Unbiased Treatment Effect Estimation under Network Interference via Neighborhood-Excluded Cross-Fitting
Abstract
Without interference, cross-fitting enables flexible covariate adjustment while preserving finite-sample unbiasedness under independent unit-level randomization. Under network interference, out-of-sample prediction alone no longer guarantees unbiasedness: assignments entering evaluation-fold Horvitz--Thompson weights may also affect outcomes in the training sample, inducing dependence between fitted predictions and those weights. We develop neighborhood-excluded cross-fitting, which constructs estimand- and design-specific training samples to restore the conditional independence needed for finite-sample unbiasedness without a correctly specified outcome model. We establish asymptotically valid design-based Wald inference for direct and indirect effects under Bernoulli randomization and for the global average treatment effect under Bernoulli cluster randomization. Neighborhood exclusion creates a trade-off in choosing the number of folds: unit-level splitting may require the number of folds to grow with average exclusion-neighborhood size, while cluster-level splitting can substantially relaxes this requirement, permitting a fixed number of folds under partial interference. For linear adjustment under Bernoulli randomization, we derive variance-optimal and confidence-interval-length-optimal procedures, establish explicit rate conditions allowing the covariate dimension to diverge, and show that the variance-optimal procedure is asymptotically no-harm. Simulations illustrate the bias from omitting neighborhood exclusion and the precision gains from adjustment. An application to a social network experiment yields confidence intervals substantially shorter than those from the unadjusted estimator.
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BibTeX
@misc{yu2026unbiased,
title = {{Unbiased Treatment Effect Estimation under Network Interference via Neighborhood-Excluded Cross-Fitting}},
author = {Haoyang Yu and Anqi Zhao and Hanzhong Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23284},
eprint = {2609.23284},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23284},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Unbiased Treatment Effect Estimation under Network Interference via Neighborhood-Excluded Cross-Fitting
AU - Haoyang Yu
AU - Anqi Zhao
AU - Hanzhong Liu
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23284
UR - https://arxiv.org/abs/2609.23284
AB - Without interference, cross-fitting enables flexible covariate adjustment while preserving finite-sample unbiasedness under independent unit-level randomization. Under network interference, out-of-sample prediction alone no longer guarantees unbiasedness: assignments entering evaluation-fold Horvitz--Thompson weights may also affect outcomes in the training sample, inducing dependence between fitted predictions and those weights. We develop neighborhood-excluded cross-fitting, which constructs estimand- and design-specific training samples to restore the conditional independence needed for finite-sample unbiasedness without a correctly specified outcome model. We establish asymptotically valid design-based Wald inference for direct and indirect effects under Bernoulli randomization and for the global average treatment effect under Bernoulli cluster randomization. Neighborhood exclusion creates a trade-off in choosing the number of folds: unit-level splitting may require the number of folds to grow with average exclusion-neighborhood size, while cluster-level splitting can substantially relaxes this requirement, permitting a fixed number of folds under partial interference. For linear adjustment under Bernoulli randomization, we derive variance-optimal and confidence-interval-length-optimal procedures, establish explicit rate conditions allowing the covariate dimension to diverge, and show that the variance-optimal procedure is asymptotically no-harm. Simulations illustrate the bias from omitting neighborhood exclusion and the precision gains from adjustment. An application to a social network experiment yields confidence intervals substantially shorter than those from the unadjusted estimator.
ER -