Estimate Time Varying Gaussian Graph Model Based On Clime

With the rapid development of global information technology, big data as an important strategic resource in our country, and promote the rapid development of all aspects. In terms of the statistical field, the conditional independence between random variable is the important information for big data, and the traditional statistical modeling method handle the relationship simple relatively, which made the traditional modeling method cannot use the big data effectively. Originated from the graph model for theoretical physics, however, it is described the conditional independence in the form of visualizations, which was more and more application in the field of big data. Gaussian graph model as a special type of graph model, whose random variable under the assumption of identically distributed in Gaussian distribution, it depicting the corresponding conditional independence relationship between variables though the non-zero elements in the precision matrix. Nevertheless some dependence relationship in events in real life is time varying, in other words, identically distributed assumption in the above hypothesis is not established, therefore, time varying gaussian graph model become a focus of research of many scholars since 2010.Whether it is gaussian graph model or time-varying gaussian graph model, we care about the estimation of the precision matrix and the estimation of the precision matrix under a given time. Tony Cai using the method CLIME (constrained l1-minimization for inverse matrix estimation) to estimate the precision matrix under the independence identically distribution in 2011. In this thesis, the method CLIME is used to estimate the time-varying precision matrix. With the different of the sample covariance matrix Tony Cai used, this paper use kernel functions as estimation of the sample covariance matrix. In other words, in order to estimate t, we use kernel functions as weighting scheme such that data close to t receives large weights than that are far away. Under the certain conditions the real covariance matrix satisfied, we give convergence rate between the real precision matrix and it’s CLIME estimator under certain norm, including spectral norm、Frobenius norm and l∞ norm. Innovation points of this paper is use the methods to estimate time-varying gaussian graph model and give the convergence rate under certain norm.