Tightening Causal Bounds via Covariate-Aware Optimal Transport
Authors: Sirui Lin, Zijun Gao, Jose Blanchet, Peter Glynn
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We analyze the convergence rate of our estimator and demonstrate the effectiveness of our approach through extensive simulations, highlighting its practical use and superior performance compared to existing methods. ... Section 5 presents the experiments on synthetic and real data. |
| Researcher Affiliation | Academia | 1Department of Management Science and Engineering, Stanford University, USA 2Marshall School of Business, University of Southern California, USA. Correspondence to: Sirui Lin <EMAIL>, Zijun Gao <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Derivation of Empirical Estimator Vip,n,m(η) Input: sample ((Yi, Zi, Wi), i I), cost function h, parameter η Construct Pn,Y (0),Z, Pm,Y (1),Z by (3a), (3b). Compute the cost matrix H Rn m, with H(j, k) = h(y(j) 0 , y(k) 1 ) + η z(j) 0 z(k) 1 2 between the n points (denoted as (y(j) 0 , z(j) 0 ), j [n]) in the support of Pn,Y (0),Z and the m points (denoted as (y(k) 1 , z(k) 1 ), k [m]) in the support of Pm,Y (1),Z. Solve the optimal transport problem: for 1 = (1, ..., 1), j,k π(j, k)H(j, k), (4) and denote the optimal solution as π ip,n,m(η). Compute Vip,n,m(η) = X j,k π ip,n,m(η)(j, k) h(y(j) 0 , y(k) 1 ). Output: Vip,n,m(η) |
| Open Source Code | Yes | The code can be found in the link: https://github. com/siruilin1998/causal OT.git. |
| Open Datasets | Yes | We utilized data from the Student Achievement and Retention (STAR) Demonstration Project (Angrist et al., 2009) |
| Dataset Splits | Yes | For completely randomized experiment with m treated units, n control units... In Figure 3 and Appendix D, we plot the results for the following three models... The first row: m = n = 500, the second row: m = n = 1500. ...approximately 30% of the students received the treatment. |
| Hardware Specification | No | The paper does not explicitly describe the hardware used for its experiments, such as specific GPU/CPU models or memory. |
| Software Dependencies | No | The paper mentions 'standard linear programming (LP) solver', 'Sinkhorn algorithm (Cuturi, 2013)', and 'existing OT packages (Flamary et al., 2021)' but does not provide specific version numbers for these software components. |
| Experiment Setup | Yes | We provide the experiment results for synthetic data, comparing our proposal with (i) an existing method for estimating Vc in our causal setting, that is, (Ji et al., 2023) using their python package Dual Bounds 3, and (ii) the unconditional OT method (Gao et al., 2025) estimating Vu. In Figure 3 and Appendix D, we plot the results for the following three models: (a) Linear location model, f0(z) = 0.6z, f1(z) = 1.6z. (b) Quadratic location model, f0(z) = 0.2z2, f1(z) = 0.6z2. (c) Scale model, f0(z) = 0.5z 0.35, f1(z) = 1.1z +0.35. ... E [|estimator Vc|], E is computed by averaging over 800 repetitions ... The Vip,n,m(η) curve decreases quickly for small η and then stabilizes as η increases... |