lepidoptera: A Domain-Agnostic Engine for Causal Simulation with Mixed Variable Types, Vine Copula Dependence, and Individual-Level Counterfactual Propagation

Counterfactual prediction estimates an individual's outcome under an alternative intervention given their factual observations. Such outcomes are generally not identifiable from observational data without additional assumptions. Even within the class of fully observed additive noise models (ANMs), different causal graphs can generate the same observational distribution yet imply different individual counterfactual outcomes. Predictions based on a single estimated graph ignore this structural uncertainty. We therefore target a Bayesian counterfactual posterior predictive distribution that combines predictions from plausible SCMs. We introduce CAFE (CounterfActual Prediction via Fast Posterior Estimation), an amortized inference framework that directly approximates the Bayesian counterfactual posterior predictive distribution. We pretrain a transformer-based model on synthetic counterfactual tasks generated from a diverse prior over ANMs. Given an observational dataset, an individual's factual observations, and an intervention, CAFE approximates the corresponding posterior predictive distribution in a single forward pass. Experiments show that CAFE accurately predicts individual counterfactual outcomes in identifiable settings and approximates the posterior predictive distribution when structural uncertainty induced by observationally indistinguishable causal graphs exists. Strong performance in realistic manufacturing and viticulture settings further demonstrates its empirical robustness beyond the assumptions of the training prior.

Method validation and study design in causal inference rely on synthetic data with known counterfactuals. Existing simulators trade off distributional realism, the ability to capture mixed-type and multimodal tabular data, against causal controllability, including explicit control over overlap, unmeasured confounding, and treatment effect heterogeneity. We introduce CausalMix, a variational generative framework that closes this gap by coupling a mixture of Gaussian latent priors with data-type-specific decoders for continuous, binary, and categorical variables. The model incorporates explicit causal controls: an overlap regularizer shaping propensity-score distributions, alongside direct parameterizations of confounding strength and effect heterogeneity. This unified objective preserves fidelity to the observed data while enabling factorial manipulation of causal mechanisms, allowing overlap, confounding strength, and treatment effect heterogeneity to be varied independently at design time. Across benchmarks, CausalMix achieves state-of-the-art distributional metrics on mixed-type tables while providing stable, fine-grained causal control. We demonstrate practical utility in a comparative safety study of metastatic castration-resistant prostate cancer treatments, using CausalMix to compare estimators under calibrated data-generating processes, tune hyperparameters, and conduct simulation-based power analyses under targeted treatment effect heterogeneity scenarios.

Synthetic tabular data are often evaluated by distributional similarity, privacy distance, or train-on-synthetic-test-on-real predictive performance, but these criteria do not ensure validity for causal inference. We show that fully generative tabular synthesizers, including GAN- and LLM-based models, can preserve predictive utility while distorting average treatment effect (ATE) estimates. The failure is structural: ATE preservation requires both a realistic covariate law and an accurate treatment-effect contrast, whereas prediction loss penalizes treatment-effect error only through an overlap-weighted term. Thus, under imbalance or limited overlap, a generator may reproduce dominant observed outcomes while underlearning intervention-relevant contrasts. We formalize this mismatch through sensitivity and loss-decomposition results. Motivated by this causal analysis and intuition, we propose a hybrid synthetic-data framework for causal inference that generates covariates while modeling treatment and outcome mechanisms separately. We evaluate the framework in three settings: ATE preservation under fully generative versus hybrid synthesis, augmentation for practical positivity problems, and diagnostic simulation engines for comparing OR, IPW, AIPW, and TMLE before real-data analysis. We also stress-test the hybrid construction across settings that vary overlap, covariate dimension, seed sample size, and treatment-effect complexity, including a logistic outcome-model misspecification check. Across controlled simulation experiments, hybrid synthesis improves causal fidelity relative to fully generative baselines; the ACTG application shows improved predictive fidelity and potential for finite-sample estimator benchmarking. LLM-based hybrid synthesis is often more faithful than CTGAN in settings where causal fidelity can be assessed.