# Efficient Identification in Linear Structural Causal Models with Auxiliary Cutsets

ICML, pp. 5501-5510, 2020.

EI

Weibo:

Abstract:

We develop a a new polynomial-time algorithm for identification of structural coefficients in linear causal models that subsumes previous stateof-the-art methods, unifying several disparate approaches to identification in this setting. Building on these results, we develop a procedure for identifying total causal effects in linear systems...More

Code:

Data:

Introduction

- Regression analysis is one of the most popular methods used to understand the relationships across multiple variables throughout the empirical sciences.
- The most common type of regression is linear, where one attempts to explain the observed data by fitting a line by minimizing the sum of the corresponding deviations.
- This method can be traced back at least to the pioneering work of Legendre and Gauss (Legendre, 1805; Gauss, 1809), in the context of astronomical observations (Stigler, 1986).
- In practice learning about causation is often the main goal of the exercise, sometimes, the very reason one engaged in the data collection and the subsequent anal-

Highlights

- Regression analysis is one of the most popular methods used to understand the relationships across multiple variables throughout the empirical sciences
- In practice learning about causation is often the main goal of the exercise, sometimes, the very reason one engaged in the data collection and the subsequent analysis in the first place
- We develop the Auxiliary Cutset Identification Algorithm (ACID), which runs in polynomial-time, and unifies and strictly subsumes existing efficient identification methods as well as more powerful methods with unknown complexity
- We developed an efficient algorithm for linear identification that subsumes the current state-of-the-art, unifying disparate approaches found in the literature
- We introduced a new method for identification of partial effects, as well as a method for exploiting those partial effects via auxiliary variables

Conclusion

- The authors developed an efficient algorithm for linear identification that subsumes the current state-of-the-art, unifying disparate approaches found in the literature.
- The authors introduced a new method for identification of partial effects, as well as a method for exploiting those partial effects via auxiliary variables.
- The authors devised a novel decomposition of total effects allowing previously incompatible methods to be combined, leading to strictly more powerful results.
- Sensitivity analysis of linear structural causal models.

Summary

## Introduction:

Regression analysis is one of the most popular methods used to understand the relationships across multiple variables throughout the empirical sciences.- The most common type of regression is linear, where one attempts to explain the observed data by fitting a line by minimizing the sum of the corresponding deviations.
- This method can be traced back at least to the pioneering work of Legendre and Gauss (Legendre, 1805; Gauss, 1809), in the context of astronomical observations (Stigler, 1986).
- In practice learning about causation is often the main goal of the exercise, sometimes, the very reason one engaged in the data collection and the subsequent anal-
## Conclusion:

The authors developed an efficient algorithm for linear identification that subsumes the current state-of-the-art, unifying disparate approaches found in the literature.- The authors introduced a new method for identification of partial effects, as well as a method for exploiting those partial effects via auxiliary variables.
- The authors devised a novel decomposition of total effects allowing previously incompatible methods to be combined, leading to strictly more powerful results.
- Sensitivity analysis of linear structural causal models.

Funding

- Kumor and Bareinboim are supported in parts by grants from NSF IIS-1704352 and IIS-1750807 (CAREER)

Reference

- Drton, M. and Weihs, L. Generic Identifiability of Linear Structural Equation Models by Ancestor Decomposition. arXiv:1504.02992 [stat], April 2015.
- Bardet, M. and Chyzak, F. On the complexity of a gröbner basis algorithm. In Algorithms Seminar, pp. 85–92, 2005.
- Bareinboim, E. and Pearl, J. Causal inference by surrogate experiments: z-identifiability. Uncertainty in Artificial Intelligence, 2012.
- Bareinboim, E. and Pearl, J. Causal inference and the datafusion problem. Proceedings of the National Academy of Sciences, 113:7345–7352, 2016.
- Bowden, R. J. and Turkington, D. A. Instrumental Variables. Number no. 8 in Econometric Society Monographs in Quantitative Economics. Cambridge University Press, Cambridge [Cambridgeshire]; New York, 1984. ISBN 978-0-521-26241-5.
- Brito, C. and Pearl, J. Generalized instrumental variables. In Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence, pp. 85–93. Morgan Kaufmann Publishers Inc., 2002.
- Chen, B. Identification and Overidentification of Linear Structural Equation Models. Advances in Neural Information Processing Systems 29, pp. 1579–1587, 2016.
- Chen, B., Pearl, J., and Bareinboim, E. Incorporating Knowledge into Structural Equation Models Using Auxiliary Variables. IJCAI 2016, Proceedings of the 25th International Joint Conference on Artificial Intelligence, pp. 7, 2016.
- Chen, B., Kumor, D., and Bareinboim, E. Identification and model testing in linear structural equation models using auxiliary variables. International Conference on Machine Learning, pp. 757–766, 2017.
- Fisher, F. M. The Identification Problem in Econometrics. McGraw-Hill, 1966.
- Foygel, R., Draisma, J., and Drton, M. Half-trek criterion for generic identifiability of linear structural equation models. The Annals of Statistics, pp. 1682–1713, 2012.
- García-Puente, L. D., Spielvogel, S., and Sullivant, S. Identifying causal effects with computer algebra. In Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, pp. 193–200, 2010.
- Gauss, C. Theoria motus, corporum coelesium, lib. 2, sec. iii, perthes u. Besser Publ, pp. 205–224, 1809.
- Gessel, I. M. and Viennot, X. Determinants, paths, and plane partitions. preprint, 1989.
- Hastie, T., Tibshirani, R., and Friedman, J. The elements of statistical learning: data mining, inference, and prediction. Springer Science & Business Media, 2009.
- Koller, D. and Friedman, N. Probabilistic Graphical Models: Principles and Techniques. MIT press, 2009.
- Kumor, D., Chen, B., and Bareinboim, E. Efficient identification in linear structural causal models with instrumental cutsets. In Advances in Neural Information Processing Systems, pp. 12477–12486, 2019.
- Kumor, D., Cinelli, C., and Bareinboim, E. Efficient identification in linear structural causal models with auxiliary cutsets. Technical Report R-56, 2020. https://causalai.net/r56.pdf.
- Lee, S., Correa, J. D., and Bareinboim, E. General identifiability with arbitrary surrogate experiments. In Proceedings of the Thirty-Fifth Conference Annual Conference on Uncertainty in Artificial Intelligence, Corvallis, OR, 20AUAI Press.
- Legendre, A. M. Nouvelles méthodes pour la détermination des orbites des comètes. F. Didot, 1805.
- Cinelli, C. and Hazlett, C. Making sense of sensitivity: Pearl, J. Causality: Models, Reasoning and Inference. Camextending omitted variable bias. Journal of the Royal bridge University Press, 2000.
- Picard, J.-C. and Queyranne, M. On the structure of all minimum cuts in a network and applications. Mathematical Programming, 22(1):121–121, December 1982. ISSN 1436-4646. doi: 10.1007/BF01581031.
- Spirtes, P., Glymour, C. N., and Scheines, R. Causation, prediction, and search. MIT press, 2000.
- Stigler, S. M. The history of statistics: The measurement of uncertainty before 1900. Harvard University Press, 1986.
- Sullivant, S., Talaska, K., and Draisma, J. Trek separation for Gaussian graphical models. The Annals of Statistics, pp. 1665–1685, 2010.
- Tian, J. Identifying linear causal effects. In AAAI, pp. 104– 111, 2004.
- Tian, J. Identifying direct causal effects in linear models. In Proceedings of the National Conference on Artificial Intelligence, volume 20, pp. 346. Menlo Park, CA; Cambridge, MA; London; AAAI Press; MIT Press; 1999, 2005.
- Tian, J. A Criterion for Parameter Identification in Structural Equation Models. In Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence, pp. 8, Vancouver, BC, Canada, 2007.
- Van der Zander, B. and Liskiewicz, M. On Searching for Generalized Instrumental Variables. In Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS-16), 2016.
- Van der Zander, B., Textor, J., and Liskiewicz, M. Efficiently Finding Conditional Instruments for Causal Inference. IJCAI 2015, Proceedings of the 24th International Joint Conference on Artificial Intelligence, 2015.
- Weihs, L., Robinson, B., Dufresne, E., Kenkel, J., McGee II, K. K. R., Reginald, M. I., Nguyen, N., Robeva, E., and Drton, M. Determinantal generalizations of instrumental variables. Journal of Causal Inference, 6(1), 2018.
- Wright, P. G. Tariff on Animal and Vegetable Oils. Macmillan Company, New York, 1928.
- Wright, S. Correlation and causation. J. agric. Res., 20: 557–580, 1921.

Full Text

Tags

Comments