Decomposing Epistemic Uncertainty for Causal Decision Making

TL;DR

The paper tackles causal decision-making from observational data under unobserved confounding by separating epistemic uncertainty into non-identifiability and finite-sample effects. It introduces UA-DCM, a framework that constructs a confidence set around the empirical distribution and solves min-max / max-min problems over neural causal models to bound interventional quantities like $P(Y|do(X))$ and $ATE(X)$. A key contribution is the decomposition into a nonID region (unreducible by more data) and a sample-band (reducible with more data), which yields actionable moves: collect more samples, observe additional variables (e.g., instruments), or return a best action. The approach is validated on synthetic graphs and real data, showing when data collection or instrument observation can meaningfully tighten bounds, and providing a practical protocol for decision-making under uncertainty with finite samples.

Abstract

Causal inference from observational data provides strong evidence for the best action in decision-making without performing expensive randomized trials. The effect of an action is usually not identifiable under unobserved confounding, even with an infinite amount of data. Recent work uses neural networks to obtain practical bounds to such causal effects, which is often an intractable problem. However, these approaches may overfit to the dataset and be overconfident in their causal effect estimates. Moreover, there is currently no systematic approach to disentangle how much of the width of causal effect bounds is due to fundamental non-identifiability versus how much is due to finite-sample limitations. We propose a novel framework to address this problem by considering a confidence set around the empirical observational distribution and obtaining the intersection of causal effect bounds for all distributions in this confidence set. This allows us to distinguish the part of the interval that can be reduced by collecting more samples, which we call sample uncertainty, from the part that can only be reduced by observing more variables, such as latent confounders or instrumental variables, but not with more data, which we call non-ID uncertainty. The upper and lower bounds to this intersection are obtained by solving min-max and max-min problems with neural causal models by searching over all distributions that the dataset might have been sampled from, and all SCMs that entail the corresponding distribution. We demonstrate via extensive experiments on synthetic and real-world datasets that our algorithm can determine when collecting more samples will not help determine the best action. This can guide practitioners to collect more variables or lean towards a randomized study for best action identification.

Figures (8)

• Figure 1: Left: The case of infinite observational data. An identifiable causal effect can be estimated pointwise as in (a). Otherwise, we obtain bounds as in (b). Right: Given finite samples, we cannot pointwise estimate since the true distribution lies in a continuum of a confidence set. We can only obtain an interval as in (c). When the effect is not identifiable, we obtain a larger bound as in (d). Our goal is to analyze which part of this interval is due to non-identifiability and cannot be reduced by collecting more samples.
• Figure 2: The proposed inner and outer causal effect bounds.
• Figure 3: Experiment Results on Parents Labor Supply Dataset
• Figure 4: Causal graphs used in experiments
• Figure : $\mathrm{Explore }$$\epsilon$-$\mathrm{ball}$

Theorems & Definitions (49)

• Definition 1: Structural causal model (SCM) pearl2009causality
• Definition 2: Causal effect and do-intervention
• Definition 3: Deep causal models (DCM) kocaoglu2018causalganxia2021causalrahman2024modular
• Theorem 1
• Definition 4: Causal effect with DCM
• Theorem 2
• Theorem 3
• Definition 5: sample and nonID Uncertainty (Figure \ref{['fig:bound-illustration']})
• Proposition 1
• Proposition 2