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The Uncertainty Principle

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

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Model uncertainty estimates for deep learning mammographic density prediction using ordinal and classification

Steven Squires¹, Grey Kuling², D Gareth Evans³

¹University of Exeter, Exeter, United Kingdom.

Biomedical Physics & Engineering Express

|January 19, 2026

Summary

Deep learning models can now estimate uncertainty in mammographic density predictions, crucial for breast cancer risk assessment. This advancement provides valuable insights without compromising accuracy.

Keywords:

artificial intelligence breast cancer risk deep learning mammographic density uncertainty estimates

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Area of Science:

Radiology
Artificial Intelligence
Oncology

Background:

Mammographic density is a key breast cancer risk factor.
Deep learning models can predict mammographic density.
Standard models lack uncertainty estimates, limiting clinical utility.

Purpose of the Study:

Develop deep learning models with built-in uncertainty estimates.
Maintain or improve predictive performance for mammographic density.
Enhance clinical and research applications of breast cancer risk assessment.

Main Methods:

Analyzed over 150,000 mammograms from the PROCAS study.
Trained classification and ordinal deep learning models on 100 density classes.
Utilized distribution and distribution-free methods for uncertainty extraction.

Main Results:

Classification and ordinal models achieved comparable predictive performance (RMSE ~8.4) to standard regression.
Uncertainty estimates correlated with inter-reader variability and mammogram view consistency.
Model uncertainty increased with differing expert density scores and inter-model variations.

Conclusions:

Classification and ordinal deep learning approaches successfully generate uncertainty estimates for mammographic density.
These methods offer valuable uncertainty quantification without sacrificing predictive accuracy.
The developed models can aid in more nuanced breast cancer risk assessment.