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Online Data Collection for Efficient Semiparametric Inference

arXiv 2411.03195 ↗First posted 5 Nov 2024stat.ML cs.LGcited by 0

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Abstract (arXiv)

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.

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References · 34

  1. 2022Semiparametric doubly robust targeted double machine learning: a reviewcited by 133
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  2. 2022Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effectscited by 7
  3. 2023Semi-parametric inference based on adaptively collected datacited by 7
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  22. 2024Constrained Design of a Binary Instrument in a Partially Linear Modelcited by 1

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