Abstract
The learning curve serves as a crucial metric for assessing human performance in perceptual learning. It may encompass various component processes, including general learning, between-session forgetting or consolidation, and within-session rapid relearning and adaptation or deterioration. Typically, empirical learning curves are constructed by aggregating tens or hundreds of trials of data in blocks or sessions. Here, we devised three inference procedures for estimating the trial-by-trial learning curve based on the multi-component functional form identified in (Zhao et al., Journal of Vision 24(5):8, 1–22, 2024): general learning, between-session forgetting, and within-session rapid relearning and adaptation. These procedures include a Bayesian inference procedure (BIP) estimating the posterior distribution of parameters for each learner independently, and two hierarchical Bayesian models (HBMv and HBMc) computing the joint posterior distribution of parameters and hyperparameters at the population, subject, and test levels. The HBMv and HBMc incorporate variance and covariance hyperparameters, respectively, between and within subjects. We applied these procedures to data from two studies investigating the interaction between feedback and training accuracy in Gabor orientation identification across about 2000 trials spanning six sessions (Liu et al., Journal of Vision 10:29–29, 2010; Liu et al., Vision Research 61:15–24, 2012) and estimated the trial-by-trial learning curves at both the subject and population levels. The HBMc generated best fits to the data and the smallest 68.2% half-width credible interval of the learning curves compared to the BIP and HBMv. The HBMc with the multi-component functional form provides a general framework for trial-by-trial analysis of the component processes in perceptual learning and for predicting the learning curve in unmeasured time points.
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Data Availability
The data that support the findings of this study are available from the corresponding author upon request.
Source Code Availability
The source code is available upon reasonable request.
Notes
The test level is an essential component of the general HBM framework, enabling the modeling of repeated tests. We have retained it in the development to maintain continuity with our previous work and to enable researchers to fit and test the HBM using split data (e.g., interleaved staircases) in perceptual learning.
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This research was supported by the National Eye Institute (EY017491).
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ZLL and BD designed the original experiments. JL conducted the experiments. YZ and ZLL developed the models, analyzed the data and wrote the manuscript. YZ, JL, BD and ZLL revised the manuscript.
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ZLL has intellectual and equity interests in Adaptive Sensory Technology, Inc. (San Diego, CA) and Jiangsu Juehua Medical Technology Co, LTD (Jiangsu, China). The interests are not related to this study. YZ, JL, and BD have no competing interests.
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Zhao, Y., Liu, J., Dosher, B.A. et al. Estimating the Trial-by-Trial Learning Curve in Perceptual Learning with Hierarchical Bayesian Modeling. J Cogn Enhanc (2024). https://doi.org/10.1007/s41465-024-00300-6
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DOI: https://doi.org/10.1007/s41465-024-00300-6