# Online Data Collection for Efficient Semiparametric Inference

arXiv: https://arxiv.org/abs/2411.03195 · HTML: https://mlsanity.com/paper/2411.03195/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 119 references that are in the map.
- First posted on arXiv 5 Nov 2024.

## Builds on (most cited first, 30 of 34)

- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Active Feature Acquisition with Generative Surrogate Models](https://mlsanity.com/paper/2010.02433/) (2020)
- [Active Statistical Inference](https://mlsanity.com/paper/2403.03208/) (2024)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [Using Experiments to Correct for Selection in Observational Studies](https://mlsanity.com/paper/2006.09676/) (2020)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyond](https://mlsanity.com/paper/1912.12945/) (2019)
- [Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables](https://mlsanity.com/paper/2003.12659/) (2020)
- [Semiparametric Efficient Inference in Adaptive Experiments](https://mlsanity.com/paper/2311.18274/) (2023)
- [Causal Effect Identification from Multiple Incomplete Data Sources: A General Search-based Approach](https://mlsanity.com/paper/1902.01073/) (2019)
- [Revisiting the General Identifiability Problem](https://mlsanity.com/paper/2206.01081/) (2022)
- [Efficient Online Estimation of Causal Effects by Deciding What to Observe](https://mlsanity.com/paper/2108.09265/) (2021)
- [Adaptive Neyman Allocation](https://mlsanity.com/paper/2309.08808/) (2023)
- [Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effects](https://mlsanity.com/paper/2201.10743/) (2022)
- [Semi-parametric inference based on adaptively collected data](https://mlsanity.com/paper/2303.02534/) (2023)
- [Adaptive Instrument Design for Indirect Experiments](https://mlsanity.com/paper/2312.02438/) (2023)
- [Adaptive Experimentation When You Can't Experiment](https://mlsanity.com/paper/2406.10738/) (2024)
- [A General Identification Algorithm For Data Fusion Problems Under Systematic Selection](https://mlsanity.com/paper/2404.06602/) (2024)
- [Anytime-Valid Inference for Double/Debiased Machine Learning of Causal Parameters](https://mlsanity.com/paper/2408.09598/) (2024)
- [Efficient Estimation Under Data Fusion](https://mlsanity.com/paper/2111.14945/) (2021)
- [Sequential Underspecified Instrument Selection for Cause-Effect Estimation](https://mlsanity.com/paper/2302.05684/) (2023)
- [Double machine learning and design in batch adaptive experiments](https://mlsanity.com/paper/2309.15297/) (2023)
- [Data fusion for efficiency gain in ATE estimation: A practical review with simulations](https://mlsanity.com/paper/2407.01186/) (2024)
- [Towards a Unified Theory for Semiparametric Data Fusion with Individual-Level Data](https://mlsanity.com/paper/2409.09973/) (2024)
- [Identification Methods With Arbitrary Interventional Distributions as Inputs](https://mlsanity.com/paper/2004.01157/) (2020)
- [Estimation of Local Average Treatment Effect by Data Combination](https://mlsanity.com/paper/2109.05175/) (2021)
- [Contrasting Identifying Assumptions of Average Causal Effects: Robustness and Semiparametric Efficiency](https://mlsanity.com/paper/2111.15233/) (2021)
- [Efficient estimation and data fusion under general semiparametric restrictions on outcome mean functions](https://mlsanity.com/paper/2406.06941/) (2024)
- [Identification and multiply robust estimation of causal effects via instrumental variables from an auxiliary population](https://mlsanity.com/paper/2407.18166/) (2024)
- [The Adaptive Doubly Robust Estimator for Policy Evaluation in Adaptive Experiments and a Paradox Concerning Logging Policy](https://mlsanity.com/paper/2010.03792/) (2020)

## 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.