Conformal Bayesian Computation

2021/06/11 by Edwin Fong, Chris Holmes, Fong, Edwin +1 · 1 voice · 12 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #stat.CO #stat.ME

paper · pdf · doi:10.48550/arxiv.2106.06137

openalex publication_date 2021/06/11 · arxiv published 2021/06/11 · arxiv updated 2021/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, p(y | x), characterize subjective beliefs on outcomes of interest, y, conditional on predictors, x. Bayesian prediction is well-calibrated when the model is true, but the predictive intervals may exhibit poor empirical coverage when the model is misspecified, under the so called \calM-open perspective. In contrast, conformal inference provides finite sample frequentist guarantees on predictive confidence intervals without the requirement of model fidelity. Using 'add-one-in' importance sampling, we show that conformal Bayesian predictive intervals are efficiently obtained from re-weighted posterior samples of model parameters. Our approach contrasts with existing conformal methods that require expensive refitting of models or data-splitting to achieve computational efficiency. We demonstrate the utility on a range of examples including extensions to partially exchangeable settings such as hierarchical models.

Citations

• Least angle regression
• Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC

Cited by

• CBMA: Improving conformal prediction through Bayesian model averaging
• Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distribution to Multivariate Settings
• Conformalized Bayesian Inference, with Applications to Random Partition Models
• The Interplay between Bayesian Inference and Conformal Prediction
• Efficient scenario analysis in real-time Bayesian election forecasting via sequential meta-posterior sampling
• Stop Reducing Responsibility in LLM-Powered Multi-Agent Systems to Local Alignment
• Optimizing In-Context Learning for Efficient Full Conformal Prediction
• Prediction-Oriented Subsampling from Data Streams
• Trustworthy scientific inference with generative models
• Approximating Full Conformal Prediction for Neural Network Regression with Gauss-Newton Influence
• Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces
• Nonparametric predictive inference for discrete data via Metropolis-adjusted Dirichlet sequences

Discussions

• I like this paper about conformalizing credible intervals arxiv.org/abs/2106.06137, it's probably the first paper on the topic I understood because it was written directly in my language. [bsky, 4 points, 0 comments]

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