Local uncertainty sampling for large-scale multiclass logistic regression

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. We propose a general subsampling scheme for large-scale multiclass 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 evaluated and compared to other methods via both simulated and real-world datasets, and these results match and confirm our theoretical analysis.