Psychometric functions typically characterize binary sensory decisions along a single stimulus dimension. However, real-life sensory tasks vary along a greater variety of dimensions (e.g. color, contrast and luminance for visual stimuli). Approaches to characterizing high-dimensional sensory spaces either require strong parametric assumptions about these additional contextual dimensions, or fail to leverage known properties of classical psychometric curves. We overcome both limitations by introducing a semi-parametric model of sensory discrimination that applies traditional psychophysical models along a stimulus intensity dimension, but puts Gaussian process (GP) priors on the parameters of these models with respect to the remaining dimensions. By combining the flexibility of the GP with the deep literature on parametric psychophysics, our semi-parametric models achieve good performance with much less data than baselines on both synthetic and real-world, high-dimensional psychophysics datasets. We additionally show strong performance in a Bayesian active learning setting, and present a novel active learning paradigm for the semi-parametric model.

Level set estimation (LSE) is the problem of identifying regions where an unknown function takes values above or below a specified threshold. Active sampling strategies for efficient LSE have primarily been studied in continuous-valued functions. Motivated by applications in human psychophysics where common experimental designs produce binary responses, we study LSE active sampling with Bernoulli outcomes. With Gaussian process classification surrogate models, the look-ahead model posteriors used by state-of-the-art continuous-output methods are intractable. However, we derive analytic expressions for look-ahead posteriors of sublevel set membership, and show how these lead to analytic expressions for a class of look-ahead LSE acquisition functions, including information-based methods. Benchmark experiments show the importance of considering the global look-ahead impact on the entire posterior. We demonstrate a clear benefit to using this new class of acquisition functions on benchmark problems, and on a challenging real-world task of estimating a high-dimensional contrast sensitivity function.