Source-linked AI summary
Variational Inference and Bayesian CNNs for Uncertainty Estimation in Multi-Factorial Bone Age Prediction
Stefan Eggenreich, Christian Payer, Martin Urschler, Darko Štern
TL;DR
Automatic age-estimation methods often provide point estimates without quantifying predictive uncertainty, despite its importance in age assessment. This paper applies Variational Inference to a Bayesian CNN for multi-factorial MRI age prediction, distinguishing model and data uncertainty. The Bayesian CNN is reported as more accurate than a standard CNN and provides uncertainty estimates.
Problem
Automatic age-estimation methods predict point estimates without quantifying predictive uncertainty, which is important in decision-making.
Source: §1 · p. 2Method
Results
1.04 ± 0.88 y vs. 1.12 ± 0.93 y mean absolute deviation: the probabilistic BCNN was more accurate than the standard CNN and estimated uncertainty.
Source: §3 · pp. 2, 4Takeaways & Limitations
Data uncertainty in age estimation can be interpreted as the range of possible chronological ages among subjects with the same biological age.
Source: §1 · p. 2Evaluating predictive uncertainty is challenging because its ground truth is unavailable.
Source: §3 · p. 3
Abstract
from arXiv · showhide
Additionally to the extensive use in clinical medicine, biological age (BA) in legal medicine is used to assess unknown chronological age (CA) in applications where identification documents are not available. Automatic methods for age estimation proposed in the literature are predicting point estimates, which can be misleading without the quantification of predictive uncertainty. In our multi-factorial age estimation method from MRI data, we used the Variational Inference approach to estimate the uncertainty of a Bayesian CNN model. Distinguishing model uncertainty from data uncertainty, we interpreted data uncertainty as biological variation, i.e. the range of possible CA of subjects having the same BA.
1 Motivation
Biological age estimation is used in clinical diagnosis and to assess unknown chronological age in legal medicine, where methods that provide only point estimates leave predictive uncertainty unquantified. The paper proposes a Bayesian CNN for multi-factorial MRI age estimation and interprets data uncertainty as biological variation.
1 Motivation
- Radiological age assessment combines hand-bone X-rays with clavicle CT and dental panoramic X-rays to extend assessment to around 24 years, as recommended by AGFAD.MRI-based research seeks to avoid ionizing radiation, while automatic methods avoid discrete staging schemes and subjective fusion of anatomical sites.Source: §1 · p. 1
- Automatic age estimators provide point estimates without predictive uncertainty, which matters because high-uncertainty predictions can mislead in decision-making.The motivation is especially relevant to legal-medicine assessments of unknown chronological age.Source: §1 · pp. 1–2
- The proposed Bayesian CNN estimates age from multi-factorial MRI data using Variational Inference and distinguishes model uncertainty from data uncertainty.Data uncertainty is interpreted as the range of possible chronological ages among subjects with the same biological age.Source: §1 · p. 2
2 Method
The method uses Variational Inference to approximate a Bayesian CNN's weight posterior and estimate predictive uncertainty. It models data uncertainty with a Gaussian output and evaluates the approach on wrist and clavicle MRI slices.
2 Method
- Bayes by Backprop approximates the intractable weight posterior with a tractable variational distribution by learning parameters that minimize a loss function.The experiments use one sampled weight set as proposed by.Source: §2 · p. 2
- A Gaussian output layer models data uncertainty, while distributions over weights capture model uncertainty; the study compares models that include either, both, or neither.The BCNN with σ learns both the mean and variance, the plain BCNN learns only the mean, and the CNN with σ models aleatoric uncertainty.Source: §2 · p. 2
- The evaluation used 2D middle slices of wrist and clavicle bones from 328 subjects aged approximately 13–25 years, with a 70:30 train-test split.Biological age and data uncertainty were averaged over 20 sampled-weight inference passes; experiments used combined wrist and clavicle bones or wrist bones alone.Source: §2 · p. 2
3 Results and Discussion
The Bayesian CNN was more accurate than the standard CNN and estimated uncertainty for multi-factorial MRI age prediction. Its uncertainty patterns also reflected the limits of wrist-only age estimation after age 18.
3 Results and Discussion
- For forensic age estimation, probabilistic BCNN (with σ) achieved higher accuracy than standard CNN, with mean absolute deviations of 1.04 ± 0.88 y versus 1.12 ± 0.93 y, despite using only 2D middle slices of wrist and clavicle bones.Source: §3 · p. 2
- 1.15 ± 0.88 vs. 1.04 ± 0.88 y: adding a Gaussian output layer to the plain BCNN improved accuracy.The authors attribute the difference to modeling data uncertainty at the network output.Source: §3 · p. 3
- For subjects older than 18, wrist-only aleatoric uncertainty rises rapidly as wrist aging information saturates, while clavicle input helps distinguish ages.The increase is more prominent when the BCNN separates data and model uncertainty; the paper notes that ground-truth predictive uncertainty is unavailable.Source: §3 · p. 3, Figure 1 · p. 3
- The authors conclude that, compared with a standard CNN, a Bayesian CNN provides more accurate results and estimates uncertainty for multi-factorial MRI age estimation.A small increase in aleatoric uncertainty with wrist and clavicle input is interpreted as reflecting less distinguishable ossification progress in clavicle bones.Source: §3 · pp. 3–4