time (RT) to
make each choice captures additional information about the decision process,
however existing models incorporating RTs for choice prediction do so in fully
parametric settings or over discrete stimulus sets. This is in part because the
de-facto standard model for choice RTs, the diffusion decision model (DDM),
does not admit tractable, differentiable inference. The DDM thus cannot be
easily integrated with flexible models for continuous, multivariate function
approximation, particularly Gaussian process (GP) models. We propose a novel
differentiable approximation to the DDM likelihood using a family of known,
skewed three-parameter distributions. We then use this new likelihood to
incorporate RTs into GP models for binary choices. Our RT-choice GPs enable
both better latent value estimation and held-out choice prediction relative to
baselines, which we demonstrate on three real-world multivariate datasets
covering both human psychophysics and preference learning applications.