The meta model seeks to answer "what would the outcome be if we were to deploy a different

Estimating counterfactual outcome of different treatments from observational data is an important problem to assist decision making in a variety of fields. Among the various forms of treatment specification, bundle treatment has been widely adopted in many scenarios, such as recommendation systems and online marketing. The bundle treatment usually can be abstracted as a high dimensional binary vector, which makes it more challenging for researchers to remove the confounding bias in observational data. In this work, we assume the existence of low dimensional latent structure underlying bundle treatment. Via the learned latent representations of treatments, we propose a novel variational sample re-weighting (VSR) method to eliminate confounding bias by decorrelating the treatments and confounders. Finally, we conduct extensive experiments to demonstrate that the predictive model trained on this re-weighted dataset can achieve more accurate counterfactual outcome prediction.

Estimating the effects of continuous-valued interventions from observational data is a critically important task for climate science, healthcare, and economics. Recent work focuses on designing neural network architectures and regularization functions to allow for scalable estimation of average and individual-level dose-response curves from high-dimensional, large-sample data. Such methodologies assume ignorability (observation of all confounding variables) and positivity (observation of all treatment levels for every covariate value describing a set of units), assumptions problematic in the continuous treatment regime. Scalable sensitivity and uncertainty analyses to understand the ignorance induced in causal estimates when these assumptions are relaxed are less studied. Here, we develop a continuous treatment-effect marginal sensitivity model (CMSM) and derive bounds that agree with the observed data and a researcher-defined level of hidden confounding. We introduce a scalable algorithm and uncertainty-aware deep models to derive and estimate these bounds for high-dimensional, large-sample observational data. We work in concert with climate scientists interested in the climatological impacts of human emissions on cloud properties using satellite observations from the past 15 years. This problem is known to be complicated by many unobserved confounders.

Estimating causal effects from observational data remains a fundamental challenge in causal inference, especially in the presence of latent confounders. This paper focuses on estimating causal effects in Gaussian Linear Structural Causal Models (GL-SCMs), which are widely used due to their analytical tractability. However, parameter estimation in GL-SCMs is often infeasible with finite data, primarily due to overparameterization. To address this, we introduce the class of Centralized Gaussian Linear SCMs (CGL-SCMs), a simplified yet expressive subclass where exogenous variables follow standardized distributions. We show that CGL-SCMs are equally expressive in terms of causal effect identifiability from observational distributions and present a novel EM-based estimation algorithm that can learn CGL-SCM parameters and estimate identifiable causal effects from finite observational samples. Our theoretical analysis is validated through experiments on synthetic data and benchmark causal graphs, demonstrating that the learned models accurately recover causal distributions.

Detecting unobserved confounders is crucial for reliable causal inference in observational studies. Existing methods require either linearity assumptions or multiple heterogeneous environments, limiting applicability to nonlinear single-environment settings. To bridge this gap, we propose Kernel Regression Confounder Detection (KRCD), a novel method for detecting unobserved confounding in nonlinear observational data under single-environment conditions. KRCD leverages reproducing kernel Hilbert spaces to model complex dependencies. By comparing standard and higherorder kernel regressions, we derive a test statistic whose significant deviation from zero indicates unobserved confounding. Theoretically, we prove two key results: First, in infinite samples, regression coefficients coincide if and only if no unobserved confounders exist. Second, finite-sample differences converge to zero-mean Gaussian distributions with tractable variance. Extensive experiments on synthetic benchmarks and the Twins dataset demonstrate that KRCD not only outperforms existing baselines but also achieves superior computational efficiency.

Unsupervised representation learning seeks to recover latent generative factors, yet standard methods relying on statistical independence often fail to capture causal dependencies. A central challenge is identifiability: as established in disentangled representation learning and nonlinear ICA literature, disentangling causal variables from observational data is impossible without supervision, auxiliary signals, or strong inductive biases. In this work, we propose the Latent Additive Noise Model Causal Autoencoder (LANCA) to operationalize the Additive Noise Model (ANM) as a strong inductive bias for unsupervised discovery. Theoretically, we prove that while the ANM constraint does not guarantee unique identifiability in the general mixing case, it resolves component-wise indeterminacy by restricting the admissible transformations from arbitrary diffeo-morphisms to the affine class. Methodologically, arguing that the stochastic encoding inherent to V AEs obscures the structural residuals required for latent causal discovery, LANCA employs a deterministic Wasserstein Auto-Encoder (W AE) coupled with a differentiable ANM Layer. This architecture transforms residual independence from a passive assumption into an explicit optimization objective. Empirically, LANCA outperforms state-of-the-art baselines on synthetic physics benchmarks (Pendulum, Flow), and on photorealistic environments (CANDLE), where it demonstrates superior robustness to spurious correlations arising from complex background scenes.

Evaluating observational estimators of causal effects demands information that is rarely available: unconfounded interventions and outcomes from the population of interest, created either by randomization or adjustment. As a result, it is customary to fall back on simulators when creating benchmark tasks. Simulators offer great control but are often too simplistic to make challenging tasks, either because they are hand-designed and lack the nuances of real-world data, or because they are fit to observational data without structural constraints. In this work, we propose a general, repeatable strategy for turning observational data into sequential structural causal models and challenging estimation tasks by following two simple principles: 1) fitting real-world data where possible, and 2) creating complexity by composing simple, hand-designed mechanisms. We implement these ideas in a highly configurable software package and apply it to the well-known Adult income data set to construct the IncomeSCM simulator. From this, we devise multiple estimation tasks and sample data sets to compare established estimators of causal effects. The tasks present a suitable challenge, with effect estimates varying greatly in quality between methods, despite similar performance in the modeling of factual outcomes, highlighting the need for dedicated causal estimators and model selection criteria.

Causal disentanglement aims to learn about latent causal factors behind data, holding the promise to augment existing representation learning methods in terms of interpretability and extrapolation. Recent advances establish identifiability results assuming that interventions on (single) latent factors are available; however, it remains debatable whether such assumptions are reasonable due to the inherent nature of intervening on latent variables. Accordingly, we reconsider the fundamentals and ask what can be learned using just observational data.We provide a precise characterization of latent factors that can be identified in nonlinear causal models with additive Gaussian noise and linear mixing, without any interventions or graphical restrictions. In particular, we show that the causal variables can be identified up to a -wise transformation and that further disentanglement is not possible. We transform these theoretical results into a practical algorithm consisting of solving a quadratic program over the score estimation of the observed data. We provide simulation results to support our theoretical guarantees and demonstrate that our algorithm can derive meaningful causal representations from purely observational data.