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This study introduces estimation with functional confounders (EFC), a new causal inference setting. EFC enables causal effect estimation even when standard positivity assumptions are violated, using functional interventions or gradient field analysis.

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Area of Science:

  • Causal inference
  • Statistical modeling
  • Machine learning

Background:

  • Causal inference typically requires ignorability and positivity assumptions.
  • Positivity is often violated in real-world observational data.
  • Estimation with functional confounders (EFC) is a novel setting where confounders are functions of observed data.

Purpose of the Study:

  • To investigate causal inference under the EFC setting where positivity is violated.
  • To identify conditions and methods for estimating causal effects in EFC.
  • To develop and evaluate a novel estimation procedure for EFC.

Main Methods:

  • Investigated functional interventions and functional positivity for effect estimation.
  • Developed conditions for nonparametric effect estimation using gradient fields.
  • Introduced Level-set Orthogonal Descent Estimation (LODE) for effect estimation in EFC.

Main Results:

  • Demonstrated that causal effects are estimable under specific conditions in EFC.
  • Derived error bounds for the LODE estimation procedure.
  • Validated the proposed methods using simulated and real-world data.

Conclusions:

  • EFC offers a framework for causal inference when standard positivity fails.
  • Functional interventions and gradient-based methods provide pathways for effect estimation in EFC.
  • LODE is a viable method for estimating causal effects in the EFC setting, with demonstrated empirical value.