论文标题
用于嘈杂数据集的基于稀疏学习的分层正则化网络
Hierarchical regularization networks for sparsification based learning on noisy datasets
论文作者
论文摘要
我们提出了一种层次学习策略，旨在为大型嘈杂数据集生成稀疏表示形式和相关模型。层次结构遵循在更详细的尺度上确定的近似空间。为了在每个量表上促进模型的概括，我们还使用置换操作员在多个维度上引入了一个新颖的，基于投影的惩罚运算符，以结合邻近性和订购信息。本文对重建内核希尔伯特空间（RKHS）的重建中的近似特性进行了详细分析，重点是预测和与产生稀疏表示相关的错误函数的最佳性和一致性。结果表明，该方法作为数据降低和建模策略在合成（单变量和多元）和真实数据集（时间序列）上的性能。通过提出的方法生成的测试数据集的稀疏模型也被证明可以有效地重建基础过程并保留可推广性。
We propose a hierarchical learning strategy aimed at generating sparse representations and associated models for large noisy datasets. The hierarchy follows from approximation spaces identified at successively finer scales. For promoting model generalization at each scale, we also introduce a novel, projection based penalty operator across multiple dimension, using permutation operators for incorporating proximity and ordering information. The paper presents a detailed analysis of approximation properties in the reconstruction Reproducing Kernel Hilbert Spaces (RKHS) with emphasis on optimality and consistency of predictions and behavior of error functionals associated with the produced sparse representations. Results show the performance of the approach as a data reduction and modeling strategy on both synthetic (univariate and multivariate) and real datasets (time series). The sparse model for the test datasets, generated by the presented approach, is also shown to efficiently reconstruct the underlying process and preserve generalizability.
