Estimating Average Treatment Effects in Causal Latent Factor Models with Unobserved Confounding

Khái niệm cốt lõi

This article introduces a novel doubly robust estimator for average treatment effects in the presence of unobserved confounding, leveraging matrix completion techniques to handle large-scale data with repeated measurements across units.

Tóm tắt

The article presents a framework for estimating average treatment effects (ATEs) in modern data-rich environments with unobserved confounding. The key contributions are:

Proposed a doubly robust (DR) estimator that combines outcome imputation, inverse probability weighting, and a novel cross-fitting procedure for matrix completion. The DR estimator is shown to have better finite-sample guarantees than alternative outcome-based and assignment-based estimators.

Derived formal guarantees for the DR estimator, including a central limit theorem showing it converges to a mean-zero Gaussian distribution at a parametric rate, under weak conditions on the matrix completion algorithm used.

Introduced a novel matrix completion algorithm called Cross-Fitted-SVD that satisfies the required properties to enable the theoretical guarantees for the DR estimator. Cross-Fitted-SVD uses a cross-fitting approach to ensure independence between the matrix completion estimates and the noise in the data.

Demonstrated through simulations that the DR estimator outperforms the outcome imputation and inverse probability weighting estimators, even when the latter exhibit substantial biases.

The article provides a principled framework for causal inference in modern data-rich settings with unobserved confounding, leveraging the availability of large numbers of outcomes to control for latent confounding factors.

Thống kê

"λ ≤ pi,j ≤ 1 - λ, for all i ∈ [N] and j ∈ [M], where 0 < λ ≤ 1/2 is a constant."
"ε(a)
i,j has subGaussian norm bounded by a constant σ for every i ∈ [N] and a ∈ {0, 1}."
"θmax ≜ Σa∈{0,1} ||Θ(a)||max is bounded."

Trích dẫn

"This article introduces a new estimator of average treatment effects under unobserved confounding in modern data-rich environments featuring large numbers of units and outcomes."
"We derive finite-sample and asymptotic guarantees, and show that the error of the new estimator converges to a mean-zero Gaussian distribution at a parametric rate."
"Simulation results demonstrate the practical relevance of the formal properties of the estimators analyzed in this article."

Thông tin chi tiết chính được chắt lọc từ

Doubly Robust Inference in Causal Latent Factor Models

by Alberto Abad... lúc arxiv.org 04-16-2024

https://arxiv.org/pdf/2402.11652.pdf

Yêu cầu sâu hơn

How can the proposed framework be extended to handle time-varying treatments and outcomes

To extend the proposed framework to handle time-varying treatments and outcomes, we can incorporate a time dimension into the data and analysis. This would involve considering the temporal aspect of the treatment assignments and potential outcomes. One approach could be to introduce lagged variables or time indicators to capture the time-varying nature of the treatments and outcomes. Additionally, time-series analysis techniques such as autoregressive models or panel data methods could be utilized to account for the dynamic nature of the data. By incorporating time as a factor in the analysis, the framework can be adapted to handle longitudinal data and time-dependent causal effects.

What are the implications of relaxing the independence assumptions between the noise in potential outcomes and treatment assignments

Relaxing the independence assumptions between the noise in potential outcomes and treatment assignments can have several implications. When the independence assumptions are relaxed, it may introduce additional complexity into the modeling process. The presence of correlated errors between potential outcomes and treatment assignments could lead to biased estimates and affect the validity of the causal inference. In such cases, it becomes crucial to carefully consider the underlying relationships between the variables and incorporate appropriate control measures to address the confounding factors. Advanced statistical techniques like instrumental variables or structural equation modeling may be necessary to account for the correlated errors and ensure the robustness of the estimation.

Can the doubly robust estimation approach be applied to other causal inference settings beyond the latent factor model, such as network interference or spillover effects

The doubly robust estimation approach can indeed be applied to various other causal inference settings beyond the latent factor model. For instance, in settings involving network interference or spillover effects, where the treatment effects on one unit may depend on the treatments received by other connected units, the doubly robust estimator can be valuable. By incorporating network structures or spatial dependencies into the model, the estimator can account for the complex interactions and dependencies among units. This allows for the estimation of causal effects while controlling for unobserved confounders and addressing the challenges posed by network interference. The flexibility and robustness of the doubly robust approach make it suitable for a wide range of causal inference scenarios, including those involving network effects.