An Automated Approach to Causal Inference in Discrete Settings

Guilherme Duarte; Noam Finkelstein; Dean Knox; Jonathan Mummolo; Ilya Shpitser

doi:10.1080/01621459.2023.2216909

An Automated Approach to Causal Inference in Discrete Settings

Guilherme Duarte, Noam Finkelstein, Dean Knox, Jonathan Mummolo, Ilya Shpitser

Research output: Contribution to journal › Article › peer-review

Abstract

Applied research conditions often make it impossible to point-identify causal estimands without untenable assumptions. Partial identification—bounds on the range of possible solutions—is a principled alternative, but the difficulty of deriving bounds in idiosyncratic settings has restricted its application. We present a general, automated numerical approach to causal inference in discrete settings. We show causal questions with discrete data reduce to polynomial programming problems, then present an algorithm to automatically bound causal effects using efficient dual relaxation and spatial branch-and-bound techniques. The user declares an estimand, states assumptions, and provides data—however incomplete or mismeasured. The algorithm then searches over admissible data-generating processes and outputs the most precise possible range consistent with available information—that is, sharp bounds—including a point-identified solution if one exists. Because this search can be computationally intensive, our procedure reports and continually refines non-sharp ranges guaranteed to contain the truth at all times, even when the algorithm is not run to completion. Moreover, it offers an ε-sharpness guarantee, characterizing the worst-case looseness of the incomplete bounds. These techniques are implemented in our Python package, autobounds. Analytically validated simulations show the method accommodates classic obstacles—including confounding, selection, measurement error, noncompliance, and nonresponse. Supplementary materials for this article are available online.

Original language	American English
Journal	Journal of the American Statistical Association
DOIs	https://doi.org/10.1080/01621459.2023.2216909
State	Accepted/In press - 2023
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Causal inference
Constrained optimization
Linear programming
Partial identification
Polynomial programming

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10.1080/01621459.2023.2216909

Cite this

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title = "An Automated Approach to Causal Inference in Discrete Settings",

abstract = "Applied research conditions often make it impossible to point-identify causal estimands without untenable assumptions. Partial identification—bounds on the range of possible solutions—is a principled alternative, but the difficulty of deriving bounds in idiosyncratic settings has restricted its application. We present a general, automated numerical approach to causal inference in discrete settings. We show causal questions with discrete data reduce to polynomial programming problems, then present an algorithm to automatically bound causal effects using efficient dual relaxation and spatial branch-and-bound techniques. The user declares an estimand, states assumptions, and provides data—however incomplete or mismeasured. The algorithm then searches over admissible data-generating processes and outputs the most precise possible range consistent with available information—that is, sharp bounds—including a point-identified solution if one exists. Because this search can be computationally intensive, our procedure reports and continually refines non-sharp ranges guaranteed to contain the truth at all times, even when the algorithm is not run to completion. Moreover, it offers an ε-sharpness guarantee, characterizing the worst-case looseness of the incomplete bounds. These techniques are implemented in our Python package, autobounds. Analytically validated simulations show the method accommodates classic obstacles—including confounding, selection, measurement error, noncompliance, and nonresponse. Supplementary materials for this article are available online.",

keywords = "Causal inference, Constrained optimization, Linear programming, Partial identification, Polynomial programming",

author = "Guilherme Duarte and Noam Finkelstein and Dean Knox and Jonathan Mummolo and Ilya Shpitser",

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year = "2023",

doi = "10.1080/01621459.2023.2216909",

language = "American English",

journal = "Journal of the American Statistical Association",

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AU - Duarte, Guilherme

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AU - Knox, Dean

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AU - Shpitser, Ilya

PY - 2023

Y1 - 2023

N2 - Applied research conditions often make it impossible to point-identify causal estimands without untenable assumptions. Partial identification—bounds on the range of possible solutions—is a principled alternative, but the difficulty of deriving bounds in idiosyncratic settings has restricted its application. We present a general, automated numerical approach to causal inference in discrete settings. We show causal questions with discrete data reduce to polynomial programming problems, then present an algorithm to automatically bound causal effects using efficient dual relaxation and spatial branch-and-bound techniques. The user declares an estimand, states assumptions, and provides data—however incomplete or mismeasured. The algorithm then searches over admissible data-generating processes and outputs the most precise possible range consistent with available information—that is, sharp bounds—including a point-identified solution if one exists. Because this search can be computationally intensive, our procedure reports and continually refines non-sharp ranges guaranteed to contain the truth at all times, even when the algorithm is not run to completion. Moreover, it offers an ε-sharpness guarantee, characterizing the worst-case looseness of the incomplete bounds. These techniques are implemented in our Python package, autobounds. Analytically validated simulations show the method accommodates classic obstacles—including confounding, selection, measurement error, noncompliance, and nonresponse. Supplementary materials for this article are available online.

AB - Applied research conditions often make it impossible to point-identify causal estimands without untenable assumptions. Partial identification—bounds on the range of possible solutions—is a principled alternative, but the difficulty of deriving bounds in idiosyncratic settings has restricted its application. We present a general, automated numerical approach to causal inference in discrete settings. We show causal questions with discrete data reduce to polynomial programming problems, then present an algorithm to automatically bound causal effects using efficient dual relaxation and spatial branch-and-bound techniques. The user declares an estimand, states assumptions, and provides data—however incomplete or mismeasured. The algorithm then searches over admissible data-generating processes and outputs the most precise possible range consistent with available information—that is, sharp bounds—including a point-identified solution if one exists. Because this search can be computationally intensive, our procedure reports and continually refines non-sharp ranges guaranteed to contain the truth at all times, even when the algorithm is not run to completion. Moreover, it offers an ε-sharpness guarantee, characterizing the worst-case looseness of the incomplete bounds. These techniques are implemented in our Python package, autobounds. Analytically validated simulations show the method accommodates classic obstacles—including confounding, selection, measurement error, noncompliance, and nonresponse. Supplementary materials for this article are available online.

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KW - Constrained optimization

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KW - Polynomial programming

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An Automated Approach to Causal Inference in Discrete Settings

Abstract

ASJC Scopus subject areas

Keywords

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