发表机构
Karolinska Institutet; KTH Royal Institute of Technology（卡罗林斯卡学院; 皇家理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对有限基漂移模型，提出有限探针总变差证书，推导后验 TV 上置信界，通过合成实验验证方法，为有限密度类或归一化有限基密度近似量提供条件诊断。
AI 中文摘要
漂移目标通过在有限多个位置观测到的有噪向量场，比较目标分布与模型分布。我们探究这种固定测量系统能得出何种分布结论。对于可积反对称相互作用及声明有限密度基中的绝对连续律，未归一化采样分子满足 vec(Vₓ)=Mc，其中 c 为反对称失配，M 为依赖探针的量。该恒等式可得出后验总变差（TV）上置信界，其兼顾保留的向量场噪声、估计算子误差，以及归一化密度近似量在基张成空间内经外部验证的 L¹ 残差半径；若可观测性余量非正，则返回平凡 TV 界并弃权（不执行）。该校验从保留样本重新计算此分子；归一化漂移统计需单独的联合分子-分母分析。对于高斯-RBF 相互作用，全局包络支持无截断的分布自由及经验-伯恩斯坦半径，同时为原始漂移目标中的拉普拉斯相似度提供伴随界。我们通过总体 Gram 矩阵表征随机探针可观测性，识别秩与对称性退化，并证明大带宽坍缩趋向均值匹配。合成研究验证了高斯与拉普拉斯分子、单独预指定的有界向量及方差自适应半径、蒙特卡洛校准算子、归一化有限基近似量周围的非零残差半径、外圆化可观测性界及设计的弃权（不执行）。联合基大小/维度应力路径将评估扩展至 m=8。该结果是针对有限密度类或带外部残差半径的归一化有限基密度近似量的条件诊断，而非来自小训练漂移的通用保证。
英文摘要
Drifting objectives compare a target and model distribution through a vector field observed noisily at finitely many locations. We ask what distributional conclusion such a frozen measurement system warrants. For integrable antisymmetric interactions and absolutely continuous laws in a declared finite density basis, the unnormalized sampled numerator satisfies $\operatorname{vec}(V_X)=Mc$, where $c$ is an antisymmetric mismatch and $M$ is probe-dependent. This identity yields an a posteriori total-variation (TV) upper confidence bound accounting for held-out field noise, estimated-operator error, and externally validated $L^1$ residual radii around normalized density approximants in the span; a nonpositive observability margin returns the trivial TV bound and abstains. The audit recomputes this numerator from held-out samples; a normalized drift statistic requires a separate joint numerator--denominator analysis. For Gaussian-RBF interactions, a global envelope supports distribution-free and empirical-Bernstein radii without truncation, with companion bounds for the Laplace similarity in the original drifting objective. We characterize random-probe observability by a population Gram matrix, identify rank and symmetry degeneracies, and prove large-bandwidth collapse toward mean matching. Synthetic studies exercise Gaussian and Laplace numerators, separately prespecified bounded-vector and variance-adaptive radii, Monte Carlo-calibrated operators, nonzero residual radii around normalized finite-basis approximants, outward-rounded observability bounds, and designed abstention. A joint basis-size/dimension stress path extends evaluation through $m=8$. The result is a conditional diagnostic for a finite density class, or for normalized finite-basis density approximants with external residual radii, not a universal guarantee from small training drift.
Comments39 pages, 8 figures. Reproducibility code and numerical outputs: https://github.com/SamAndersson-C/finite-drift-certification
