The thresholded feature has recently emerged as an extremely efficient, yet rough empirical approximation, of the time-consuming sparse coding inference process. Such an approximation has not yet been rigorously examined, and standard dictionaries often lead to non-optimal performance when used for computing thresholded features. In this paper, we first present two theoretical recovery guarantees for the thresholded feature to exactly recover the nonzero support of the sparse code. Motivated by them, we then formulate the Dictionary Learning for Thresholded Features (DLTF) model, which learns an optimized dictionary for applying the thresholded feature. In particular, for the $(k, 2)$ norm involved, a novel proximal operator with log-linear time complexity $O(m\log m)$ is derived. We evaluate the performance of DLTF on a vast range of synthetic and real-data tasks, where DLTF demonstrates remarkable efficiency, effectiveness, and robustness in all experiments. In addition, we briefly discuss the potential link between DLTF and deep learning building blocks.

中文翻译：

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使用稀疏支持恢复学习简单的阈值特征

阈值特征最近已成为耗时的稀疏编码推理过程的一种极其有效但粗略的经验近似。这种近似尚未经过严格检查，标准词典在用于计算阈值特征时通常会导致非最佳性能。在本文中，我们首先提出了阈值特征的两个理论恢复保证，以准确恢复稀疏代码的非零支持。在他们的推动下，我们制定了阈值特征的字典学习(DLTF) 模型，该模型学习用于应用阈值特征的优化字典。特别是，对于 $(k, 2)$ 涉及范数，一种具有对数线性时间复杂度的新型近端算子 $O(m\log m)$ 是派生的。我们评估了 DLTF 在大量合成和真实数据任务上的性能，其中 DLTF 在所有实验中都表现出卓越的效率、有效性和稳健性。此外，我们简要讨论了 DLTF 和深度学习构建块之间的潜在联系。