Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging
This addresses the problem of model mistakes and hallucinations in biological imaging, offering formal guarantees for practitioners, though it is incremental as it builds on existing base models.
The paper tackles the lack of statistical guarantees in image-to-image regression by developing uncertainty quantification techniques that provide confidence intervals for each pixel, validated on tasks like quantitative phase microscopy and accelerated MRI.
Image-to-image regression is an important learning task, used frequently in biological imaging. Current algorithms, however, do not generally offer statistical guarantees that protect against a model's mistakes and hallucinations. To address this, we develop uncertainty quantification techniques with rigorous statistical guarantees for image-to-image regression problems. In particular, we show how to derive uncertainty intervals around each pixel that are guaranteed to contain the true value with a user-specified confidence probability. Our methods work in conjunction with any base machine learning model, such as a neural network, and endow it with formal mathematical guarantees -- regardless of the true unknown data distribution or choice of model. Furthermore, they are simple to implement and computationally inexpensive. We evaluate our procedure on three image-to-image regression tasks: quantitative phase microscopy, accelerated magnetic resonance imaging, and super-resolution transmission electron microscopy of a Drosophila melanogaster brain.