Bayesian adaptive estimation of high-dimensional psychometric functions: A particle filtering approach

Abstract

Many interesting stimulus spaces are high-dimensional. Exhaustively measuring perceptual decisions in these spaces is infeasible, creating the need for adaptive experimental methods that efficiently explore the space. Current adaptive methods are either not suited to classical, well characterized psychophysical tasks (e.g. Gibbs Sampling with People is not applicable to estimate multidimensional psychometric functions in binary response tasks) or do not scale well to more than 4 dimensions (e.g. QUEST+). Here, we propose a method that estimates the posterior distribution of a multidimensional (logistic) psychometric function with lapses. It selects the next stimulus in the experiment such that the expected information gain is maximized. We use a particle filtering approach to approximate the posterior distribution online. This allows us to update the posterior even for high-dimensional spaces fast enough to be feasible between trials (order of 1 sec). In simulations, we show that with this method the entropy decreases between two and three times faster than when sampling stimuli randomly for a 15-dimensional feature space (an 18-parameter psychometric function, with a 15-dimensional hyperplane, an intercept, lower and upper asymptotes). We have tested the algorithm in up to 50 dimensions and found that it is still fast and reliable. We validate the algorithm in a human experiment on facial gender categorization. We compute Active Appearance Model (AAM) features (around 500.000 dimensions) for faces of the Chicago Face Database, perform dimensionality reduction to 15 dimensions using PCA and then create a pool of new face images by morphing between faces in the 15-dimensional space. Human participants label the faces as “male” or “female”. As in the simulation we show that the adaptive method is at least twice as efficient as random sampling at minimizing the entropy. This method allows us to measure perceptual decision functions in stimulus spaces that were previously infeasible.