压缩独立成分分析：理论与算法
Compressive Independent Component Analysis: Theory and Algorithms
摘要：
压缩学习形成了压缩感知和统计学习之间令人兴奋的交叉点，其中利用稀疏性和结构的形式来减少学习任务的存储器和/或计算复杂性。在本文中，我们看看独立成分分析（ICA）模型通过压缩学习镜头。特别是，我们表明，基于累积量的ICA模型的解决方案具有特定的结构，诱导一个低维的模型集，驻留在累积量张量空间。通过显示一个限制等距属性持有随机累积量，例如高斯系综，我们证明了压缩ICA方案的存在。此后，我们提出了两种算法的形式的迭代投影梯度（IPG）和交替最陡下降（ASD）算法压缩ICA，其中的顺序压缩断言从限制等距属性是通过经验结果实现。我们提供了CICA算法的分析，包括有限样本的影响。压缩的影响的特点是草图大小和ICA估计的统计效率之间的权衡。通过考虑合成和真实的数据集，我们显示了大量的内存增益超过著名的ICA算法，通过使用建议的CICA算法之一。最后，我们总结了论文的开放性问题，包括来自新兴压缩学习领域的有趣挑战。
英文摘要：
Compressive learning forms the exciting intersection between compressed sensing and statistical learning where one exploits forms of sparsity and structure to reduce the memory and/or computational complexity of the learning task. In this paper, we look at the independent component analysis (ICA) model through the compressive learning lens. In particular, we show that solutions to the cumulant based ICA model have particular structure that induces a low dimensional model set that resides in the cumulant tensor space. By showing a restricted isometry property holds for random cumulants e.g. Gaussian ensembles, we prove the existence of a compressive ICA scheme. Thereafter, we propose two algorithms of the form of an iterative projection gradient (IPG) and an alternating steepest descent (ASD) algorithm for compressive ICA, where the order of compression asserted from the restricted isometry property is realised through empirical results. We provide analysis of the CICA algorithms including the effects of finite samples. The effects of compression are characterised by a trade-off between the sketch size and the statistical efficiency of the ICA estimates. By considering synthetic and real datasets, we show the substantial memory gains achieved over well-known ICA algorithms by using one of the proposed CICA algorithms. Finally, we conclude the paper with open problems including interesting challenges from the emerging field of compressive learning.
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。
