Gibbs Sampling with People

A core problem in cognitive science and machine learning is to understand how humans derive semantic representations from perceptual objects, such as color from an apple, pleasantness from a musical chord, or trustworthiness from a face. Markov Chain Monte Carlo with People (MCMCP) is a prominent method for studying such representations, in which participants are presented with binary choice trials constructed such that the decisions follow a Markov Chain Monte Carlo acceptance rule. However, MCMCP's binary choice paradigm generates relatively little information per trial, and its local proposal function makes it slow to explore the parameter space and find the modes of the distribution. Here we therefore generalize MCMCP to a continuous-sampling paradigm, where in each iteration the participant uses a slider to continuously manipulate a single stimulus dimension to optimize a given criterion such as 'pleasantness'. We formulate both methods from a utility-theory perspective, and show that the new method can be interpreted as 'Gibbs Sampling with People' (GSP). Further, we introduce an aggregation parameter to the transition step, and show that this parameter can be manipulated to flexibly shift between Gibbs sampling and deterministic optimization. In an initial study, we show GSP clearly outperforming MCMCP; we then show that GSP provides novel and interpretable results in three other domains, namely musical chords, vocal emotions, and faces. We validate these results through large-scale perceptual rating experiments. The final experiments combine GSP with a state-of-the-art image synthesis network (StyleGAN) and a recent network interpretability technique (GANSpace), enabling GSP to efficiently explore high-dimensional perceptual spaces, and demonstrating how GSP can be a powerful tool for jointly characterizing semantic representations in humans and machines.