Causal Inference with Unobserved Confounding

Causal inference from observational data can provide strong evidence for finding the best action in a decision-making scenario without having to perform expensive randomized trials. The causal effect of an action is often not pointwise identifiable even with infinite data due to unobserved confounding factors. Furthermore, having only finitely many samples adds another layer of uncertainty to causal effect estimation. Several existing methods can be used to obtain upper and lower bounds to the causal effect, ranging from symbolic methods to the more recent neural network-based approaches, which implicitly incorporate both sources of uncertainty. However, these methods do not inform whether collecting more samples may or may not help identify the best action from observational data, leaving experts in the dark about their data collection strategies. We address this problem with a novel framework that can distinguish the range of causal effect values that might be eliminated by collecting more samples from the range of values that, with high probability, cannot be eliminated with more observational samples. We show that this partitioning can be obtained by solving max-min and min-max optimization problems. We leverage neural causal models to approximately recover this decomposition in practice. We demonstrate via experiments on synthetic and real-world datasets that our algorithm can determine when collecting more samples will not help determine the best action. Our framework can help practitioners decide when to resort to non-observational studies or seek to measure some of the unmeasured confounders for optimal decision-making.

Granger causality characterizes directed predictive dependencies in multivariate time series, but recovering such dependencies becomes challenging in the presence of latent confounding. Cross-environment invariance provides a natural source of information in heterogeneous settings, yet invariance alone can be insufficient: when latent-to-observed mechanisms remain stable, hidden confounders can induce predictive dependencies that are just as invariant as genuine Granger-causal relations. We show that interventions provide an additional source of identifying information by inducing structured variation in observed mechanisms, while stable latent pathways need not exhibit the same cross-environment changes. In practice, however, neither the intervened environments nor the affected mechanisms are known. We propose GRACE, a framework for learning Granger causality under latent confounding from intervention-induced heterogeneity. GRACE decomposes multivariate dynamics into a shared Granger mechanism, sparse environment-specific deviations that capture edge-level interventions, and a latent component that accounts for confounding. Under a linear generative model, we show that GRACE can recover which environments intervene on a given edge when the edge is perturbed in at least one but fewer than half of the environments and the intervention effect is sufficiently large to survive sparsity shrinkage; the recovered intervention pattern then provides a certificate for the corresponding Granger causal edge. Experiments on synthetic and real-world time series demonstrate improved Granger causal structure recovery under latent confounding and unknown interventions.

Causal inference in spatial domains faces two intertwined challenges: (1) unmeasured spatial factors, such as weather, air pollution, or mobility, that confound treatment and outcome, and (2) interference from nearby treatments that violate standard no-interference assumptions. While existing methods typically address one by assuming away the other, we show they are deeply connected: interference reveals structure in the latent confounder. Leveraging this insight, we propose the Spatial Deconfounder, a two-stage method that reconstructs a substitute confounder from local treatment vectors using a conditional variational autoencoder (C-VAE) with a spatial prior, then estimates causal effects with a flexible outcome model. We show that this enables nonparametric identification of direct and spillover effects under weak assumptions--without multiple treatment types or a known latent-field model. Empirically, we extend SpaCE, a benchmark suite for spatial confounding, to include treatment interference, and show that the Spatial Deconfounder consistently improves effect estimation across real-world environmental health and social science datasets. By turning local interference into a multi-cause proxy for latent spatial confounding, our framework advances robust causal inference for spatial data.

Long-term treatment effect estimation is a significant but challenging problem in many applications. Existing methods rely on ideal assumptions, such as no unobserved confounders or binary treatment, to estimate long-term average treatment effects. However, in numerous real-world applications, these assumptions could be violated, and average treatment effects are insufficient for personalized decision-making. In this paper, we address a more general problem of estimating long-term Heterogeneous Dose-Response Curve (HDRC) while accounting for unobserved confounders and continuous treatment. Specifically, to remove the unobserved confounders in the long-term observational data, we introduce an optimal transport weighting framework to align the long-term observational data to an auxiliary short-term experimental data. Furthermore, to accurately predict the heterogeneous effects of continuous treatment, we establish a generalization bound on counterfactual prediction error by leveraging the reweighted distribution induced by optimal transport. Finally, we develop a long-term HDRC estimator building upon the above theoretical foundations. Extensive experiments on synthetic and semi-synthetic datasets demonstrate the effectiveness of our approach.

Transportation policy assessment often involves causal questions, yet traditional travel behaviour lacks the ability of distinguishing causal association from non-causal correlations. We present the deep CAusal infeRence mOdel for traveL behavIour aNAlysis (CAROLINA), a novel framework that addresses both observed and unobserved confounders in discrete choice modelling through causal discovery and the strengths of deep neural networks. Within this interpretable framework, we also introduce a Generative Counterfactual model for forecasting individuals' behaviour by adapting the Normalizing Flow method. Through the case studies of virtual reality-based pedestrian crossing behaviour, revealed preference travel behaviour from London, and synthetic data, we demonstrate the effectiveness of our proposed models in isolating causal relationships from confounding associations. Our proposed causal framework enhances predictive accuracy by employing data-driven algorithms, while maintaining interpretability. In addition, the counterfactual results show that intervention mechanisms that can reduce pedestrian stress levels lead to a 35.35% increase in individuals experiencing shorter waiting times. External interventions that reduce travel distances of non-mandatory trips in London lead to a 47% increase in the possible use of active and public transit modes.

Causal discovery aims to learn causal structures up to certain symmetries. Diverse populations or changing environments give rise to heterogeneous data in the following sense: each population/environment is a ``source'' which idiosyncratically determines the forms of causal effects. From this perspective, the source is a latent common cause for every observed variable. While some methods for causal discovery can work around latent confounding in special cases, a global confounder poses a significant challenge. The only known ways to deal with latent global confounding involve making assumptions that limit structural equations and/or noise functions. We demonstrate that globally confounded causal structures can still be identified with arbitrary structural equations and noise functions, so long as the number of latent classes remains small relative to the size and sparsity of the underlying DAG. The approach relies on agglomerating variables into large-enough matrices of moments, whose ranks directly reveal graphical properties of the causal structure. We also provide a statistical test to test the rank of these matrices.

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. In this paper, we tackle the primary challenges in causal inference with negative controls: identifying and estimating these bridge functions. Previous work has typically relied on completeness conditions for identification, imposed uniqueness assumptions for estimation, and focused on parametric models for the bridge functions. Instead, we provide an alternative identification strategy that assumes the existence of two bridge functions rather than completeness conditions. We also provide new estimators for these functions based on minimax learning formulations. These estimators accommodate general function classes such as Reproducing Kernel Hilbert Spaces and neural networks. We study finite-sample convergence results both for estimating bridge functions themselves and for the final estimation of the causal parameter under a variety of combinations of assumptions. We avoid uniqueness conditions on the bridge functions as much as possible.