Modern deep learning heavily relies on large labeled datasets, which often comse with high costs in terms of both manual labeling and computational resources. To mitigate these challenges, researchers have explored the use of informative subset selection techniques, including coreset selection and active learning. Specifically, coreset selection involves sampling data with both input ($\bx$) and output ($\by$), active learning focuses solely on the input data ($\bx$). In this study, we present a theoretically optimal solution for addressing both coreset selection and active learning within the context of linear softmax regression. Our proposed method, COPS (unCertainty based OPtimal Sub-sampling), is designed to minimize the expected loss of a model trained on subsampled data. Unlike existing approaches that rely on explicit calculations of the inverse covariance matrix, which are not easily applicable to deep learning scenarios, COPS leverages the model's logits to estimate the sampling ratio. This sampling ratio is closely associated with model uncertainty and can be effectively applied to deep learning tasks. Furthermore, we address the challenge of model sensitivity to misspecification by incorporating a down-weighting approach for low-density samples, drawing inspiration from previous works. To assess the effectiveness of our proposed method, we conducted extensive empirical experiments using deep neural networks on benchmark datasets. The results consistently showcase the superior performance of COPS compared to baseline methods, reaffirming its efficacy.

通过开发一个新的算法 COPS，我们提出了一个理论上最佳的解决方案，以最小化从样本数据训练的模型的预期损失。我们的方法在深度学习任务中可以有效地应用，通过使用模型的对数几率来估计采样比例，并通过低密度样本的降权方法来解决模型对错误规范的敏感性挑战。实证实验表明，COPS相对于基线方法具有卓越的性能。

通过不确定性估计进行最佳样本选择及其在深度学习中的应用