Local Uncertainty Sampling for Large-Scale Multi-Class Logistic Regression
This work addresses computational efficiency for statisticians and data scientists working with large datasets, though it appears incremental as it builds on existing subsampling approaches.
The paper tackles the computational challenge of large-scale multi-class logistic regression by proposing a subsampling scheme that reduces estimator variance compared to uniform random sampling, achieving significant improvements when classes are imbalanced.
A major challenge for building statistical models in the big data era is that the available data volume far exceeds the computational capability. A common approach for solving this problem is to employ a subsampled dataset that can be handled by available computational resources. In this paper, we propose a general subsampling scheme for large-scale multi-class logistic regression and examine the variance of the resulting estimator. We show that asymptotically, the proposed method always achieves a smaller variance than that of the uniform random sampling. Moreover, when the classes are conditionally imbalanced, significant improvement over uniform sampling can be achieved. Empirical performance of the proposed method is compared to other methods on both simulated and real-world datasets, and these results match and confirm our theoretical analysis.