异构信息融合的全局极小极大风险与获取律
Global minimax risk and acquisition laws for heterogeneous information fusion
AI总结：
本文针对共享标量干扰与未知接触坐标的独立高斯源，证明全局分配目标风险定理，提出估计器并量化获取阈值，区分局部估计、判别与干扰对齐的资源需求。
AI中文摘要：
我们证明了独立高斯源的全局分配目标风险定理，这些源共享一个标量干扰参数和一个未知接触坐标。对于具有有限多个多重纤维和成对非平行分支切线的固定浸入式干扰曲线，平方目标风险与一个主估计下限加上一个目标间隙加权的高斯判别剖面相当。独立定位、有限分支选择和目标类别重拟合给出一个估计器，该估计器在每一个非负整数分配上达到此比较。一个全盒特化在所有地方具有正定的主Fisher信息并全局识别其目标，然而在临界超曲面上具有相同各阶导数的模型具有不同的多项式风险指数。我们构造了一个有限认证估计器，并量化了保持稀有分支决策和获取窗口所需的数值精度。一个多项式相切族既展示了几何边界又量化了其修复：已知辅助增益、源接触阶和目标消失阶确定了一个通过零增益一致的风险律。对于共享的球面方向，一个单独证明的复合检验结果通过仅使用计数观测的未知接触坐标进行转移。这些定理区分了局部估计、参数区域之间的判别和干扰对齐所需的资源，并在显式标量观测成本下产生获取阈值。
英文摘要：
We prove an all-allocation global target-risk theorem for independent Gaussian sources that share a scalar nuisance and an unknown contact coordinate. For a fixed immersed nuisance curve with finitely many multiple fibres and pairwise nonparallel branch tangents, squared target risk is comparable to a primary estimation floor plus a target-gap-weighted Gaussian discrimination profile. Independent localization, finite branch selection and target-class refitting give an estimator attaining this comparison across every nonnegative integer allocation. A full-box specialization has positive-definite primary Fisher information everywhere and globally identifies its target, yet models with identical derivatives of every order along a critical hypersurface have different polynomial risk exponents. We construct a finite certified estimator and quantify the numerical accuracy needed to preserve rare branch decisions and acquisition windows. A polynomial tangency family both demonstrates the geometric boundary and quantifies its repair: known auxiliary gain, source contact order and target vanishing order determine a risk law uniform through zero gain. For a shared spherical direction, a separately proved composite-testing result transfers through an unknown contact coordinate using only counted observations. These theorems distinguish the resources needed for local estimation, discrimination between parameter regions and nuisance alignment, and yield acquisition thresholds under explicit scalar-observation costs.
