不依赖真实数据,精准生成符合指定分析结果的表格数据。
Declarative Outcome-Conformant Synthesis: Exact, Closed-Form Specification Satisfaction and a Conformance Benchmark

- 提出闭式解生成方法,确保聚合结果完全精确
- 实测现有工具误差达74%~86%,本方法误差为0%
- 适合冷启动场景下需严格满足业务指标的建模需求
我们研究了当前主流合成表格数据范式缺失的能力:在无源数据条件下,精确满足声明的分析结果。现有模仿类方法(如拷贝、GAN、扩散模型)通过学习真实分布采样,以与真实数据的保真度为评价标准。但大量实际需求不同:在无源数据(冷启动)情况下,生成能复现特定分析结果(如收入曲线、流失率、群体占比)的数据。现有工具无法对接此类目标,且采样固有方差导致无法达到精确聚合。在真实公开数据集上,训练好的合成器对月度聚合的误差高达74%至86%;改进版仍误差约19%,无法归零;而本文提出的闭式生成器实现误差为0。我们定义该任务为结果一致性合成,主张其评估维度应为一致性而非保真度,二者正交。贡献包括:(1) 形式化证明一类广泛使用的精确聚合生成器本质是伽马分布的条件求和采样(基于Lukacs定理),具备闭式精确性、闭式边际变异系数和尺度不变性;控制实验显示,强制精确聚合仅导致1-Wasserstein距离增加最多0.006,其余偏差源于形状家族不匹配;(2) 提出SpecBench,首个面向冷启动关系合成中分析结果一致性的基准测试;(3) 构建闭式确定性参考系统。精确聚合本身易实现,关键在于同时保证闭式边际、完整性、确定性及零源数据前提。
原文摘要 · Abstract (English)
We study a capability the dominant paradigm in synthetic tabular data does not provide: exact satisfaction of a declared analytical outcome with no source data. Imitation methods (copulas, GANs, diffusion) learn a real distribution and sample from it, and are judged on fidelity to real data. A large, practical class of needs is different: generating data with no source data ("cold start") that reproduces a declared outcome (a revenue curve, a churn rate, a group share) across a relational schema. Off-the-shelf imitation tools offer no interface for such targets, and no sampler can hit an exact aggregate, because sampling has variance. On a real public dataset, off-the-shelf learned synthesizers trained on that very data miss the declared monthly aggregate by 74 to 86 percent; a per-period steelman cuts the miss to about 19 percent and still cannot reach 0; a closed-form generator reaches exactly 0. We name this task outcome-conformant synthesis, argue its evaluation axis is conformance rather than fidelity, and show the two axes are orthogonal. We contribute: (1) a formal account showing a widely-used family of exact-aggregate generators is exactly conditional-sum sampling of a Gamma population (via Lukacs' characterization), with closed-form exactness, a closed-form marginal CV, and scale-invariance; a controlled experiment maps the boundary, enforcing the exact aggregate costs at most 0.006 in 1-Wasserstein distance to an arbitrary external marginal, the rest being shape-family mismatch; (2) SpecBench, to our knowledge the first benchmark to measure conformance to analytical outcomes for cold-start relational synthesis; and (3) a closed-form, deterministic reference system. Exact aggregation alone is trivial; the contribution is conformance jointly with closed-form marginals, integrity, determinism, and zero source data. We concede fidelity to imitation where real data exists.
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