# Optimal Distributed Subsampling for Maximum Quasi-Likelihood Estimators with Massive Data

arXiv: https://arxiv.org/abs/2005.10435 · HTML: https://mlsanity.com/paper/2005.10435/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2020.

## Built on by (most cited first, 13 of 13)

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- [Nonuniform Negative Sampling and Log Odds Correction with Rare Events Data](https://mlsanity.com/paper/2110.13048/) (2021)
- [An optimal transport approach for selecting a representative subsample with application in efficient kernel density estimation](https://mlsanity.com/paper/2206.01182/) (2022)
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- [Fundamental Bias in Inverting Random Sampling Matrices with Application to Sub-sampled Newton](https://mlsanity.com/paper/2502.13583/) (2025)
- [On the Subbagging Estimation for Massive Data](https://mlsanity.com/paper/2103.00631/) (2021)
- [Optimal Sampling Designs for Multi-dimensional Streaming Time Series with Application to Power Grid Sensor Data](https://mlsanity.com/paper/2303.08242/) (2023)
- [Markov subsampling based Huber Criterion](https://mlsanity.com/paper/2112.06134/) (2021)
- [A Selective Review on Statistical Methods for Massive Data Computation: Distributed Computing, Subsampling, and Minibatch Techniques](https://mlsanity.com/paper/2403.11163/) (2024)
- [Core-elements Subsampling for Alternating Least Squares](https://mlsanity.com/paper/2509.18024/) (2025)
- [Scale-invariant Optimal Sampling for Rare-events Data with Sparse Models](https://mlsanity.com/paper/2608.22597/) (2026)
- [Subdata Selection for Measurement-Constrained Linear Regression under Model Misspecification](https://mlsanity.com/paper/2610.19351/) (2026)

## Abstract (arXiv)

Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the data volume is so large that nonuniform subsampling probabilities cannot be calculated all at once, then subsampling with replacement is infeasible to implement. This paper solves this problem using Poisson subsampling. We first derive optimal Poisson subsampling probabilities in the context of quasi-likelihood estimation under the A- and L-optimality criteria. For a practically implementable algorithm with approximated optimal subsampling probabilities, we establish the consistency and asymptotic normality of the resultant estimators. To deal with the situation that the full data are stored in different blocks or at multiple locations, we develop a distributed subsampling framework, in which statistics are computed simultaneously on smaller partitions of the full data. Asymptotic properties of the resultant aggregated estimator are investigated. We illustrate and evaluate the proposed strategies through numerical experiments on simulated and real data sets.