提出非线性约束下误差缩减的理论证明，解决概率预测中的关键难题。
Nonlinear reconciliation: Error reduction theorems
- 基于曲率符号恒定的超曲面，推导出误差缩减的精确定理。
- 扩展至曲率变号及高余维流形，覆盖更广泛的实际场景。
- 开源JAX工具包JNLR，支持复现与工程落地。
预测调和是一种在需满足约束条件的预测中应用的后处理技术，近二十年来备受关注。近期研究尝试将调和方法推广至概率预测场景，但针对非线性约束的误差缩减定理仍缺乏严格证明。本文填补了这一空白，为多种非线性超曲面及向量值函数类建立了误差缩减定理。具体而言，我们推导出曲率符号恒定超曲面情形下，对Panagiotelis等（2021）定理3.1的精确类比；同时给出了曲率符号不恒定超曲面以及余维大于1的一般流形情况下的误差缩减定理。为支持可复现性与实际应用，本文发布了基于JAX的Python工具包JNLR，实现所提定理与调和流程。
原文摘要 · Abstract (English)
Forecast reconciliation, an ex-post technique applied to forecasts that must satisfy constraints, has been a prominent topic in the forecasting literature over the past two decades. Recently, several efforts have sought to extend reconciliation methods to the probabilistic settings. Nevertheless, formal theorems demonstrating error reduction in nonlinear constraints, analogous to those presented in Panagiotelis et al.(2021), are still lacking. This paper addresses that gap by establishing such theorems for various classes of nonlinear hypersurfaces and vector-valued functions. Specifically, we derive an exact analog of Theorem 3.1 from Panagiotelis et al.(2021) for hypersurfaces with constant-sign curvature. Additionally, we provide an error reduction theorem for the broader case of hypersurfaces with non-constant-sign curvature and for general manifolds with codimension > 1. To support reproducibility and practical adoption, we release a JAX-based Python package, JNLR, implementing the presented theorems and reconciliation procedures.
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