Partial identification provides informative causal guarantees when point identification is impossible, but existing approaches based on optimal transport (OT) become computationally and statistically intractable in high-dimensional settings. This limitation is particularly severe when both potential outcomes and confounders are high-dimensional, where classical OT-based bounds suffer from the curse of dimensionality and unfavorable convergence rates. To address this challenge, we propose a novel estimator that decomposes the transport problem into a low-dimensional signal subspace and a high-dimensional residual subspace. Unlike existing projection-based methods that discard residual information, we recover the residual transport energy using the Sliced Wasserstein distance, which is computationally efficient and robust to high dimensions. We establish interpretable conditions controlling the approximation gap based on residual structure and provide a data-driven rule for signal dimension selection. Empirical results show that our estimator consistently outperforms projection-only baselines by recovering lost transport energy, yielding more informative causal bounds while remaining computationally tractable in high dimensions.

翻译：当点识别不可行时，部分识别提供了具有信息量的因果保证，但现有基于最优传输（OT）的方法在高维场景下在计算和统计上变得难以处理。当潜在结果和混杂因素均为高维时，这一局限性尤为严重，因为经典基于OT的界存在维度灾难问题，且收敛速率不理想。为应对这一挑战，我们提出了一种新型估计器，将传输问题分解为低维信号子空间和高维残差子空间。与现有基于投影的丢弃残差信息的方法不同，我们利用切片Wasserstein距离恢复残差传输能量，该方法计算高效且对高维具有鲁棒性。我们基于残差结构建立了控制近似误差的可解释性条件，并提出了信号维度选择的数据驱动准则。实证结果表明，我们的估计器通过恢复丢失的传输能量，始终优于仅依赖投影的基线方法，在保持高维计算可行性的同时，能够给出更具信息量的因果界。