Uncertainty for Neural Networks, and Other Large Complicated Models

Last update: 08 Dec 2024 00:34
First version:

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Yet Another Inadequate Placeholder

Clarifications:
1. I'm only interested in uncertainty in the predictions, not the parameters --- for the type of data-mining-ish application I'm thinking of, "all parameters are nuisance parameters"
2. Neural networks are obviously big these days but I suspect principles / methods will be more generally applicable (and hence more enduring)
3. That said, neural networks may be especially nice because everything's continuous and it's fit by minimization.

See also:
• Adversarial Examples
• Conformal Prediction [A well-established set of techniques increasingly used for these problems, and probably where I'd start in any actual application]
• Propagation of Error to the Rescue? [A half-baked (at best) idea I had years ago and never did any actual work on]

Recommended:
• A. Feder Cooper, Katherine Lee, Madiha Zahrah Choksi, Solon Barocas, Christopher De Sa, James Grimmelmann, Jon Kleinberg, Siddhartha Sen, Baobao Zhang, "Is My Prediction Arbitrary? The Confounding Effects of Variance in Fair Classification Benchmarks", arxiv:2301.11562
• Janis Postels, Francesco Ferroni, Huseyin Coskun, Nassir Navab, Federico Tombari, "Sampling-free Epistemic Uncertainty Estimation Using Approximated Variance Propagation", arxiv:1908.00598
• Peter Schulam, Suchi Saria, "Can You Trust This Prediction? Auditing Pointwise Reliability After Learning", arxiv:1901.00403

To read:
• Nilesh A. Ahuja, Ibrahima Ndiour, Trushant Kalyanpur, Omesh Tickoo, "Probabilistic Modeling of Deep Features for Out-of-Distribution and Adversarial Detection", arxiv:1909.11786
• Charles Corbière, Nicolas Thome, Avner Bar-Hen, Matthieu Cord, Patrick Pérez, "Addressing Failure Prediction by Learning Model Confidence", arxiv:1910.04851
• Jean Feng, Arjun Sondhi, Jessica Perry, Noah Simon, "Selective prediction-set models with coverage guarantees", arxiv:1906.05473
• Zhaohan Daniel Guo, Mohammad Gheshlaghi Azar, Bilal Piot, Bernardo A. Pires, Rémi Munos, "Neural Predictive Belief Representations", arxiv:1811.06407
• Liat Ein-Dor and Ido Kanter, "Confidence in prediction by neural networks", Physical Review E 60 (1999): 799--802
• Varun Gupta, Christopher Jung, Georgy Noarov, Mallesh M. Pai, Aaron Roth, "Online Multivalid Learning: Means, Moments, and Prediction Intervals", arxiv:2101.01739
• Eyke Hüllermeier, Willem Waegeman, "Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods", arxiv:1910.09457
• Danijel Kivaranovic, Kory D. Johnson, Hannes Leeb, "Adaptive, Distribution-Free Prediction Intervals for Deep Networks", arxiv:1905.10634
• Max-Heinrich Laves, Sontje Ihler, Karl-Philipp Kortmann, Tobias Ortmaier, "Well-calibrated Model Uncertainty with Temperature Scaling for Dropout Variational Inference", arxiv:1909.13550
• Tengyuan Liang, "Universal Prediction Band via Semi-Definite Programming", Journal of the Royal Statistical Society B 84 (2022): 1558--1580 [An alternative]
• Zhen Lin, Shubhendu Trivedi, Jimeng Sun
  • "Locally Valid and Discriminative Prediction Intervals for Deep Learning Models", arxiv:2106.00225
  • "Conformal Prediction Intervals with Temporal Dependence", arxiv:2205.12940
  • "Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models", arxiv:2305.19187
• Alexander Meinke, Matthias Hein, "Towards neural networks that provably know when they don't know", arxiv:1909.12180
• Fabricio Olivetti de Franca, Gabriel Kronberger, "Prediction Intervals and Confidence Regions for Symbolic Regression Models based on Likelihood Profiles", arxiv:2209.06454
• Raanan Y. Rohekar, Yaniv Gurwicz, Shami Nisimov, Gal Novik, "Modeling Uncertainty by Learning a Hierarchy of Deep Neural Connections", arxiv:1905.13915