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The paper targets a specific weakness of Bayesian predictive regions: they can be miscalibrated under model misspecification, and cheaper approximations like variational inference lose accuracy. SCOPE uses conformal nonconformity-score gradients to find the few parameter directions that move a region's boundary, runs MCMC only in that subspace, and handles the rest with a projected variational approximation. The reported results (a 0.002-nat median test-NLL gap to full HMC and a 12-15x speedup on real benchmarks) are promising, but they come from the authors' own benchmarks, so practitioners should check how well they transfer to their models.
SCOPE Before You Sample: Conformal Scores Guide Posterior Exploration for Fast and Calibrated Bayesian Predictive Inference
arXiv:2610.17146v1 Announce Type: cross Abstract: 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.
Abstract: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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.17146 [stat.ML]
(or arXiv:2610.17146v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.17146 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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