Online Data Collection for Efficient Semiparametric Inference

TL;DR

This paper introduces online data collection strategies for semiparametric inference, enabling sequential, cost-effective data gathering from multiple sources to improve estimation accuracy under budget constraints.

Contribution

It formalizes the online moment selection problem and proposes two policies with proven zero regret, advancing adaptive data collection methods for semiparametric models.

Findings

Policies outperform fixed data collection methods.

Both policies achieve zero asymptotic MSE regret.

Validated on synthetic and real-world causal inference tasks.

Abstract

While many works have studied statistical data fusion, they typically assume that the various datasets are given in advance. However, in practice, estimation requires difficult data collection decisions like determining the available data sources, their costs, and how many samples to collect from each source. Moreover, this process is often sequential because the data collected at a given time can improve collection decisions in the future. In our setup, given access to multiple data sources and budget constraints, the agent must sequentially decide which data source to query to efficiently estimate a target parameter. We formalize this task using Online Moment Selection, a semiparametric framework that applies to any parameter identified by a set of moment conditions. Interestingly, the optimal budget allocation depends on the (unknown) true parameters. We present two online data collection policies, Explore-then-Commit and Explore-then-Greedy, that use the parameter estimates at a given time to optimally allocate the remaining budget in the future steps. We prove that both policies achieve zero regret (assessed by asymptotic MSE) relative to an oracle policy. We empirically validate our methods on both synthetic and real-world causal effect estimation tasks, demonstrating that the online data collection policies outperform their fixed counterparts.