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Causal-StoNet: Causal Inference for High-Dimensional Complex Data
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Proposes Causal-StoNet, a stochastic neural network with the treatment as a visible unit in a middle layer, trained by adaptive SGHMC with sparse mixture-Gaussian priors, for ATE/CATE estimation in high-dimensional, missing-data settings.
Problem
Causal inference (ATE and CATE) with high-dimensional covariates, unknown nonlinear outcome and propensity functions, and missing values, where existing methods typically handle only one of these difficulties.
Approach
Embed the binary treatment as a visible unit in an intermediate layer of a stochastic neural network (StoNet), so the network jointly models outcome and propensity score, with sparse mixture-Gaussian priors for covariate selection and adaptive SGHMC for training with latent-variable imputation.
Key results
- On 10 ACIC 2019 datasets, Causal-StoNet achieves out-of-sample ATE MAE 0.0542 (sd 0.0132), versus 0.0867 for the best competitor TMLE(Lasso).
- On the Twins data, Causal-StoNet gives ATE estimate -0.0232 (sd 0.0042), closest to the stated true ATE of -2.48%, versus DSE -0.0405 and ARBE -0.0096.
- On an ACIC CATE dataset, Causal-StoNet attains the lowest ATE error (0.0118) but a higher PEHE (0.0893) than CMDE (0.0823).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Causal-StoNet instead of DSE | ATE estimation · ACIC 2019, 10 synthetic datasets, in-sample | ATE MAE: 0.0776(0.0193) -> 0.0501(0.0118) | Helped |
| Use Causal-StoNet instead of ARBE | ATE estimation · ACIC 2019, 10 synthetic datasets, out-of-sample | ATE MAE: 0.1335(0.0179) -> 0.0542(0.0132) | Helped |
| Use Causal-StoNet instead of CMDE | CATE estimation · ACIC 2019, heterogeneous treatment effect | epsilon_ATE: 0.0444 -> 0.0118 | Helped |
| Use Causal-StoNet instead of CMDE | CATE estimation · ACIC 2019, heterogeneous treatment effect | epsilon_PEHE: 0.0823 -> 0.0893 | Hurt |
| Use Causal-StoNet instead of DONUT | ATE estimation · Twins data, three-fold cross-validation | ATE estimate standard deviation: 0.0128 -> 0.0042 | Helped |
Surprising findings
- On the ACIC CATE task, Causal-StoNet lags CMDE, CEVAE and X-Learner-BART in PEHE despite achieving the lowest ATE error.
Limitations
- Consistency and asymptotic guarantees rely on strong assumptions (sparse DNN structure, Laplace approximation, growth-rate conditions) that are hard to verify in practice.
- On CATE estimation Causal-StoNet does not beat the best baselines in PEHE.
- Extensions to multi-level, continuous treatments, MNAR and mediation are described without experiments.
Experimental setup
Datasets: ACIC 2019 Data Challenge Twins birth data (1989-1991) simulated data (p=1000)
Benchmarks: ACIC 2019 Data Challenge Twins data simulated nonlinear data
Metrics: MAE of ATE PEHE FSR NSR ATE absolute error
Baselines: DSE ARBE TMLE DONUT X-learner Dragonnet CMDE CEVAE GANITE CFRNet
Builds on: StoNet sparse deep learning adaptive SGHMC double machine learning targeted maximum likelihood estimation
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