Contrast response function estimation with nonparametric Bayesian active learning

Abstract

Multidimensional psychometric functions can typically be estimated nonparametrically for greater accuracy or parametrically for greater efficiency. By recasting the estimation problem from regression to classification, however, powerful machine learning tools can be leveraged to provide an adjustable balance between accuracy and efficiency. Contrast sensitivity functions (CSFs) are behaviorally estimated curves that provide insight into both peripheral and central visual function. Because estimation can be impractically long, current clinical workflows must make compromises such as limited sampling across spatial frequency or strong assumptions on CSF shape. This article describes the development of the machine learning contrast response function (MLCRF) estimator, which quantifies the expected probability of success in performing a contrast detection or discrimination task. A machine learning CSF can then be derived from the MLCRF. Using simulated eyes created from canonical CSF curves and actual human contrast response data, the accuracy and efficiency of the machine learning contrast sensitivity function (MLCSF) was evaluated to determine its potential utility for research and clinical applications. With stimuli selected randomly, the MLCSF estimator converged slowly toward ground truth. With optimal stimulus selection via Bayesian active learning, convergence was nearly an order of magnitude faster, requiring only tens of stimuli to achieve reasonable estimates. Inclusion of an informative prior provided no consistent advantage to the estimator as configured. MLCSF achieved efficiencies on par with quickCSF, a conventional parametric estimator, but with systematically higher accuracy. Because MLCSF design allows accuracy to be traded off against efficiency, it should be explored further to uncover its full potential.

Active Mutual Conjoint Estimation of Multiple Contrast Sensitivity Functions

“…In experiment 1, ground truth CSF models for four canonical phenotypes were constructed from idealized threshold curves (Kalloniatis & Luu, 1995; Marticorena et al, 2024). In experiment 2, ground truth CSF models were drawn from 8 experimental configurations for 9 individuals (Jigo & Carrasco, 2020).…”

“…For first-generation estimators with models marked the kernel enforces strict linearity in contrast and smoothness in spatial frequency: Note that the specific hyperparameters in this kernel differ from those in the first-generation kernel documented in (Marticorena et al, 2024), but the kernel itself is identical. For second-generation estimators the kernel encourages linearity and smoothness in contrast and smoothness only in spatial frequency: For first-generation estimators the acquisition function maximizes information gain: For second-generation estimators the acquisition function includes a sampling density consideration: where is the inverse cumulative distribution function, n is a percentile constant, and D ( x * , x ) is the distance between each candidate point x * and its corresponding nearest point in the previously collected data X .…”

“…To accommodate an assumption of local smoothness in spatial frequency, a squared exponential kernel was originally used, operating on spatial frequency alone: Where s represents a scaling factor and l represents a length constant. The overall kernel for the first-generation MLCRF was a simple linear combination of the constituent kernels (Marticorena et al, 2024): Performance of the original MLCSF estimator indicated that while overall accuracy was good, threshold values at very high spatial frequencies were less accurate than average for some phenotypes. In particular, the CSF’s with very steep falloffs at high spatial frequencies required shorter squared exponential length constants to fit accurately, leading to inappropriate rippling at lower spatial frequencies, thus lowering overall accuracy.…”

“…As in previous work, the conceptual starting point for a machine learning CSF estimation procedure is a probabilistic classifier that separates two regions in feature space designated “success” and “failure” (Marticorena et al, 2024; Song et al, 2015). Success for a contrast detection task is defined as a button press immediately following the delivery of a Gabor stimulus of a given spatial frequency and contrast.…”

Multi-species numerical validation of an efficient algorithm for auditory brainstem response hearing threshold estimation

“…Adaptive sampling strategies that update stimulus selection schemes has been used throughout psychophysics, in particular, for vision (see e.g., Watson, 2017, Song et al, 2018, Lesmes et al, 2006, Lesmes et al, 2010, Dorr et al, 2017, and Marticorena et al, 2024). Bayesian adaptive sampling has also been successfully applied in the auditory domain.…”