Partial Identification with Proxy of Latent Confoundings via Sum-of-ratios Fractional Programming

Zhiheng Zhang, Xinyan Su
Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, PMLR 244:4140-4172, 2024.

Abstract

Causal effect estimation is a crucial theoretical tool in uncertainty analysis. The challenge of unobservable confoundings has raised concerns regarding quantitative causality computation. To address this issue, proxy control has become popular, employing auxiliary variables W as proxies for the confounding variables U. However, proximal methods rely on strong assumptions, such as reversibility and completeness, that are challenging to interpret empirically and verify. Consequently, their applicability in real-world scenarios is limited, particularly when the proxies lack informativeness. In our paper, we have developed a novel optimization method named Partial Identification with Proxy of Latent Confoundings via Sum-of-Ratios Fractional Programming (PI-SFP). This method does not impose any additional restrictions upon proxies and only assumes the mild partial observability of the transition matrix P(W | U). We have theoretically proven the global convergence of PI-SFP to the valid bound of the causal effect and analyzed the conditions under which the bounds could be tight. Our synthetic and real-world experiments validate our theoretical framework.

Cite this Paper

BibTeX
@InProceedings{pmlr-v244-zhang24a, title = {Partial Identification with Proxy of Latent Confoundings via Sum-of-ratios Fractional Programming}, author = {Zhang, Zhiheng and Su, Xinyan}, booktitle = {Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence}, pages = {4140--4172}, year = {2024}, editor = {Kiyavash, Negar and Mooij, Joris M.}, volume = {244}, series = {Proceedings of Machine Learning Research}, month = {15--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v244/main/assets/zhang24a/zhang24a.pdf}, url = {https://proceedings.mlr.press/v244/zhang24a.html}, abstract = {Causal effect estimation is a crucial theoretical tool in uncertainty analysis. The challenge of unobservable confoundings has raised concerns regarding quantitative causality computation. To address this issue, proxy control has become popular, employing auxiliary variables W as proxies for the confounding variables U. However, proximal methods rely on strong assumptions, such as reversibility and completeness, that are challenging to interpret empirically and verify. Consequently, their applicability in real-world scenarios is limited, particularly when the proxies lack informativeness. In our paper, we have developed a novel optimization method named Partial Identification with Proxy of Latent Confoundings via Sum-of-Ratios Fractional Programming (PI-SFP). This method does not impose any additional restrictions upon proxies and only assumes the mild partial observability of the transition matrix P(W | U). We have theoretically proven the global convergence of PI-SFP to the valid bound of the causal effect and analyzed the conditions under which the bounds could be tight. Our synthetic and real-world experiments validate our theoretical framework.} }
Endnote
%0 Conference Paper %T Partial Identification with Proxy of Latent Confoundings via Sum-of-ratios Fractional Programming %A Zhiheng Zhang %A Xinyan Su %B Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2024 %E Negar Kiyavash %E Joris M. Mooij %F pmlr-v244-zhang24a %I PMLR %P 4140--4172 %U https://proceedings.mlr.press/v244/zhang24a.html %V 244 %X Causal effect estimation is a crucial theoretical tool in uncertainty analysis. The challenge of unobservable confoundings has raised concerns regarding quantitative causality computation. To address this issue, proxy control has become popular, employing auxiliary variables W as proxies for the confounding variables U. However, proximal methods rely on strong assumptions, such as reversibility and completeness, that are challenging to interpret empirically and verify. Consequently, their applicability in real-world scenarios is limited, particularly when the proxies lack informativeness. In our paper, we have developed a novel optimization method named Partial Identification with Proxy of Latent Confoundings via Sum-of-Ratios Fractional Programming (PI-SFP). This method does not impose any additional restrictions upon proxies and only assumes the mild partial observability of the transition matrix P(W | U). We have theoretically proven the global convergence of PI-SFP to the valid bound of the causal effect and analyzed the conditions under which the bounds could be tight. Our synthetic and real-world experiments validate our theoretical framework.
APA
Zhang, Z. & Su, X.. (2024). Partial Identification with Proxy of Latent Confoundings via Sum-of-ratios Fractional Programming. Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 244:4140-4172 Available from https://proceedings.mlr.press/v244/zhang24a.html.

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