大规模动态高斯马尔科夫过程的参数估计

发布时间：2018-06-27 05:21

本文选题：大规模 + 空时信号结构　；参考：《北京邮电大学》2017年硕士论文

【摘要】：基于图结构的数据分析是当前大数据集处理中最热门的技术之一,它可以很好地描述同一时刻时间间序列的相互关系,以及不同时刻时间序列的内部关系。然而在实际应用中,图结构往往未知,比如同一板块的股票价格之间虽具有较强的相关性,但往往无法直接套用现有的图结构。因此,很有必要从有限的样本中学习有效的图拓扑结构。本论文针对大规模动态高斯马尔科夫过程的图结构参数估计问题开展研究。本文的主要贡献如下:1.基于一阶高斯马尔科夫过程的联合图结构参数估计,分析联合数据图结构及噪声图结构的构造,定性地确定权重参数的取值范围;并采用交替梯度下降法对联合图结构进行阈值筛选,从而得到稀疏的图结构,证明了分组阈值q算法(GTQ)这一过程的收敛性并通过仿真验证其收敛性。2.基于聚类的一阶高斯马尔科夫过程的图结构参数估计,从谱聚类算法出发,将聚类嵌入动态线性系统中,并提出确定聚类数K的算法。通过仿真研究不同网络规模、阈值q对聚类性能、聚类数K的影响以及算法复杂分析,同时通过不同的图模型对比GTG、CDG、MRCE、JGSE在模型拓扑识别率与模型估计准确率方面的性能,最后将其运用到实际股票市场的数据。3.基于稀疏自适应的迭代最小二乘图结构参数估计,从批-最小二乘(B-LSM)算法出发提出迭代最小二乘(ILSM)算法,利用先验估计的图结构和相关的新息信息,进行在线图结构的估计。同时在误差可控的范围内利用信号结构的共稀疏性,提出稀疏自适应-迭代最小二乘(ASP-LSM)算法,提高拓扑识别的能力,最后通过实验仿真验证ASP-LSM算法的性能,并将其运用于实际股票市场的数据。
[Abstract]:Data analysis based on graph structure is one of the most popular techniques in big data set processing. It can well describe the interrelation of time series at the same time and the internal relationship of different time series. However, in practical applications, the graph structure is often unknown. For example, although there is a strong correlation between the stock prices of the same plate, it is often unable to directly apply the existing graph structure. Therefore, it is necessary to learn effective graph topology from finite samples. In this paper, the problem of graph structure parameter estimation for large-scale dynamic Gao Si Markov processes is studied. The main contributions of this paper are as follows: 1. Based on the joint graph structure parameter estimation of first-order Gao Si Markov process, the structure of joint data graph and noise graph is analyzed, and the value range of weight parameter is determined qualitatively. The alternating gradient descent method is used to filter the joint graph structure, and the sparse graph structure is obtained. The convergence of the process of grouping threshold Q algorithm (GTQ) is proved and its convergence is verified by simulation. Based on the estimation of the graph structure parameters of the first-order Gao Si Markov process, the clustering is embedded into the dynamic linear system based on the spectral clustering algorithm, and an algorithm to determine the clustering number K is proposed. The effects of different network size, threshold Q on clustering performance, clustering number K and algorithm complexity are studied by simulation. At the same time, the performance of model topology recognition rate and model estimation accuracy are compared by using different graph models. Finally, it is applied to the actual stock market data. 3. Based on sparse adaptive iterative least square graph structure parameter estimation, an iterative least squares (ILSM) algorithm based on batch least squares (B-LSM) algorithm is proposed. The on-line graph structure is estimated by using the graph structure of prior estimation and related innovation information. At the same time, the sparse adaptive iterative least squares (ASP-LSM) algorithm is proposed to improve the ability of topology recognition by using the common sparsity of signal structure in the range of error control. Finally, the performance of ASP-LSM algorithm is verified by experimental simulation. And apply it to the actual stock market data.
【学位授予单位】：北京邮电大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP311.13;O211.61

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