An interactive companion to the paper论文的交互式导读
Can data from one observation protocol evaluate another that was never used?
一种观测协议采集的数据，能否评估另一种从未实施过的协议？
Not always. Even an infinite benchmark can be compatible with different latent temporal structures, and those structures can assign different predictive values to the same alternative protocol.
未必。即使基准数据趋于无穷，它仍可能同时兼容多种不同的潜在时间依赖结构；而这些结构会对同一个替代协议给出不同的预测价值。
Throughout, a protocol’s value is the fraction of target variation that the best possible predictor could explain from the measurements that protocol would collect.
本文中，协议的“价值”指理想预测器仅利用该协议所采集的测量时，能够解释的目标总体变异比例。
There is also a four-minute narrated story and a ten-minute technical tour.
Section 3 · Theorem 3, the smallest case第 3 节 · 定理 3：最小的例子
Same benchmark. Two compatible worlds. Two different answers.
同一个基准。两个兼容世界。两个不同答案。
Take four time points of a stationary process and let the target be their mean. Protocol A observes the first point; protocol B would observe the second and third. Drag ε below: everything A can measure stays where it is, while the value of B moves.
取一个平稳过程上的四个时间点，目标是它们的平均。协议 A 只观测第一个点；协议 B 打算观测第二和第三个点。拖动下面的 ε：A 能测到的一切都不变，B 的价值却在变。
What protocol A can measure协议 A 能测到的量
| world世界 K_+ | world世界 K_− | |
|---|---|---|
| Var(Y_A) | 1.000000 | 1.000000 |
| Cov(Y_A, Θ) | 0.388250 | 0.388250 |
| Var(Θ) | 0.428012 | 0.428012 |
Value of protocol B协议 B 的价值
What moves变的是什么
Only Cov(Z_1, Z_2) = ρ(1) ± ε changes along the invisible direction δ = (0, 1, −2, 1). Each new measurement keeps its link to the target; their overlap with each other does not stay fixed.
沿不可见方向 δ = (0, 1, −2, 1) 只有 Cov(Z_1, Z_2) = ρ(1) ± ε 在变。每个新测量与目标的联系不变，变的是它们彼此之间的重叠。
Both worlds produce exactly the same joint distribution of A’s measurement and the target, so no amount of additional sampling under A can tell them apart. Yet B is worth 0.682 in one and 0.827 in the other.
两个世界产生完全相同的“A 的测量—目标”联合分布，因此在协议 A 下再增加多少样本，也无法区分它们。可协议 B 的价值，在一个世界里是 0.682，在另一个世界里是 0.827。
What the benchmark leaves open is not how each new measurement relates to the target. It is how redundant the new measurements are with one another, a dependence protocol A never observes.
基准数据没有确定的，并不是每个新测量与目标的关系，而是这些新测量彼此之间有多冗余——协议 A 从未观测到这种依赖。
Identification. The benchmark determines the value of an undeployed protocol only when every latent model compatible with the benchmark assigns that protocol the same value.
可识别性。只有当所有与基准数据相容的潜在模型都赋予替代协议同一个价值时，该价值才被基准数据识别。
Three questions, in the order they must be answered
三个问题，必须按顺序回答
The paper is organised around this sequence. Each step only makes sense once the previous one has been settled.
论文按这个顺序展开。每一步都要在前一步解决之后才有意义。
-
1
Identify识别
Is the value determined by the available data?
现有数据是否已经确定了这个价值？
Characterise the latent variation the realised benchmark cannot see, and test whether that variation changes the value of the proposed protocol.
找出已实施基准看不见的潜在变化，并判断这些变化是否会改变拟议协议的价值。
Section 3第 3 节
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2
Calibrate校准
Which additional measurements remove the ambiguity that matters?
补充哪些测量，能消除真正相关的歧义？
Targeted augmentation can identify one specified value. A small, densely observed calibration subset supports comparison across a whole family of protocols.
定向补测可以识别一个指定协议的价值；小规模密集校准子集则可以支持对整个协议族的比较。
Section 4第 4 节
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3
Design设计
Which protocol is best at the resolution the data can support?
在数据可支持的分辨率上，哪个协议更好？
Optimise timing, support, repetition, noise and cost only after candidate values are identified and their differences are large enough to distinguish.
只有在候选价值可识别、且差异足以被区分之后，才去优化测量时刻、窗口、重复、噪声与成本。
Section 5第 5 节
Section 4 · calibration第 4 节 · 校准
More subjects are not always the data you need.
真正缺少的，未必是更多受试者。
When an ambiguity is invisible under the realised protocol, adding units reproduces the same information. A smaller group observed more intensively can be worth more than many additional units observed in the same sparse way.
当某种歧义对已实施协议不可见时，继续增加样本只会重复同一组信息。一个规模较小但观测更密集的子集，可能比在相同稀疏协议下继续扩样更有用。
In practice this suggests pairing a large routine cohort with a smaller calibration subset, observed densely and chosen with future protocol decisions in mind.
落到研究设计上，就是让大规模常规队列配合一个小规模、密集观测的校准子集，后者专门为未来的协议决策而设计。
How the calibration subset is used校准子集怎么用
From m densely observed units, form the sample covariance, subtract the calibration noise, floor the eigenvalues so the result is a valid covariance, and rescale to a correlation matrix. Plugging the estimate into every candidate’s value gives a family-uniform error of order C\,\norm{\hat K − K}^{β} (Theorem 10), which falls at the root-m rate at a fixed model (Theorem 11).
用 m 个密集观测对象：计算样本协方差，扣除校准噪声，给特征值设下限以保证是合法协方差，再标准化为相关矩阵。把估计代入每个候选协议的价值，得到整个候选族上一致的误差 C\,\norm{\hat K − K}^{β}（定理 10）；在固定模型下，它以根号 m 的速率下降（定理 11）。
Corollary 12 · simulation under known data-generating laws推论 12 · 已知生成机制下的模拟
Calibration determines how finely protocols can be compared.
校准数据决定协议能比较到多细。
A finer candidate family may contain better protocols, but its leading candidates can differ by very small amounts. Those differences mean something only when the calibration error is smaller than the gaps being compared.
更细的候选类可能包含更好的协议，但领先候选之间的价值差距也可能非常小。只有当校准误差小于这些差距时，这种精细比较才有意义。
If the largest protocol-value error is ε, selecting the empirical best costs at most about 2ε, plus any optimisation error. Differences below that scale cannot be told apart from calibration uncertainty.
若所有协议价值估计的最大误差为 ε，按估计值选择协议的损失至多约为 2ε，再加上优化误差。低于这一尺度的差异，无法与校准不确定性区分。
The useful granularity of optimisation is set by the data, not by the optimiser.
优化能细到什么程度，由数据决定，而不是由优化器决定。
Section 5 · Proposition 13 and Table 1 · simulation第 5 节 · 命题 13 与表 1 · 模拟
The best observation schedule depends on the target.
最佳观测方案取决于要预测的目标。
A protocol that reconstructs the latent trajectory well need not be the best one for predicting a particular aggregate of that trajectory. The paper derives the exact marginal value of adding a measurement and uses it for cost-constrained, target-aware search.
能较好重建整条潜在轨迹的协议，不一定最适合预测某个特定的轨迹聚合量。论文推导了新增一次测量的精确边际价值，并据此在预算约束下做针对目标的搜索。
In 25 fully enumerated simulation settings, greedy search with a single swap reached at least 98.7% of the target-specific optimum.
在 25 个可穷举的模拟设置中，贪心搜索加一次交换，至少达到了目标特定最优值的 98.7%。
The exact marginal gain精确的边际收益
With residual covariance P_S = K − Q_S, adding action a updates Q_{S ∪ a} = Q_S + v v^\top / s, where v = P_S ℓ_a and s = ℓ_a^\top P_S ℓ_a + r_a; for the mean target the gain is (ω^\top P_S ℓ_a)^2 / s. The objective is monotone but not submodular, so the search is checked against exhaustive enumeration rather than given an approximation ratio.
记残差协方差 P_S = K − Q_S，加入动作 a 后 Q_{S ∪ a} = Q_S + v v^\top / s，其中 v = P_S ℓ_a，s = ℓ_a^\top P_S ℓ_a + r_a；均值目标下的收益为 (ω^\top P_S ℓ_a)^2 / s。目标函数单调但不是次模的，因此搜索结果用穷举对照来检验，而不声称近似比。
Section 6.4 · retrospective analysis of fully annotated recordings第 6.4 节 · 基于完整标注记录的回溯分析
Coarse layout differences were clearer than exact learned locations.
粗粒度布局的差异，比精确学到的位置更清楚。
Because every epoch of these recordings is annotated, any protocol can be reconstructed after the fact and scored on held-out subjects. At matched budgets, spreading the observations out did better than a contiguous block.
这些记录的每一段都有标注，因此任何协议都可以事后重建，并在留出的受试者上评分。在相同预算下，把观测分散开，比集中在一个连续块里效果更好。
| Data数据 | Target目标 | Budget预算 | Dispersed分散 | Contiguous连续 |
|---|---|---|---|---|
| Sleep-EDF | REM fractionREM 比例 | 4 epochs (2 min)4 个片段（2 分钟） | 0.682 | 0.648 |
| 16 epochs (8 min)16 个片段（8 分钟） | 0.738 | 0.659 | ||
| Long-Term AF | AF burden房颤负担 | 4 × 15-min windows (1 h)4 个 15 分钟窗口（1 小时） | 0.971 | 0.696 |
| 16 × 15-min windows (4 h)16 个 15 分钟窗口（4 小时） | 0.998 | 0.851 |
The contrast for Sleep was not uniform across the two source studies. Exact target-aware Sleep supports, learned from the data, did not hold up as well: they were unstable across targets and subject resamples, and showed no stable held-out advantage over fixed dispersion (−0.044 on the original sample; median −0.012, range [−0.126, +0.097] over 1000 subject resamples).
睡眠数据中的这一对比，在两个来源研究之间并不一致。从数据中学到的精确目标特定睡眠锚点则不够稳健：在不同目标与受试者重抽样之间不稳定，也没有表现出相对固定分散方案的稳定留出优势（原样本上为 −0.044；1000 次受试者重抽样的中位数为 −0.012，范围 [−0.126, +0.097]）。
This is the resolution result at work: broad layouts can be compared reliably even when the data do not support choosing exact anchor locations.
这正是“分辨率”结论的体现：数据足以比较粗粒度的布局，却未必足以可靠地选出精确锚点。
197 Sleep-EDF hypnograms from 100 subjects and 84 Long-Term AF records; expert annotation files only. Full charts are in the technical tour.
197 段 Sleep-EDF 分期（100 名受试者）与 84 段长程房颤记录；只使用专家标注文件。完整图表见技术导览。
The same question arises whenever what is observed changes.
只要观测方式改变，就会遇到同样的问题。
It is not specific to sampling times. Whenever a proposed measurement has never been observed jointly with the target, its value has to be identified or calibrated before feature selection or sensor optimisation can begin.
这并不限于采样时刻。只要拟议的测量从未与目标一起被观测过，就必须先识别或校准它的价值，然后才谈得上特征选择或传感器优化。
- Clinical monitoring临床监测
- Longer, repeated or dispersed recordings whose burden was never paired with the outcome.更长、重复或分散的记录，其负担从未与结局一起被观测。
- Multimodal panels多模态面板
- Overlapping assay or biomarker panels collected on different subjects.在不同对象上采集、彼此重叠的检测或生物标志物面板。
- Wearables and imaging可穿戴与影像
- Schedules that decide how often, and for how long, a device or scanner observes.决定设备或扫描多久看一次、每次看多长的采集方案。
- Environmental sensing环境传感
- New sensor locations or reading frequencies for exposure and exceedance-time targets.为暴露量或超标时长目标新增的传感器位置或读数频率。
Identification before optimisation
先识别，再优化
Existing data do not automatically determine the value of measurements that were never made. The goal is not always to recover the full latent system; it is to remove the ambiguity that changes the protocol values under consideration. Calibration then decides which differences can be resolved, and design should work at that resolution.
现有数据不会自动确定那些从未实施过的测量的价值。要做的未必是恢复完整的潜在系统，而是消除会改变候选协议价值的那部分歧义。校准数据随后决定哪些差异可以分辨，观测设计应当在这一分辨率上进行。
- Manuscript (PDF)论文全文（PDF）35 pages, arXiv version35 页，arXiv 版本
- Code and data代码与数据reproduction package: methods library, every experiment, cached annotations;
make verify-quick复现包：方法库、全部实验、缓存的标注数据；make verify-quick - Technical tour技术导览ten narrated chapters with the formulas and the real-data charts十个有声章节，含公式与真实数据图表
- Key figures核心图PNG files for slides and posts供幻灯片与社交媒体使用的 PNG
- Zhang, X. (2026). Counterfactual Evaluation of Temporal Observation Protocols.Zhang, X. (2026). Counterfactual Evaluation of Temporal Observation Protocols.
- Contact联系作者zhangxizhe@gmail.com