Contrast response function estimation with nonparametric Bayesian active learning

Dom C.P. Marticorena, Quinn Wai Wong, Jake Browning, Ken Wilbur, Samyukta Jayakumar, Pinakin Gunvant Davey, Aaron R. Seitz, Jacob R. Gardner, Dennis L. Barbour

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number6
Pages (from-to)1-18
Number of pages18
JournalJournal of Vision
Issue number1
StatePublished - 2024


  • active learning
  • bayesian modeling
  • contrast sensitivity
  • machine learning
  • psychophysics


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