Causal Estimation with Functional Confounders
- URL: http://arxiv.org/abs/2102.08533v1
- Date: Wed, 17 Feb 2021 02:16:21 GMT
- Title: Causal Estimation with Functional Confounders
- Authors: Aahlad Puli, Adler J. Perotte, Rajesh Ranganath
- Abstract summary: Causal inference relies on two fundamental assumptions: ignorability and positivity.
We study causal inference when the true confounder value can be expressed as a function of the observed data.
In this setting, ignorability is satisfied, however positivity is violated, and causal inference is impossible in general.
- Score: 24.54466899641308
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Causal inference relies on two fundamental assumptions: ignorability and
positivity. We study causal inference when the true confounder value can be
expressed as a function of the observed data; we call this setting estimation
with functional confounders (EFC). In this setting, ignorability is satisfied,
however positivity is violated, and causal inference is impossible in general.
We consider two scenarios where causal effects are estimable. First, we discuss
interventions on a part of the treatment called functional interventions and a
sufficient condition for effect estimation of these interventions called
functional positivity. Second, we develop conditions for nonparametric effect
estimation based on the gradient fields of the functional confounder and the
true outcome function. To estimate effects under these conditions, we develop
Level-set Orthogonal Descent Estimation (LODE). Further, we prove error bounds
on LODE's effect estimates, evaluate our methods on simulated and real data,
and empirically demonstrate the value of EFC.
Related papers
- Two-Stage Nuisance Function Estimation for Causal Mediation Analysis [8.288031125057524]
We propose a two-stage estimation strategy that estimates the nuisance functions based on the role they play in the structure of the bias of the influence function-based estimator of the mediation functional.
We provide analysis of the proposed method, as well as sufficient conditions for consistency and normality of the estimator of the parameter of interest.
arXiv Detail & Related papers (2024-03-31T16:38:48Z) - Doubly Robust Proximal Causal Learning for Continuous Treatments [56.05592840537398]
We propose a kernel-based doubly robust causal learning estimator for continuous treatments.
We show that its oracle form is a consistent approximation of the influence function.
We then provide a comprehensive convergence analysis in terms of the mean square error.
arXiv Detail & Related papers (2023-09-22T12:18:53Z) - Benchmarking Bayesian Causal Discovery Methods for Downstream Treatment
Effect Estimation [137.3520153445413]
A notable gap exists in the evaluation of causal discovery methods, where insufficient emphasis is placed on downstream inference.
We evaluate seven established baseline causal discovery methods including a newly proposed method based on GFlowNets.
The results of our study demonstrate that some of the algorithms studied are able to effectively capture a wide range of useful and diverse ATE modes.
arXiv Detail & Related papers (2023-07-11T02:58:10Z) - B-Learner: Quasi-Oracle Bounds on Heterogeneous Causal Effects Under
Hidden Confounding [51.74479522965712]
We propose a meta-learner called the B-Learner, which can efficiently learn sharp bounds on the CATE function under limits on hidden confounding.
We prove its estimates are valid, sharp, efficient, and have a quasi-oracle property with respect to the constituent estimators under more general conditions than existing methods.
arXiv Detail & Related papers (2023-04-20T18:07:19Z) - Linking a predictive model to causal effect estimation [21.869233469885856]
This paper first tackles the challenge of estimating the causal effect of any feature (as the treatment) on the outcome w.r.t. a given instance.
The theoretical results naturally link a predictive model to causal effect estimations and imply that a predictive model is causally interpretable.
We use experiments to demonstrate that various types of predictive models, when satisfying the conditions identified in this paper, can estimate the causal effects of features as accurately as state-of-the-art causal effect estimation methods.
arXiv Detail & Related papers (2023-04-10T13:08:16Z) - Partial counterfactual identification and uplift modeling: theoretical
results and real-world assessment [0.4129225533930965]
This paper discusses how it is possible to derive bounds on the probability of counterfactual statements based on uplift terms.
We show that tightness of such bounds depends on the information of the feature set on the uplift term.
We propose a point estimator based on the assumption of conditional independence between the counterfactual outcomes.
arXiv Detail & Related papers (2022-11-14T10:45:55Z) - Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing.
We study the case where probability distributions are not known a priori but need to be estimated from data.
arXiv Detail & Related papers (2022-08-29T16:16:22Z) - Inference on Strongly Identified Functionals of Weakly Identified
Functions [71.42652863687117]
We study a novel condition for the functional to be strongly identified even when the nuisance function is not.
We propose penalized minimax estimators for both the primary and debiasing nuisance functions.
arXiv Detail & Related papers (2022-08-17T13:38:31Z) - Causal Effect Estimation using Variational Information Bottleneck [19.6760527269791]
Causal inference is to estimate the causal effect in a causal relationship when intervention is applied.
We propose a method to estimate Causal Effect by using Variational Information Bottleneck (CEVIB)
arXiv Detail & Related papers (2021-10-26T13:46:12Z) - Causal Inference Under Unmeasured Confounding With Negative Controls: A
Minimax Learning Approach [84.29777236590674]
We study the estimation of causal parameters when not all confounders are observed and instead negative controls are available.
Recent work has shown how these can enable identification and efficient estimation via two so-called bridge functions.
arXiv Detail & Related papers (2021-03-25T17:59:19Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.