网络上的分布式自适应估计算法研究

发布时间：2018-05-11 09:09

本文选题：分布式信息处理 + 自适应估计　；参考：《浙江大学》2016年博士论文

【摘要】：网络上的分布式数据收集与分析有极其广泛的应用范围。网络上的分布式估计是指一个区域内的各个节点基于其收集的数据合作地估计所感兴趣的参数。在实际应用中,分布式信息处理存在着节点存储空间有限等约束,而自适应信息处理采用流式的信息处理方式,且只需存储少量的实时数据,因而能够节约存储空间。在本文中,作者考虑了网络上分布式自适应估计算法的研究问题。对于该问题,作者不仅考虑了线性数据模型而且考虑了非线性数据模型。在线性数据模型下,作者进一步地考虑了数据特性与参数特性。在大多数的分布式自适应估计算法中,研究者假设只有输出数据是有噪声的,而输入数据是完全精确的。但是,在实际环境中,输入输出数据可能都是有噪声的。因而噪声只加载在输入数据上的假设是不切实际的。当输入输出都有噪声时,总体最小二乘法能够最小化输入输出数据的扰动,因而会比最小二乘法有更好的性能。对于参数特性,许多自然以及人造信号都有很高的稀疏性。研究表明利用稀疏性能够提高学习性能。本文中,作者使用l1或者l0范数稀疏惩罚项来考虑待估矢量的稀疏性。另外,不同于单任务估计问题,作者进一步地考虑了不同节点的待估参数可以不同的情况,即多任务估计问题。对于多任务问题,虽然不同节点的任务可能不同,但是不同的任务间可能存在相似性。因而,不同任务间的合作能够提高学习性能。显然,设计任务间的合作策略是多任务估计问题的关键点。在本文中,作者提出一种自适应的任务间的合作策略,以提高算法对不同程度的任务间差异性的鲁棒性。对于多任务分布式估计问题,作者还考虑了待估参数的联合稀疏性。作者使用l2,1或者l2,o混合范数来利用各个任务相同的结构信息。在非线性数据模型下,基于极限学习机理论,作者把分布式非线性学习问题转化为线性学习问题,并提出分布式极限学习机算法。需要注意算法构建输入输出间的非线性映射的能力并没有改变。基于上述的讨论可知,分布式非线性自适应算法的设计与性能分析与分布式线性自适应算法的设计与性能分析非常类似。对于本文所提出的分布式自适应估计算法,作者给出了均值及均方性能分析。这些算法的性能分析与现存的分布式算法的性能分析不同,并且比现存的分布式算法的性能分析更加困难。因而,这些算法的性能分析是本文的主要贡献。另外,作者给出仿真实验来验证这些算法的有效性及优点。
[Abstract]:Distributed data collection and analysis on the network has a wide range of applications. Distributed estimation on a network refers to the cooperative estimation of the parameters of interest by each node in a region based on the collected data. In practical applications, distributed information processing has some constraints such as limited storage space of nodes, while adaptive information processing adopts streaming information processing mode, and only a small amount of real-time data is stored, so it can save storage space. In this paper, the author considers the distributed adaptive estimation algorithm on the network. For this problem, the author considers not only the linear data model but also the nonlinear data model. In the linear data model, the author further considers the characteristics of data and parameters. In most distributed adaptive estimation algorithms, researchers assume that only the output data is noisy and the input data is completely accurate. However, in a real environment, input and output data may be noisy. Therefore, the assumption that the noise is only loaded on the input data is impractical. When there is noise in the input and output, the global least square method can minimize the disturbance of the input and output data, so it has better performance than the least square method. Many natural and artificial signals are highly sparse for parameter characteristics. The study shows that using sparsity can improve learning performance. In this paper, the sparse penalty term of L _ 1 or l _ 0 norm is used to consider the sparsity of the vector to be estimated. In addition, different from the single-task estimation problem, the author further considers that the parameters to be estimated at different nodes can be different, that is, the multi-task estimation problem. For multitask problems, although the tasks of different nodes may be different, there may be similarities among different tasks. Therefore, the cooperation between different tasks can improve learning performance. Obviously, the key point of multi-task estimation is to design a cooperative strategy between tasks. In this paper, the author proposes an adaptive inter-task cooperation strategy to improve the robustness of the algorithm to different degrees of inter-task differences. For the multitask distributed estimation problem, the joint sparsity of the parameters to be estimated is also considered. The authors use the mixed norm of L _ 2N _ 1 or L _ 2O to utilize the same structural information for each task. Based on the theory of extreme learning machine, the distributed nonlinear learning problem is transformed into a linear learning problem under nonlinear data model, and a distributed extreme learning machine algorithm is proposed. It is important to note that the ability of the algorithm to construct nonlinear mapping between inputs and outputs has not changed. Based on the above discussion, it can be seen that the design and performance analysis of the distributed nonlinear adaptive algorithm is very similar to the design and performance analysis of the distributed linear adaptive algorithm. For the distributed adaptive estimation algorithm proposed in this paper, the mean and mean square performance analysis are given. The performance analysis of these algorithms is different from that of existing distributed algorithms and is more difficult than that of existing distributed algorithms. Therefore, the performance analysis of these algorithms is the main contribution of this paper. In addition, the author gives a simulation experiment to verify the effectiveness and advantages of these algorithms.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP301.6

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