Model Releases
Weighted Bayesian Conformal Prediction
arXiv:2604.06464v1 Announce Type: new Abstract: Conformal prediction provides distribution-free prediction intervals with finite-sample coverage guarantees, and recent work by Snell & Griffiths refra
arXiv:2604.06464v1 Announce Type: new Abstract: Conformal prediction provides distribution-free prediction intervals with finite-sample coverage guarantees, and recent work by Snell & Griffiths reframes it as Bayesian Quadrature (BQ-CP), yielding powerful data-conditional guarantees via Dirichlet posteriors over thresholds. However, BQ-CP fundamentally requires the i.i.d. assumption -- a limitation the authors themselves identify. Meanwhile, weighted conformal prediction handles distribution shift via importance weights but remains frequentist, producing only point-estimate thresholds. We propose extbf{Weighted Bayesian Conformal Prediction (WBCP)}, which generalizes BQ-CP to arbitrary importance-weighted settings by replacing the uniform Dirichlet Dir(1,ldots,1) with a weighted Dirichlet Dir(neff dot ilde{w}_1, ldots, neff dot ilde{w}_n), where neff is Kish's effective sample size. We prove four theoretical results: (1)~neff is the unique concentration parameter matching frequentist and Bayesian variances; (2)~posterior standard deviation decays as O(1/sqrt{neff}); (3)~BQ-CP's stochastic dominance guarantee extends to per-weight-profile data-conditional guarantees; (4)~the HPD threshold provides O(1/sqrt{neff}) improvement in conditional coverage. We instantiate WBCP for spatial prediction as Geographical BQ-CP, where kernel-based spatial weights yield per-location posteriors with interpretable diagnostics. Experiments on synthetic and real-world spatial datasets demonstrate that WBCP maintains coverage guarantees while providing substantially richer uncertainty information.
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Source: arXiv cs.LG | 2026-04-10