Key science questions, such as galaxy distance estimation and weather forecasting, often require knowing the full predictive distribution of a target variable $y$ given complex inputs $\mathbf{x}$. Despite recent advances in machine learning and physics-based models, it remains challenging to assess whether an initial model is calibrated for all $\mathbf{x}$, and when needed, to reshape the densities of $y$ toward "instance-wise" calibration. This paper introduces the LADaR (Local Amortized Diagnostics and Reshaping of Conditional Densities) framework and proposes a new computationally efficient algorithm ($\texttt{Cal-PIT}$) that produces interpretable local diagnostics and provides a mechanism for adjusting conditional density estimates (CDEs). $\texttt{Cal-PIT}$ learns a single interpretable local probability--probability map from calibration data that identifies where and how the initial model is miscalibrated across feature space, which can be used to morph CDEs such that they are well-calibrated. We illustrate the LADaR framework on synthetic examples, including probabilistic forecasting from image sequences, akin to predicting storm wind speed from satellite imagery. Our main science application involves estimating the probability density functions of galaxy distances given photometric data, where $\texttt{Cal-PIT}$ achieves better instance-wise calibration than all 11 other literature methods in a benchmark data challenge, demonstrating its utility for next-generation cosmological analyses.

翻译：关键科学问题，如星系距离估计和天气预报，通常需要获知目标变量$y$在给定复杂输入$\mathbf{x}$情况下的完整预测分布。尽管机器学习和基于物理的模型已取得最新进展，评估初始模型是否对所有$\mathbf{x}$都保持校准，以及在需要时如何将$y$的密度重塑以实现"实例级"校准，仍然具有挑战性。本文提出了LADaR（条件密度的局部摊销诊断与重塑）框架，并设计了一种新的计算高效算法（$\texttt{Cal-PIT}$）。该算法能够生成可解释的局部诊断结果，并提供调整条件密度估计（CDEs）的机制。$\texttt{Cal-PIT}$从校准数据中学习单一的可解释局部概率-概率映射，该映射能识别初始模型在特征空间中何处以及如何存在校准偏差，进而可用于调整CDEs，使其达到良好校准状态。我们在合成示例（包括类似于从卫星图像预测风暴风速的图像序列概率预测）上演示了LADaR框架。我们的主要科学应用涉及根据测光数据估计星系距离的概率密度函数。在基准数据挑战中，$\texttt{Cal-PIT}$相比其他11种文献方法实现了更好的实例级校准，证明了其对于下一代宇宙学分析的价值。