Bayesian active probabilistic classification for psychometric field estimation

Abstract

Psychometric functions are typically estimated by fitting a parametric model to categorical subject responses. Procedures to estimate unidimensional psychometric functions (i.e., psychometric curves) have been subjected to the most research, with modern adaptive methods capable of quickly obtaining accurate estimates. These capabilities have been extended to some multidimensional psychometric functions (i.e., psychometric fields) that are easily parameterizable, but flexible procedures for general psychometric field estimation are lacking. This study introduces a nonparametric Bayesian psychometric field estimator operating on subject queries sequentially selected to improve the estimate in some targeted way. This estimator implements probabilistic classification using Gaussian processes trained by active learning. The accuracy and efficiency of two different actively sampled estimators were compared to two non-actively sampled estimators for simulations of one of the simplest psychometric fields in common use: the pure-tone audiogram. The actively sampled methods achieved estimate accuracy equivalent to the non-actively sampled methods with fewer observations. This trend held for a variety of audiogram phenotypes representative of the range of human auditory perception. Gaussian process classification is a general estimation procedure capable of extending to multiple input variables and response classes. Its success with a two-dimensional psychometric field informed by binary subject responses holds great promise for extension to complex perceptual models currently inaccessible to practical estimation.

Conjoint psychometric field estimation for bilateral audiometry

“…This method can rapidly identify a class boundary for a target function of interest, but because uncertainty sampling attempts to query exactly where p(y = 1|x) = 0.5 (in the binary case), the model underexplores the input space. In the context of psychometric fields, the transition from one class to another (i.e., the psychometric spread) is not as readily estimated in this case (Song et al, 2018).…”

“…Three different pairings of ground-truth audiograms (normal-normal, normal-pathologic, and pathologic-pathologic) therefore reflect conditions with varying putative estimation benefit from considering both ears conjointly. These canonical audiogram phenotypes have been used previously to evaluate the accuracy (Song et al, 2017) and efficiency (Song et al, 2018) of disjoint machine-learning audiometry.…”

“…An alternative approach to psychometric field estimation recasts the key inference step from parametric logistic regression to nonparametric or semiparametric probabilistic classification (Song, Garnett, & Barbour, 2017;Song, Sukesan, & Barbour, 2018). This framework naturally scales to multiple input dimensions, provides great flexibility for estimating a wide variety of functions, and sets the stage for other novel theoretical advances.…”

“…This framework naturally scales to multiple input dimensions, provides great flexibility for estimating a wide variety of functions, and sets the stage for other novel theoretical advances. One such advance involves actively learning which stimuli would be most valuable to deliver in order to rapidly converge onto an accurate estimate (Song et al, 2018;Song et al, 2015b). This procedure, referred to as active testing, yields estimation efficiencies at least as high as those of adaptive parametric testing.…”

“…Estimating full psychometric field audiograms at the same frequency resolution using serial logistic regression would require up to 20 h and is rarely performed for obvious reasons (Allen & Wightman, 1994). An appropriately designed active learning procedure can estimate a full audiogram in less time than is required to estimate a threshold audiogram using conventional methods (Song et al, 2018;Song et al, 2015b).…”