# Uncertainty Quantification by Ensemble Learning for Computational Optical Form Measurements

arXiv: https://arxiv.org/abs/2103.01259 · HTML: https://mlsanity.com/paper/2103.01259/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 55 references that are in the map.
- First posted on arXiv 1 Mar 2021.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [Unmasking Clever Hans Predictors and Assessing What Machines Really Learn](https://mlsanity.com/paper/1902.10178/) (2019)
- [Recent Trends in Deep Learning Based Natural Language Processing](https://mlsanity.com/paper/1708.02709/) (2017)
- [DeepTest: Automated Testing of Deep-Neural-Network-driven Autonomous Cars](https://mlsanity.com/paper/1708.08559/) (2017)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning](https://mlsanity.com/paper/2002.06470/) (2020)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Why M Heads are Better than One: Training a Diverse Ensemble of Deep Networks](https://mlsanity.com/paper/1511.06314/) (2015)
- [A Variational U-Net for Conditional Appearance and Shape Generation](https://mlsanity.com/paper/1804.04694/) (2018)
- [Quality of Uncertainty Quantification for Bayesian Neural Network Inference](https://mlsanity.com/paper/1906.09686/) (2019)
- [Concolic Testing for Deep Neural Networks](https://mlsanity.com/paper/1805.00089/) (2018)
- [Deeply Uncertain: Comparing Methods of Uncertainty Quantification in Deep Learning Algorithms](https://mlsanity.com/paper/2004.10710/) (2020)
- [Deep Iterative Reconstruction for Phase Retrieval](https://mlsanity.com/paper/1904.11301/) (2019)
- [Calibration-free quantitative phase imaging using data-driven aberration modeling](https://mlsanity.com/paper/2007.13038/) (2020)
- [Detecting unusual input to neural networks](https://mlsanity.com/paper/2006.08278/) (2020)
- [Deep Neural Networks for Computational Optical Form Measurements](https://mlsanity.com/paper/2007.00319/) (2020)

## Built on by (most cited first, 11 of 11)

- [Deep Ensembles from a Bayesian Perspective](https://mlsanity.com/paper/2105.13283/) (2021)
- [Uncertainty Quantification for Deep Unrolling-Based Computational Imaging](https://mlsanity.com/paper/2207.00698/) (2022)
- [An Uncertainty-aware Loss Function for Training Neural Networks with Calibrated Predictions](https://mlsanity.com/paper/2110.03260/) (2021)
- [BayTTA: Uncertainty-aware medical image classification with optimized test-time augmentation using Bayesian model averaging](https://mlsanity.com/paper/2406.17640/) (2024)
- [Conformalized Generative Bayesian Imaging: An Uncertainty Quantification Framework for Computational Imaging](https://mlsanity.com/paper/2504.07696/) (2025)
- [Aleatoric uncertainty for Errors-in-Variables models in deep regression](https://mlsanity.com/paper/2105.09095/) (2021)
- [Cycle Consistency-based Uncertainty Quantification of Neural Networks in Inverse Imaging Problems](https://mlsanity.com/paper/2305.12852/) (2023)
- [Neural Network-Based Processing and Reconstruction of Compromised Biophotonic Image Data](https://mlsanity.com/paper/2403.14324/) (2024)
- [Toward Robust Uncertainty Estimation with Random Activation Functions](https://mlsanity.com/paper/2302.14552/) (2023)
- [Flow-Induced Diagonal Gaussian Processes](https://mlsanity.com/paper/2509.17153/) (2025)
- [Taylor-Sensus Network: Embracing Noise to Enlighten Uncertainty for Scientific Data](https://mlsanity.com/paper/2409.07942/) (2024)

## Abstract (arXiv)

Uncertainty quantification by ensemble learning is explored in terms of an application from computational optical form measurements. The application requires to solve a large-scale, nonlinear inverse problem. Ensemble learning is used to extend a recently developed deep learning approach for this application in order to provide an uncertainty quantification of its predicted solution to the inverse problem. By systematically inserting out-of-distribution errors as well as noisy data the reliability of the developed uncertainty quantification is explored. Results are encouraging and the proposed application exemplifies the ability of ensemble methods to make trustworthy predictions on high dimensional data in a real-world application.