A Neural Framework for Generalized Causal Sensitivity Analysis

TL;DR

This paper tackles causal sensitivity analysis under unobserved confounding by introducing NeuralCSA, a neural framework that unifies a broad class of sensitivity models (GTSMs) and supports binary and continuous treatments as well as multiple causal queries. The key idea is to learn a latent distribution shift in the unobserved confounders caused by treatment via two conditional normalizing flows, enabling valid bounds on general causal queries through a two-stage procedure with theoretical guarantees. The main contributions are (i) defining GTSMs to subsume MSM, f-sensitivity, and Rosenbaum models, (ii) proposing NeuralCSA with Stage 1 observational distribution learning and Stage 2 interventional shift learning, and (iii) proving a sufficiency theorem ensuring that the two-stage approach yields valid upper and lower bounds, along with extensive empirical validation on synthetic, semi-synthetic, and real-world data demonstrating accuracy and practical utility. The framework enables practitioners to perform robust sensitivity analyses across diverse settings, including multi-outcome interventional densities, without analytic solvability, thereby enhancing decision-making under unobserved confounding.

Abstract

Unobserved confounding is common in many applications, making causal inference from observational data challenging. As a remedy, causal sensitivity analysis is an important tool to draw causal conclusions under unobserved confounding with mathematical guarantees. In this paper, we propose NeuralCSA, a neural framework for generalized causal sensitivity analysis. Unlike previous work, our framework is compatible with (i) a large class of sensitivity models, including the marginal sensitivity model, f-sensitivity models, and Rosenbaum's sensitivity model; (ii) different treatment types (i.e., binary and continuous); and (iii) different causal queries, including (conditional) average treatment effects and simultaneous effects on multiple outcomes. The generality of NeuralCSA is achieved by learning a latent distribution shift that corresponds to a treatment intervention using two conditional normalizing flows. We provide theoretical guarantees that NeuralCSA is able to infer valid bounds on the causal query of interest and also demonstrate this empirically using both simulated and real-world data.

Figures (11)

• Figure 1: Idea behind NeuralCSA to learn the latent distribution shift due to treatment intervention (). Orange nodes denote observed (random) variables. Blue nodes denote unobserved variables pre-intervention. Green nodes indicate unobserved variables post-intervention under a GTSM $\mathcal{M}$. Observed confounders $X$ are empty for simplicity.
• Figure 2: Causal graph. Observed variables are colored orange and unobserved blue. We allow for arbitrary dependence between $X$ and $U$.
• Figure 3: Overview of the two-stage procedure.
• Figure 4: Architecture of NeuralCSA.
• Figure 5: Validating the correctness of NeuralCSA (ours) by comparing with optimal closed-form solutions (CF) for the MSM on simulated data. Left: Dataset 1, binary treatment. Right: Dataset 2, continuous treatment. Reported: mean $\pm$ standard deviation over 5 runs.

Theorems & Definitions (10)

• Definition 1
• Definition 2
• Lemma 1
• Definition 3: Transformation-invariance
• Lemma 2
• Theorem 1: Sufficiency of two-stage procedure
• Lemma 3
• proof
• proof
• proof