摘要翻译：
基于L2空间中的迭代投影，提出了一种新的非线性函数估计的在线学习范式，其概率测度反映了输入信号的随机性。该学习算法利用字典子空间的再生核，基于函数的有限维空间都有一个以Gram矩阵为特征的再生核。L2-空间几何在原理上提供了最佳的去相关性质。该学习范式与传统的基于核的学习范式有两个显著的不同：(i)整个空间不是再生核Hilbert空间；(ii)最小均方误差估计给出了字典子空间中所需非线性函数的最佳逼近。它保持了计算内积以及当字典增长时更新Gram矩阵的效率。基于自适应投影次梯度法的变度量版本，分析了该算法的单调逼近性、渐近最优性和收敛性。数值算例表明，该算法对实际数据的有效性优于多种方法，包括扩展的Kalman滤波器和许多批处理机器学习方法，如多层感知器。
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英文标题：
《Online Nonlinear Estimation via Iterative L2-Space Projections:
  Reproducing Kernel of Subspace》
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作者：
Motoya Ohnishi and Masahiro Yukawa
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  We propose a novel online learning paradigm for nonlinear-function estimation tasks based on the iterative projections in the L2 space with probability measure reflecting the stochastic property of input signals. The proposed learning algorithm exploits the reproducing kernel of the so-called dictionary subspace, based on the fact that any finite-dimensional space of functions has a reproducing kernel characterized by the Gram matrix. The L2-space geometry provides the best decorrelation property in principle. The proposed learning paradigm is significantly different from the conventional kernel-based learning paradigm in two senses: (i) the whole space is not a reproducing kernel Hilbert space and (ii) the minimum mean squared error estimator gives the best approximation of the desired nonlinear function in the dictionary subspace. It preserves efficiency in computing the inner product as well as in updating the Gram matrix when the dictionary grows. Monotone approximation, asymptotic optimality, and convergence of the proposed algorithm are analyzed based on the variable-metric version of adaptive projected subgradient method. Numerical examples show the efficacy of the proposed algorithm for real data over a variety of methods including the extended Kalman filter and many batch machine-learning methods such as the multilayer perceptron.
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PDF链接：
https://arxiv.org/pdf/1712.04573