Efficient Identification in Linear Structural Causal Models with Auxiliary Cutsets

Daniel Kumor
Daniel Kumor
Carlos Cinelli
Carlos Cinelli

ICML, pp. 5501-5510, 2020.

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We developed an efficient algorithm for linear identification that subsumes the current state-of-the-art, unifying disparate approaches found in the literature

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

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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)
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