CONTRA：通过归一化流变换实现符合预测区域
CONTRA: Conformal Prediction Region via Normalizing Flow Transformation
AI总结：
CONTRA通过归一化流变换定义非符合分数，生成高密度区域到输出空间的锐利预测区域，优于传统超矩形或椭圆形符合区域，且能增强其他预测模型的可靠性。
摘要：
密度估计和可靠的输出预测区域对于监督和无监督学习至关重要。尽管符合预测能有效生成覆盖保证的区域，但因依赖一维非符合分数而难以处理多维输出。为此，我们引入CONTRA：通过归一化流变换实现符合预测区域。CONTRA利用归一化流的潜在空间定义基于与中心距离的非符合分数，使高密度区域在潜在空间映射到输出空间的锐利预测区域，超越传统超矩形或椭圆形符合区域。进一步，对于其他预测模型优于流模型的场景，我们扩展CONTRA以通过在残差上训练简单归一化流来增强任何此类模型，生成可靠的预测区域。我们证明CONTRA及其扩展保持保证的覆盖概率，并在各种数据集上优于现有方法生成准确的预测区域。我们得出结论，CONTRA是有效的（条件）密度估计工具，解决了未被充分探索的多维预测区域挑战。
英文摘要：
Density estimation and reliable prediction regions for outputs are crucial in supervised and unsupervised learning. While conformal prediction effectively generates coverage-guaranteed regions, it struggles with multi-dimensional outputs due to reliance on one-dimensional nonconformity scores. To address this, we introduce CONTRA: CONformal prediction region via normalizing flow TRAnsformation. CONTRA utilizes the latent spaces of normalizing flows to define nonconformity scores based on distances from the center. This allows for the mapping of high-density regions in latent space to sharp prediction regions in the output space, surpassing traditional hyperrectangular or elliptical conformal regions. Further, for scenarios where other predictive models are favored over flow-based models, we extend CONTRA to enhance any such model with a reliable prediction region by training a simple normalizing flow on the residuals. We demonstrate that both CONTRA and its extension maintain guaranteed coverage probability and outperform existing methods in generating accurate prediction regions across various datasets. We conclude that CONTRA is an effective tool for (conditional) density estimation, addressing the under-explored challenge of delivering multi-dimensional prediction regions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
