异构数据集的个性化字典学习
Personalized Dictionary Learning for Heterogeneous Datasets
AI总结：
本文提出个性化字典学习（PerDL）问题，旨在从异构数据集中学习稀疏线性表示，将共享与独特特征建模为全局和局部字典，并提出PerMA元算法在合适条件下以线性速率恢复字典，同时自动从强学习器借用力量改善弱学习器预测。
摘要：
我们引入了一个相关且具有挑战性的问题，称为个性化字典学习（PerDL），其目标是从共享某些共性的异构数据集中学习稀疏线性表示。在PerDL中，我们将每个数据集的共享和独特特征建模为全局字典和局部字典。PerDL的挑战不仅继承自经典的字典学习（DL），还由于共享和独特特征的未知性质而产生。在本文中，我们严格地表述了这个问题，并提供了可以证明全局和局部字典能够被解耦的条件。在这些条件下，我们提供了一种名为个性化匹配与平均（PerMA）的元算法，该算法可以从异构数据集中恢复全局和局部字典。PerMA非常高效；在合适的条件下，它以线性速率收敛到真实值。此外，它会自动从强学习器中借用力量来改善弱学习器的预测。作为提取全局和局部字典的通用框架，我们展示了PerDL在不同学习任务中的应用，例如在不平衡数据集上进行训练和视频监控。
英文摘要：
We introduce a relevant yet challenging problem named Personalized Dictionary Learning (PerDL), where the goal is to learn sparse linear representations from heterogeneous datasets that share some commonality. In PerDL, we model each dataset's shared and unique features as global and local dictionaries. Challenges for PerDL not only are inherited from classical dictionary learning (DL), but also arise due to the unknown nature of the shared and unique features. In this paper, we rigorously formulate this problem and provide conditions under which the global and local dictionaries can be provably disentangled. Under these conditions, we provide a meta-algorithm called Personalized Matching and Averaging (PerMA) that can recover both global and local dictionaries from heterogeneous datasets. PerMA is highly efficient; it converges to the ground truth at a linear rate under suitable conditions. Moreover, it automatically borrows strength from strong learners to improve the prediction of weak learners. As a general framework for extracting global and local dictionaries, we show the application of PerDL in different learning tasks, such as training with imbalanced datasets and video surveillance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
