Latent confounding in high-dimensional nonlinear models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908482434760704 |
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| author | Wang, Yuhao Shah, Rajen |
| author_facet | Wang, Yuhao Shah, Rajen |
| contents | We consider the the problem of identifying causal effects given a high-dimensional treatment vector in the presence of low-dimensional latent confounders. We assume a parametric structural causal model in which the outcome is permitted to depend on a sparse linear combination of the treatment vector and confounders nonlinearly. We consider a generalisation of the LAVA estimator of Chernozhukov et al. [2017] for estimating the treatment effects and show that under the so-called `dense confounding' assumption that each confounder can affect a wide range of observed treatment variables, one can estimate the causal parameters at the same rate as possible without confounding. Notably, the results permit a form of weak confounding in that the minimum non-zero singular value of the loading matrix of the confounders can grow more slowly than the $\sqrt{p}$, where $p$ is the dimension of the treatment vector. We further use our generalised LAVA procedure within a generalised covariance measure-based test for edges in a causal DAG in the presence of latent confounding. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_06274 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Latent confounding in high-dimensional nonlinear models Wang, Yuhao Shah, Rajen Statistics Theory Methodology We consider the the problem of identifying causal effects given a high-dimensional treatment vector in the presence of low-dimensional latent confounders. We assume a parametric structural causal model in which the outcome is permitted to depend on a sparse linear combination of the treatment vector and confounders nonlinearly. We consider a generalisation of the LAVA estimator of Chernozhukov et al. [2017] for estimating the treatment effects and show that under the so-called `dense confounding' assumption that each confounder can affect a wide range of observed treatment variables, one can estimate the causal parameters at the same rate as possible without confounding. Notably, the results permit a form of weak confounding in that the minimum non-zero singular value of the loading matrix of the confounders can grow more slowly than the $\sqrt{p}$, where $p$ is the dimension of the treatment vector. We further use our generalised LAVA procedure within a generalised covariance measure-based test for edges in a causal DAG in the presence of latent confounding. |
| title | Latent confounding in high-dimensional nonlinear models |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2508.06274 |