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Variational Counterfactual Intervention Planning to Achieve Target Outcomes
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Proposes VCIP, which reformulates counterfactual target achievement as maximizing the likelihood of reaching a target outcome, trained with a variational ELBO and g-formula correction on observational data, and outperforms counterfactual-estimation baselines on a simulated tumor dataset and MIMIC-III.
Problem
Finding intervention sequences that steer a temporal system to a specified target outcome, where counterfactual outcomes are unobservable so prediction errors of counterfactual estimators compound and bias intervention selection.
Approach
Instead of predicting potential outcomes and comparing them to the target, model the conditional likelihood of achieving the target directly with a latent-state variational model, and use the g-formula to bridge interventional and observational likelihoods so training uses only observational data.
Key results
- On the tumor dataset (γ=4), VCIP achieves target distance 1.09 at τ=12 versus 1.47 for best baseline RMSN, a 25.9% improvement.
- With gamma=4 and tau=4, VCIP's GRP is 0.972 and RCS 0.869, compared to RMSN's 0.796 and 0.251 in the ablation table.
- VCIP ranking GRP on MIMIC-III is reported as significantly outperforming baselines across horizons τ=2,4,6,8 (figure only).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use VCIP rather than counterfactual-estimation baselines for intervention-sequence optimization | Tumor simulation, γ = 4 · Tumor simulation, same train/test intervention strategies, τ = 1 to 12 | target distance: VCIP 1.09 ± 0.29; RMSN 1.47 ± 0.35 at τ = 12 | Helped |
| Use VCIP rather than counterfactual-estimation baselines for intervention-sequence optimization | Tumor simulation · Distinct train/test intervention strategies, τ = 1 to 12 | target distance: VCIP 1.36 ± 0.26; RMSN 1.83 ± 0.22 at τ = 12 | Helped |
| Add g-formula confounding adjustment to VCIP (ablation) | VCIP · Tumor simulation, γ = 4, τ = 2 | GRP: 0.791 ± 0.334 -> 0.944 ± 0.091 | Helped |
| Add g-formula confounding adjustment to VCIP (ablation) | VCIP · Tumor simulation, γ = 4, τ = 4 | GRP: 0.796 ± 0.356 -> 0.972 ± 0.063 | Helped |
| Add g-formula confounding adjustment to VCIP (ablation) | VCIP · Tumor simulation, γ = 4, τ = 2 | RCS: 0.566 ± 0.508 -> 0.772 ± 0.206 | Helped |
| Add g-formula confounding adjustment to VCIP (ablation) | VCIP · Tumor simulation, γ = 4, τ = 4 | RCS: 0.595 ± 0.518 -> 0.869 ± 0.156 | Helped |
| Add g-formula confounding adjustment to VCIP (ablation) | VCIP · Tumor simulation, γ = 4 | target distance: 0.912 ± 0.194 -> 0.746 ± 0.198 | Helped |
| Add confounding adjustment to RMSN (ablation) | RMSN · Tumor simulation, γ = 4, τ = 2 | GRP: 0.797 ± 0.318 -> 0.863 ± 0.181 | Helped |
| Add confounding adjustment to RMSN (ablation) | RMSN · Tumor simulation, γ = 4, τ = 4 | GRP: 0.747 ± 0.348 -> 0.796 ± 0.267 | Helped |
| Add confounding adjustment to RMSN (ablation) | RMSN · Tumor simulation, γ = 4, τ = 2 | RCS: 0.461 ± 0.460 -> 0.400 ± 0.311 | Hurt |
| Add confounding adjustment to RMSN (ablation) | RMSN · Tumor simulation, γ = 4, τ = 4 | RCS: 0.213 ± 0.407 -> 0.251 ± 0.299 | Helped |
| Add confounding adjustment to RMSN (ablation) | RMSN · Tumor simulation, γ = 4 | target distance: 1.132 ± 0.090 -> 0.985 ± 0.215 | Helped |
Surprising findings
- Baseline counterfactual-estimation methods degrade with longer horizons due to error accumulation, while VCIP improves ranking accuracy with larger τ.
Limitations
- Theoretical guarantee is approximate, with error bounded by sum of ELBO gaps epsilon1 + epsilon2 that are not quantified.
- Gains from g-formula adjustment are less pronounced under low confounding (gamma=1,2).
- Real-world evaluation limited to MIMIC-III with diastolic blood pressure as outcome; counterfactual ground truth unavailable for real data.
Experimental setup
Datasets: simulated tumor dataset (pharmacokinetic-pharmacodynamic model) MIMIC-III
Benchmarks: simulated tumor dataset MIMIC-III
Metrics: GRP RCS (Spearman correlation) target distance
Baselines: RMSN CRN CT ACTIN
Builds on: g-formula CRN RMSN CT ACTIN
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