# More Efficient Estimation for Logistic Regression with Optimal Subsample

arXiv: https://arxiv.org/abs/1802.02698 · HTML: https://mlsanity.com/paper/1802.02698/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2018.

## Built on by (most cited first, 7 of 7)

- [Learning with Smooth Hinge Losses](https://mlsanity.com/paper/2103.00233/) (2021)
- [Nonuniform Negative Sampling and Log Odds Correction with Rare Events Data](https://mlsanity.com/paper/2110.13048/) (2021)
- [Optimal Sample Selection Through Uncertainty Estimation and Its Application in Deep Learning](https://mlsanity.com/paper/2309.02476/) (2023)
- [General bounds on the quality of Bayesian coresets](https://mlsanity.com/paper/2405.11780/) (2024)
- [A Provably Accurate Randomized Sampling Algorithm for Logistic Regression](https://mlsanity.com/paper/2402.16326/) (2024)
- [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)

## Abstract (arXiv)

In this paper, we propose improved estimation method for logistic regression based on subsamples taken according the optimal subsampling probabilities developed in Wang et al. 2018 Both asymptotic results and numerical results show that the new estimator has a higher estimation efficiency. We also develop a new algorithm based on Poisson subsampling, which does not require to approximate the optimal subsampling probabilities all at once. This is computationally advantageous when available random-access memory is not enough to hold the full data. Interestingly, asymptotic distributions also show that Poisson subsampling produces a more efficient estimator if the sampling rate, the ratio of the subsample size to the full data sample size, does not converge to zero. We also obtain the unconditional asymptotic distribution for the estimator based on Poisson subsampling. The proposed approach requires to use a pilot estimator to correct biases of un-weighted estimators. We further show that even if the pilot estimator is inconsistent, the resulting estimators are still consistent and asymptotically normal if the model is correctly specified.