Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control

Angelopoulos, Anastasios N.; Bates, Stephen; Candès, Emmanuel J.; Jordan, Michael I.; Lei, Lihua

doi:10.48550/arxiv.2110.01052

Cited by 11 publications

(15 citation statements)

References 68 publications

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“…For the proof of this fact, along with a discussion of the tighter confidence bounds used in the experiments, see previous work [4,13]. This calibration procedure is easy to implement in code, and we summarize it in Algorithm 2.…”

Section: Algorithm 2 Pseudocode For Computing λmentioning

confidence: 88%

“…Of particular interest to us is the method of conformalized quantile regression (CQR) [6]. We directly build on CQR, by replacing the the conformal subroutine with the fixed-sequence testing procedure from [4,13]. Other works have applied distribution-free uncertainty quantification to biological and medical computer vision tasks [76][77][78][79][80][81].…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

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

Angelopoulos¹,

Kohli²,

Bates³

et al. 2022

Preprint

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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.

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Section: Algorithm 2 Pseudocode For Computing λmentioning

confidence: 88%

Section: Related Workmentioning

confidence: 99%

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

Angelopoulos¹,

Kohli²,

Bates³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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“…Note on Terminology. The term calibration sometimes has a differing meaning in a variety of areas of human activity, including measurement technology, engineering, economics, and even statistics etc., see e.g., Franklin (1999); Dawkins et al (2001); Kodovskỳ and Fridrich (2009); Osborne (1991); Vovk et al (2020); Angelopoulos et al (2021). These generally mean adjusting a measurement to agree with a desired standard, within a specified accuracy.…”

Section: Related Workmentioning

confidence: 99%

T-Cal: An optimal test for the calibration of predictive models

Lee¹,

Huang²,

Hassani³

et al. 2022

Preprint

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The prediction accuracy of machine learning methods is steadily increasing, but the calibration of their uncertainty predictions poses a significant challenge. Numerous works focus on obtaining well-calibrated predictive models, but less is known about reliably assessing model calibration. This limits our ability to know when algorithms for improving calibration have a real effect, and when their improvements are merely artifacts due to random noise in finite datasets. In this work, we consider detecting miscalibration of predictive models using a finite validation dataset as a hypothesis testing problem. The null hypothesis is that the predictive model is calibrated, while the alternative hypothesis is that the deviation from calibration is sufficiently large.We find that detecting mis-calibration is only possible when the conditional probabilities of the classes are sufficiently smooth functions of the predictions. When the conditional class probabilities are Hölder continuous, we propose T-Cal, a minimax optimal test for calibration based on a debiased plug-in estimator of the 2-Expected Calibration Error (ECE). We further propose Adaptive T-Cal, a version that is adaptive to unknown smoothness. We verify our theoretical findings with a broad range of experiments, including with several popular deep neural net architectures and several standard post-hoc calibration methods. T-Cal is a practical general-purpose tool, which-combined with classical tests for discrete-valued predictors-can be used to test the calibration of virtually any probabilistic classification method. T-Cal is available at https://github.com/dh7401/T-Cal.

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“…Our work also relies on the nested set outlook on conformal prediction [13]. We also build directly on existing work involving distribution-free risk-controlling prediction sets and Learn then Test [8,3]. The LAC baseline is taken from [26], and the ordinal CDF baseline is similar to the softmax method in [5], which is in turn motivated by [15,24].…”

Section: Conformal Prediction and Distribution-free Uncertainty Quant...mentioning

confidence: 99%

Improving Trustworthiness of AI Disease Severity Rating in Medical Imaging with Ordinal Conformal Prediction Sets

Lu¹,

Angelopoulos²,

Pomerantz³

2022

Preprint

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The regulatory approval and broad clinical deployment of medical AI have been hampered by the perception that deep learning models fail in unpredictable and possibly catastrophic ways. A lack of statistically rigorous uncertainty quantification is a significant factor undermining trust in AI results. Recent developments in distribution-free uncertainty quantification present practical solutions for these issues by providing reliability guarantees for black-box models on arbitrary data distributions as formally valid finite-sample prediction intervals. Our work applies these new uncertainty quantification methods -specifically conformal prediction -to a deep-learning model for grading the severity of spinal stenosis in lumbar spine MRI. We demonstrate a technique for forming ordinal prediction sets that are guaranteed to contain the correct stenosis severity within a user-defined probability (confidence interval). On a dataset of 409 MRI exams processed by the deep-learning model, the conformal method provides tight coverage with small prediction set sizes. Furthermore, we explore the potential clinical applicability of flagging cases with high uncertainty predictions (large prediction sets) by quantifying an increase in the prevalence of significant imaging abnormalities (e.g. motion artifacts, metallic artifacts, and tumors) that could degrade confidence in predictive performance when compared to a random sample of cases.

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Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control

Cited by 11 publications

References 68 publications

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

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

T-Cal: An optimal test for the calibration of predictive models

Improving Trustworthiness of AI Disease Severity Rating in Medical Imaging with Ordinal Conformal Prediction Sets

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