Tangential Wasserstein Projections
Authors: Florian Gunsilius, Meng Hsuan Hsieh, Myung Jin Lee
JMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To demonstrate the efficiency and utility of the proposed method, we apply it in different settings and compare it to existing benchmarks such as Werenski et al. (2022) where those are computationally feasible. Furthermore, we extend the classical synthetic control estimator (Abadie and Gardeazabal, 2003; Abadie et al., 2010), a fundamental approach for counterfactual prediction in causal inference, to settings with observed individual heterogeneity in multivariate outcomes. We illustrate this by applying our method to estimate the effects of a Medicaid expansion policy in Montana, where we consider as outcome non-regular probability measures in d = 28 dimensions. For all experiments in this section, we use the POT toolbox (Flamary et al., 2021) to compute optimal transport plans and free-support barycenters. To solve the regression problem constrained to the unit simplex, we leverage the constrained optimization solver from the CVXPY toolbox (Diamond and Boyd, 2016). We compare our results to those from the experiment in Section 4.3 of Werenski et al. (2022). We follow the experimental procedure described therein, taking as experimental data the MNIST dataset of 28x28 pixel images of hand-written digits (Le Cun, 1998). |
| Researcher Affiliation | Academia | Florian Gunsilius EMAIL Department of Economics University of Michigan Ann Arbor, MI 48109-1220, USA Meng Hsuan Hsieh EMAIL Ross School of Business University of Michigan Ann Arbor, MI 48109-1234, USA Myung Jin Lee EMAIL Mays Business School Texas A&M University College Station, TX 77843-0001, USA |
| Pseudocode | No | The paper describes the methodology in three steps: (i) obtain the general tangent cone structure at the target measure, (ii) construct a tangent space from the tangent cone via barycentric projections if it does not exist, and (iii) perform a regression constrained to the unit simplex to carry out the projection in the tangent space. However, these steps are described in paragraph form and do not constitute a formally structured pseudocode or algorithm block. |
| Open Source Code | Yes | All the code used to produce the synthetic experiment results and the application to synthetic control method can be found at the following Git Hub repository: https://github.com/menghsuanhsieh/tangential-wasserstein-projection. |
| Open Datasets | Yes | We show comparison to the test case with image occlusion and with salt and pepper noise. We treat the normalized matrix as probability measures supported on a 28x28 grid. Our experiment was run using 10 control images; these control images are shown in Appendix C. For each control unit, we record the relative weights the receive in the respective projection approach. We use the Lego Bricks dataset available from Kaggle, which contains approximately 12,700 images of 16 different Lego bricks in RGBA format. We utilize the Berkeley Deep Drive dataset (Yu et al., 2020). We use the ACS data with harmonized variables made available by IPUMS, a unified source of Census and survey data collected around the world. |
| Dataset Splits | No | For the Medicaid expansion application, the paper states: "We estimate synthetic Montana , i.e. Montana had it not adopted Medicaid expansion, by estimating the optimal weights λ using data from 2010 to 2016, and solving (8) over the joint distribution of the four outcomes over the time period from 2010 to 2016... We then estimate the counterfactual joint distribution using data from 2017 to 2020". This describes a temporal split for the application, not a general training/test/validation split for model development. It also mentions "We randomly select N = 1500 observations from each unit for estimating λ" but does not specify how these are split into training, validation, or test sets. |
| Hardware Specification | Yes | 500 iterations of each of these exercises took 4 seconds to compute on an Apple M1 laptop with 8 cores and 16GB of working memory. We also computed our proposed projection in 3 minutes on an Apple M1 laptop with 8 cores and 16GB of working memory, compared to 4 hours on a cluster computer with 36 cores and 180GB of working memory for the method of Werenski et al. (2022). Our results were computed on a cluster computer with 36 cores and 180GB of RAM within 1.5 hours. |
| Software Dependencies | No | For all experiments in this section, we use the POT toolbox (Flamary et al., 2021) to compute optimal transport plans and free-support barycenters. To solve the regression problem constrained to the unit simplex, we leverage the constrained optimization solver from the CVXPY toolbox (Diamond and Boyd, 2016). The paper mentions software tools but does not provide specific version numbers for them. |
| Experiment Setup | No | The paper describes the overall experimental procedures and data used (e.g., "10 control images" for MNIST, "randomly select N = 1500 observations from each unit" for Medicaid data), but it does not provide specific hyperparameters like learning rates, batch sizes, number of epochs, or optimizer settings for any training processes described. It focuses more on the methodology and comparisons rather than the fine-grained settings for reproducibility of model training. |