Discovering Causal Models with Optimization: Confounders, Cycles, and Instrument Validity

55 Pages Posted: 8 Jul 2021 Last revised: 11 Oct 2023

See all articles by Frederick Eberhardt

Frederick Eberhardt

California Institute of Technology

Nur Kaynar

University of California, Los Angeles (UCLA) - Anderson School of Management

Auyon Siddiq

University of California, Los Angeles (UCLA) - Anderson School of Management

Date Written: June 24, 2021

Abstract

We propose a new optimization-based method for learning causal structures from observational data, a process known as causal discovery. Our method takes as input observational data over a set of variables and returns a graph in which causal relations are specified by directed edges. We consider a highly general search space that accommodates latent confounders and feedback cycles, which few extant methods do. We formulate the discovery problem as an integer program, and propose a solution technique that exploits the conditional independence structure in the data to identify promising edges for inclusion in the output graph. In the large-sample limit, our method recovers a graph that is (Markov) equivalent to the true data-generating graph. Computationally, our method is competitive with the state-of-the-art, and can solve in minutes instances that are intractable for alternative causal discovery methods. We leverage our method to develop a procedure for investigating the validity of an instrumental variable and demonstrate it on the influential instruments for estimating the returns to education from Angrist and Krueger (1991) and Card (1993). In particular, our test complements existing instrument tests by revealing the precise causal pathways that undermine instrument validity, highlighting the unique merits of the graphical perspective on causality.

Keywords: causal inference, causal discovery, instrumental variables, graphical models, optimization

Suggested Citation

Eberhardt, Frederick and Kaynar, Nur and Siddiq, Auyon, Discovering Causal Models with Optimization: Confounders, Cycles, and Instrument Validity (June 24, 2021). Available at SSRN: https://ssrn.com/abstract=3873034 or http://dx.doi.org/10.2139/ssrn.3873034

Frederick Eberhardt

California Institute of Technology ( email )

Pasadena, CA 91125
United States

Nur Kaynar (Contact Author)

University of California, Los Angeles (UCLA) - Anderson School of Management ( email )

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States

Auyon Siddiq

University of California, Los Angeles (UCLA) - Anderson School of Management ( email )

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States

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