Conformal prediction methodologies have significantly advanced the quantification of uncertainties in predictive models. Yet, the construction of confidence regions for model parameters presents a notable challenge, often necessitating stringent assumptions regarding data distribution or merely providing asymptotic guarantees. We introduce a novel approach termed CCR, which employs a combination of conformal prediction intervals for the model outputs to establish confidence regions for model parameters. We present coverage guarantees under minimal assumptions on noise and that is valid in finite sample regime. Our approach is applicable to both split conformal predictions and black-box methodologies including full or cross-conformal approaches. In the specific case of linear models, the derived confidence region manifests as the feasible set of a Mixed-Integer Linear Program (MILP), facilitating the deduction of confidence intervals for individual parameters and enabling robust optimization. We empirically compare CCR to recent advancements in challenging settings such as with heteroskedastic and non-Gaussian noise.

翻译：置信预测方法显著推进了预测模型不确定性的量化。然而，模型参数置信区域的构建仍面临显著挑战，通常需要对数据分布施加严格假设，或仅能提供渐近保证。我们提出一种称为CCR的新方法，该方法通过组合模型输出的置信预测区间来建立模型参数的置信区域。我们在对噪声的极弱假设下给出了覆盖保证，且该保证在有限样本情形下有效。我们的方法适用于分割置信预测以及包括完全或交叉置信方法在内的黑箱方法。在线性模型这一特定情形下，推导出的置信区域表现为一个混合整数线性规划（MILP）的可行解集，这便于推导单个参数的置信区间并支持鲁棒优化。我们在异方差和非高斯噪声等具有挑战性的设定下，将CCR与最新进展进行了实证比较。