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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 ISSN Print: 2576-0645 CODEN: JAMCEZ
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ArticleOpen Access http://dx.doi.org/10.26855/jamc.2025.12.004

TWDVAE: Causal Effect Estimation Model Based on Proxy Variable Type Importance

Haowei Ye

School of Mathematical Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China.

*Corresponding author:Haowei Ye

Published: December 18, 2025

Abstract

The estimation of causal effects from observational data necessitates rigorous adjustment for confounding variables. Contemporary methods based on disentangled representation learning, address this challenge by decomposing covariates into independent latent factors corresponding to treatment, outcome, and confounders. However, these approaches typically impose a uniform constraint on all covariates during the disentanglement process, neglecting the potential heterogeneity in the proxy strength between continuous and discrete variables. This paper proposes that such heterogeneity constitutes a critical consideration for accurate causal inference. We introduce the Type-Weighted Disentangled VAE (TWDVAE), a methodological framework that incorporates explicit differentiation between variable types through a structured weighting scheme within the disentanglement objective. Specifically, our approach assigns distinct weights to continuous and discrete variables according to their hypothesized proxy importance, thereby directing the learning algorithm to prioritize the more influential variable type in the latent representation. This formulation provides a principled mechanism for integrating domain knowledge about variable-type importance directly into the estimation procedure. Empirical evaluations conducted on benchmark datasets IHDP demonstrate that TWDVAE achieves statistically significant improvements over conventional approaches, with absolute reductions in estimation error. The results substantiate that acknowledging differential proxy importance across variable types enhances both the precision of causal effect estimates and the interpretability of the learned representations. This work establishes variable-type differentiation as a substantive consideration in causal infer-ence methodology and offers a framework for leveraging this insight to advance estimation accuracy.

Keyword

Causal inference; disentangled representation learning; observational data; variational autoencoder (VAE); type-weighted learning

References

[1] Glass, T. A., Goodman, S. N., Hernán, M., & Samet, J. M. Causal inference in public health. Annu Rev Public Health. 2013;34(1):61-75.

[2] Wang, Z., Zhang, J., Xu, H., Chen, X., Zhang, Y., Zhao, W. X., & Wen, J. R. Counterfactual data-augmented sequential recommendation. In: Proceedings of the 44th International ACM SIGIR Conference on Research and Development in Information Retrieval; 2021. p. 347-356.

[3] Sorace, M. The ties that unbind: intergovernmental decision rules and the policy-opinion link. J Eur Public Policy. 2023;30:1609-32.

[4] Zhang, W., Liu, L., & Li, J. Treatment effect estimation with disentangled latent factors. In: Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35; 2021. p. 10923-30.

[5] Liu, Y., Wang, J., & Li, B. EDVAE: Disentangled latent factors models in counterfactual reasoning for individual treatment effects estimation. Inf Sci. 2024;652:119578.

[6] Ding, P. A First Course in Causal Inference. CRC Press; 2024.

[7] Funk, M. J., Westreich, D., Wiesen, C., Stürmer, T., Brookhart, M. A., & Davidian, M. Doubly robust estimation of causal effects. Am J Epidemiol. 2011;173(7):761-7.

[8] Shalit, U., Johansson, F. D., & Sontag, D. Estimating individual treatment effect: generalization bounds and algorithms. In: Interna-tional Conference on Machine Learning. PMLR; 2017. p. 3076-85.

[9] Shi, C., Blei, D., & Veitch, V. Adapting neural networks for the estimation of treatment effects. Adv Neural Inf Process Syst. 2019;32.

[10] Cheng, M., Liao, X., Liu, Q., Ma, B., Xu, J., & Zheng, B. Learning disentangled representations for counterfactual regression via mutual information minimization. arXiv preprint. 2022; arXiv:2206.01022.

[11] Kingma, D. P., & Welling, M. Auto-encoding variational bayes. arXiv preprint. 2013; arXiv:1312.6114.

[12] Künzel, S. R., Sekhon, J. S., Bickel, P. J., & Yu, B. Metalearners for estimating heterogeneous treatment effects using machine learning. Proc Natl Acad Sci U S A. 2019;116(10):4156-65.

[13] Louizos, C., Shalit, U., Mooij, J. M., Sontag, D., Zemel, R., & Welling, M. Causal effect inference with deep latent-variable models. Adv Neural Inf Process Syst. 2017;30.

[14] McCormick, M. C., McCarton, C., Brooks-Gunn, J., Belt, P., & Gross, R. T. The infant health and development program: interim summary. J Dev Behav Pediatr. 1998.

Copyright

© 2025 by the author(s).
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) license, which permits non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited and is not modified or adapted.
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How to cite this paper

TWDVAE: Causal Effect Estimation Model Based on Proxy Variable Type Importance

How to cite this paper: Haowei Ye. (2025) TWDVAE: Causal Effect Estimation Model Based on Proxy Variable Type Importance. Journal of Applied Mathematics and Computation9(4), 249-257.

DOI: http://dx.doi.org/10.26855/jamc.2025.12.004