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Statistical Inference under Performativity
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Builds an end-to-end statistical inference framework under performativity: a CLT for repeated risk minimization iterates, a score-matching plus policy-perturbation variance estimator, bias-aware confidence regions for the performative stable point, and prediction-powered inference extended to the performative setting.
Problem
Performative prediction studies predictions that shift the data distribution, but existing work only covers convergence to performative stable points, not inference (confidence intervals, hypothesis tests) for the iterates of repeated risk minimization or for the policy itself.
Approach
Derives a CLT for RRM iterates under distribution shift (with covariance propagated through the Jacobian of the distribution-to-optimum map G), estimates the required score-function quantities via gradient-free score matching with policy perturbation, and combines unlabeled data through PPI++-style weighting with a data-driven choice of the weight lambda.
Key results
- PPI with optimized lambda_t gives the narrowest confidence regions while all methods approach 0.9 coverage as n grows (1000 trials, t in {2,3,4}).
- Bias-aware confidence regions for the performative stable point have coverage upper-bounding that of theta_t, with the gap vanishing as t grows.
- Both Gaussian-parametric and DNN score-matching models reach J(psi) < 0.05 and the variance-estimation error decreases with n.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use optimized λ̂_t instead of λ=0 or λ=1 | PPI under performativity · Simulation, t=2, 3, and 4 | confidence-region width | Helped |
| use optimized λ̂_t instead of λ=0 or λ=1 | PPI under performativity · Simulation, t=2, 3, and 4 | confidence-region coverage: 0.9 | No clear effect |
| use Gaussian parametric or DNN-based score matching | score matching for estimating V_t · Simulation score matching | training loss J(ψ): J(ψ)<0.05 | Helped |
| increase labeled sample size n | Gaussian parametric and DNN-based score matching · Simulation score matching | variance-estimation error | Helped |
Limitations
- Confidence regions for the performative stable point rely on bias-aware inference rather than direct inference.
- Variance estimation requires the score-matching model to be sufficiently expressive; the consistency assumption is strong.
- Experiments are limited to a small synthetic linear setting with d=2.
Experimental setup
Datasets: synthetic performative linear regression data
Benchmarks: synthetic performative linear regression
Metrics: confidence region coverage confidence region width variance estimation error score matching loss J(psi) normality (multivariate Q-Q plot)
Baselines: lambda=0 (labeled data only) lambda=1 (full unlabeled weight) repeated empirical risk minimization finite-sample bound
Builds on: performative prediction prediction-powered inference PPI++ repeated risk minimization
Closest papers by meaning
- Performative Risk Control: Calibrating Models for Reliable Deployment under Performativity (NeurIPS 2025 · similarity 0.87)
- On the Impact of Performative Risk Minimization for Binary Random Variables (ICML 2025 · similarity 0.86)
- The Stability of Online Algorithms in Performative Prediction (NeurIPS 2026 · similarity 0.86)
- Conditional Forecasts and Proper Scoring Rules for Reliable and Accurate Performative Predictions (NeurIPS 2025 · similarity 0.85)
- Predictive Performance Comparison of Decision Policies Under Confounding (ICML 2024 · similarity 0.84)
- Plug-in Performative Optimization (ICML 2024 · similarity 0.84)
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