# SCOPE Before You Sample: Conformal Scores Guide Posterior Exploration for Fast and Calibrated Bayesian Predictive Inference

arXiv: https://arxiv.org/abs/2610.17146 · HTML: https://mlsanity.com/paper/2610.17146/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 23 of 23)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Bayesian Low-rank Adaptation for Large Language Models](https://mlsanity.com/paper/2308.13111/) (2023)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Subspace Inference for Bayesian Deep Learning](https://mlsanity.com/paper/1907.07504/) (2019)
- [Bayesian Deep Learning via Subnetwork Inference](https://mlsanity.com/paper/2010.14689/) (2020)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Conformal Bayesian Computation](https://mlsanity.com/paper/2106.06137/) (2021)
- [Likelihood-informed dimension reduction for nonlinear inverse problems](https://mlsanity.com/paper/1403.4680/) (2014)
- [Calibrating general posterior credible regions](https://mlsanity.com/paper/1509.00922/) (2015)
- [Variational Bayesian Decision-making for Continuous Utilities](https://mlsanity.com/paper/1902.00792/) (2019)
- [Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networks](https://mlsanity.com/paper/2101.03906/) (2021)
- [Goal-oriented optimal approximations of Bayesian linear inverse problems](https://mlsanity.com/paper/1607.01881/) (2016)
- [Bayesian Inference on Matrix Manifolds for Linear Dimensionality Reduction](https://mlsanity.com/paper/1606.04478/) (2016)

## Abstract (arXiv)

Bayesian predictive regions account for parameter uncertainty but can be poorly calibrated under model misspecification, even with expensive full MCMC. Cheaper approximations such as variational inference reduce the cost but often yield less accurate predictive distributions. We propose SCOPE (Score-guided Conformal Posterior Exploration), which retains the predictive quality of full MCMC while achieving calibrated coverage at a fraction of its cost. The key observation is that a prediction region can depend on the posterior mainly through a few parameter directions that move the region's boundary, and these are generally not the directions of largest posterior variance. SCOPE gives nonconformity scores a new role in guiding posterior computation: score gradients on a held-out guide set, weighted toward the target boundary, identify the relevant directions. MCMC explores this subspace, while an inexpensive projected variational approximation carries the remaining uncertainty. The same guide set calibrates the region's final density level. We establish asymptotic coverage for SCOPE and provide a split variant with finite-sample validity. Controlled simulations show that score-guided exploration yields more accurate calibrated regions than non-targeted direction choices at low active rank. Across simulated and real benchmarks, SCOPE has a median test-NLL gap of only 0.002 nats relative to full Hamiltonian Monte Carlo (HMC), and on the real benchmarks it runs 12-15 times faster.