条件归一化流的多变量潜在重校准
Multivariate Latent Recalibration for Conditional Normalizing Flows
AI总结：
针对多变量条件分布校准问题，提出潜在重校准方法，在条件归一化流潜在空间中学习变换，生成带显式密度且高效的重校准分布，实验证明其提升校准误差与负对数似然。
摘要：
可靠地表征给定一组协变量条件下多变量响应变量的完整条件分布，对于可信赖的决策至关重要。然而，设定错误或校准不良的多变量模型可能对响应变量的联合分布产生较差的近似，导致不可靠的预测和次优决策。此外，标准重校准方法主要局限于单变量设置，而保形预测技术尽管能生成具有覆盖保证的多变量预测区域，却不能提供完整的概率密度函数。我们通过首先引入一种新颖的潜在校准概念来弥补这一空白，该概念在条件归一化流的潜在空间中评估概率校准。其次，我们提出了潜在重校准（LR），一种新颖的事后模型重校准方法，它学习潜在空间的变换，并具有潜在校准的有限样本界。与现有方法不同，LR生成具有显式多变量密度函数的重新校准分布，同时保持计算效率。在表格和图像数据集上的大量实验表明，LR持续改善了重新校准模型的潜在校准误差和负对数似然。
英文摘要：
Reliably characterizing the full conditional distribution of a multivariate response variable given a set of covariates is crucial for trustworthy decision-making. However, misspecified or miscalibrated multivariate models may yield a poor approximation of the joint distribution of the response variables, leading to unreliable predictions and suboptimal decisions. Furthermore, standard recalibration methods are primarily limited to univariate settings, while conformal prediction techniques, despite generating multivariate prediction regions with coverage guarantees, do not provide a full probability density function. We address this gap by first introducing a novel notion of latent calibration, which assesses probabilistic calibration in the latent space of a conditional normalizing flow. Second, we propose latent recalibration (LR), a novel post-hoc model recalibration method that learns a transformation of the latent space with finite-sample bounds on latent calibration. Unlike existing methods, LR produces a recalibrated distribution with an explicit multivariate density function while remaining computationally efficient. Extensive experiments on both tabular and image datasets show that LR consistently improves latent calibration error and the negative log-likelihood of the recalibrated models.
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