arXiv：cs.LG· Juliette Sinnott, Amir-Hossein Karimi, Mohammad Kohandel·· 4 小时前AI 评分35
高斯过程因果模型中离散结果的反事实概率推断
Probabilistic Counterfactual Inference for Discrete Outcomes in Gaussian-Process Causal Models
AI 导读
研究者提出一个统一概率框架，将 GP 预测器与显式外生噪声机制配对，为 GP-SCM 中的离散结果反事实推断推导出精确的条件噪声溯因方法：二值变量用统一阈值，名义类别用 Gumbel-max 竞争，有序变量用潜高斯切点模型。在合成 SCM 上的评估发现，对有序数据误用类别耦合会使反事实误差膨胀约三倍，且该误差不随数据量增加而下降，训练集扩大时结构方程收敛到真值而反事实误差趋于固定下限。
正文
Abstract:Counterfactual inference in Gaussian-process structural causal models (GP-SCMs) has been developed primarily for continuous endogenous variables, limiting applicability to causal graphs that contain discrete child nodes with continuous parents. We introduce a unified probabilistic framework for counterfactual inference with heterogeneous variable types by pairing GP predictors with explicit exogenous noise mechanisms. For discrete outcomes, we derive exact conditional noise-abduction procedures using a uniform threshold for binary variables, a Gumbel-max race for nominal categories, and a latent Gaussian cut-point model for ordinal ones. In each case, we propagate abducted noise through interventions while accounting for posterior uncertainty in the GP latent functions, and prove that the resulting mechanisms reproduce the fitted model's observational and interventional distributions. On synthetic SCMs with known ground-truth counterfactuals, we evaluate estimation accuracy, consistency, and robustness to coupling misspecification. A key finding is that applying a categorical coupling to ordinal data inflates counterfactual error roughly threefold even when observational fit remains comparable, and that this error does not diminish with more data. As the training set grows, the fitted structural equation converges to the truth while the counterfactual error flattens onto a floor. In the reverse direction, forcing a false order onto nominal data instead degrades the fitted equation itself. The choice of coupling must therefore be justified on structural grounds rather than read off the fit.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.08689 [cs.LG] |
| (or arXiv:2610.08689v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.08689 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Juliette Sinnott [view email]
[v1]
Tue, 6 Oct 2026 17:06:22 UTC (42 KB)
来源：arXiv：cs.LG · arxiv.org