[Paper Review] A Bayesian binary classification approach to pure tone audiometry

Marco Cox, Bert de Vries|arXiv (Cornell University)|Nov 27, 2015

Control Systems and Identification9 references3 citations

TL;DR

This paper proposes a Bayesian binary classification method, GP-PTA, for pure tone audiometry that models the hearing threshold as a smooth Gaussian process over frequency, enabling adaptive, uncertainty-aware threshold estimation with fewer measurements. By combining a probabilistic response model with active learning via the BALD criterion, it optimizes stimulus selection to reduce patient burden while providing confidence intervals on threshold estimates.

ABSTRACT

The pure tone hearing threshold is usually estimated from responses to stimuli at a set of standard frequencies. This paper describes a probabilistic approach to the estimation problem in which the hearing threshold is modelled as a smooth continuous function of frequency using a Gaussian process. This allows sampling at any frequency and reduces the number of required measurements. The Gaussian process is combined with a probabilistic response model to account for uncertainty in the responses. The resulting full model can be interpreted as a two-dimensional binary classifier for stimuli, and provides uncertainty bands on the estimated threshold curve. The optimal next stimulus is determined based on an information theoretic criterion. This leads to a robust adaptive estimation method that can be applied to fully automate the hearing threshold estimation process.

Motivation & Objective

• To address the limitations of conventional pure tone audiometry, which lacks uncertainty quantification and efficient use of prior knowledge.
• To overcome the need for redundant, fixed-frequency measurements by modeling the hearing threshold as a continuous, smooth function of frequency.
• To develop an adaptive testing protocol that minimizes the number of trials by selecting the most informative stimuli at any frequency.
• To provide objective, probabilistic stopping criteria based on uncertainty bands on the estimated threshold curve.
• To integrate perceptual uncertainty and prior knowledge naturally through a full Bayesian framework.

Proposed method

• The hearing threshold is modeled as a Gaussian process (GP) prior over frequency, enabling smooth, continuous estimation across all frequencies.
• A binary response model is used to capture uncertainty in patient responses, assuming perceptual noise with a normal distribution.
• The full model is interpreted as a two-dimensional binary classifier with a GP in frequency and a psychometric function in intensity.
• Bayesian inference is applied using Laplace approximation to estimate the posterior distribution over the threshold curve.
• The optimal next stimulus is selected using the BALD (Bayesian Active Learning by Disagreement) criterion to maximize information gain.
• An iterative active learning loop alternates between selecting the most informative stimulus and updating the posterior distribution based on the patient's response.

Experimental results

Research questions

• RQ1 Can a probabilistic model that treats the hearing threshold as a continuous function of frequency reduce the number of required audiometric tests compared to standard fixed-frequency methods?
• RQ2 How can uncertainty in patient responses be systematically modeled and incorporated into threshold estimation to improve reliability?
• RQ3 Can active learning based on information-theoretic criteria like BALD lead to faster convergence and reduced cognitive load in hearing assessments?
• RQ4 To what extent can prior knowledge about typical hearing threshold shapes be encoded and exploited using a Gaussian process prior?
• RQ5 What is the impact of continuous frequency sampling and uncertainty quantification on the accuracy and robustness of hearing threshold estimation?

Key findings

• The GP-PTA method reduces the number of required trials by adaptively selecting stimuli at any frequency based on information gain, minimizing patient burden.
• The method provides uncertainty bands on the estimated threshold curve, enabling objective stopping criteria based on desired precision.
• The optimal stimulus intensity for information gain is shown to be the mean of the posterior threshold estimate at a given frequency, confirming theoretical optimality.
• The BALD criterion leads to efficient exploration of the stimulus space, with the algorithm converging faster than conventional staircase methods.
• The full probabilistic framework naturally incorporates prior knowledge about smoothness of the threshold curve and perceptual variability, improving estimation robustness.
• Simulations demonstrate that the method achieves accurate threshold estimation with fewer measurements while maintaining high reliability through uncertainty quantification.