2022

Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging

Angelopoulos, Anastasios N, Kohli, Amit P, Bates, Stephen et al.

Understand

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.

Built on

“Über das interpolationsproblems”
Hans Hahn · 1918
Earlier work this paper cites.
“A device for quantizing, grouping, and coding amplitude-modulated pulses”, 1949
Leon Kraft · 1949
Earlier work this paper cites.
“On Pólya frequency functions III. The positivity of translation determinants whith an application to the interpolation problem by spline curves”
Isaac Schoenberg and Anne Whitney · 1953
Earlier work this paper cites.
“Two inequalities implied by unique decipherability”
Brockway McMillan · 1956
Earlier work this paper cites.
“Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth”
Joseph Needham and Lu Gwei-Djen · 1959
Earlier work this paper cites.
“Best approximation properties of the spline fit”
J.L. Walsh, J.H. Ahlberg and E.N. Nilson · 1962
Earlier work this paper cites.
“Probability inequalities for sums of bounded random variables”
Wassily Hoeffding · 1963
Earlier work this paper cites.
“Regression quantiles”
Roger Koenker and Gilbert Bassett · 1978
Earlier work this paper cites.
“Cubic convolution interpolation for digital image processing”
Robert Keys · 1981
Earlier work this paper cites.
“Neural network ensembles”
Lars Hansen and Peter Salamon · 1990
Earlier work this paper cites.
“Global nonparametric estimation of conditional quantile functions and their derivatives”
Probal Chaudhuri · 1991
Earlier work this paper cites.
“Estimating the mean and variance of the target probability distribution”
D.A. Nix and A.S. Weigend · 1994
Earlier work this paper cites.
“Direct use of regression quantiles to construct confidence sets in linear models”
Kenneth Zhou and Stephen Portnoy · 1996
Earlier work this paper cites.
“Statistical inference on heteroscedastic models based on regression quantiles”
Kenneth Zhou and Stephen Portnoy · 1998
Earlier work this paper cites.
“Elements of information theory”
Joy. Thomas and Thomas. Cover · 1999
Earlier work this paper cites.
“Machine-learning applications of algorithmic randomness”
Vladimir Vovk, Alexander Gammerman and Craig Saunders · 1999
Earlier work this paper cites.
“Example-based super-resolution”
William Freeman, Thouis Jones and Egon Pasztor · 2002
Earlier work this paper cites.
“Super-resolution through neighbor embedding”
Hong Chang, Dit-Yan Yeung and Yimin Xiong · 2004
Earlier work this paper cites.
“A non-local algorithm for image denoising”
Antoni Buades, Bartomeu Coll and Jean-Michel Morel · 2005
Earlier work this paper cites.
“A non-local algorithm for image denoising”
Antoni Buades, Bartomeu Coll and Jean-Michel Morel · 2005
Earlier work this paper cites.
“Counterfactual decomposition of changes in wage distributions using quantile regression”
José Machado and José Mata · 2005
Earlier work this paper cites.
“A simple quantile regression via support vector machine”
Changha Hwang and Jooyong Shim · 2005
Earlier work this paper cites.
“Quantile Regression”
Roger Koenker · 2005
Earlier work this paper cites.
“Algorithmic Learning in a Random World”
Vladimir Vovk, Alex Gammerman and Glenn Shafer · 2005
Earlier work this paper cites.
“Nonparametric Quantile Estimation”
Ichiro Takeuchi, Quoc Le, Timothy Sears and Alexander Smola · 2006
Earlier work this paper cites.
“Quantile regression forests”
Nicolai Meinshausen and Greg Ridgeway · 2006
Earlier work this paper cites.
“Network effects and the dynamics of migration and inequality: Theory and evidence from Mexico”
David McKenzie and Hillel Rapoport · 2007
Earlier work this paper cites.

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“Private Prediction Sets”
Original
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“Fair Conformal Predictors for Applications in Medical Imaging”
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