Abstract:We propose a general robust prediction framework, termed conformal-projective prediction (CPP), that integrates Bayesian predictive modeling with ideas from conformal prediction. Rather than assessing conformity through residual-based scores, the CPP criterion defines conformity distributionally: a candidate value for a future response is considered conforming to the extent that its inclusion in the data leaves the leave-one-out predictive distributions of the observed responses undisturbed. The framework requires only that the leave-one-out and swapped predictive distributions are available in closed form and that the swapped predictive mean is differentiable in the candidate value. Under these conditions, we establish a general bounded-influence proposition and a general local convexity lemma, and prove that CPP dominates any plug-in predictor with unbounded influence in asymptotic variance under $\epsilon$-contamination models. When the posterior mean is linear in the observations, as in Gaussian linear models, basis-expansion regression, and Gaussian process regression, the swapped predictive mean is affine in the candidate value, yielding closed-form or one-dimensional optimization solutions and an efficient rank-two computational update; all general theoretical results specialize to explicit corollaries in this setting. Simulation experiments and two data analyses under the Gaussian linear model illustrate the finite-sample advantages of the proposed method, confirming the theoretical predictions across contamination levels, sample sizes, and predictor dimensions.
| Subjects: | Methodology (stat.ME); Statistics Theory (math.ST) |
| Cite as: | arXiv:2605.24601 [stat.ME] |
| (or arXiv:2605.24601v1 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24601 arXiv-issued DOI via DataCite (pending registration) |
From: Arkaprava Roy [view email]
[v1]
Sat, 23 May 2026 14:33:26 UTC (44 KB)
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