Graphical models have attracted increasing attention in recent years, especially in settings involving high dimensional data. In particular Gaussian graphical models are used to model the conditional dependence structure among multiple Gaussian random variables. As a result of its computational efficiency the graphical lasso (glasso) has become one of the most popular approaches for fitting high dimensional graphical models. In this article we extend the graphical models concept to model the conditional * Shaojun Guo was partially supported by National Science Foundation of China (NO. 11771447). significantly outperforms possible competing methods through both simulations and an analysis of a real world EEG data set comparing alcoholic and non-alcoholic patients.Some key words: Functional data; Graphical models; Functional principal component analysis;Block sparse precision matrix, Block coordinate descent algorithm.

Summary We consider estimating a functional graphical model from multivariate functional observations. In functional data analysis, the classical assumption is that each function has been measured over a densely sampled grid. However, in practice the functions have often been observed, with measurement error, at a relatively small number of points. We propose a class of doubly functional graphical models to capture the evolving conditional dependence relationship among a large number of sparsely or densely sampled functions. Our approach first implements a nonparametric smoother to perform functional principal components analysis for each curve, then estimates a functional covariance matrix and finally computes sparse precision matrices, which in turn provide the doubly functional graphical model. We derive some novel concentration bounds, uniform convergence rates and model selection properties of our estimator for both sparsely and densely sampled functional data in the high-dimensional large-$p$, small-$n$ regime. We demonstrate via simulations that the proposed method significantly outperforms possible competitors. Our proposed method is applied to a brain imaging dataset.

Panel data analysis is an important topic in statistics and econometrics. Traditionally, in panel data analysis, all individuals are assumed to share the same unknown parameters, e.g. the same coefficients of covariates when the linear models are used, and the differences between the individuals are accounted for by cluster effects. This kind of modelling only makes sense if our main interest is on the global trend, this is because it would not be able to tell us anything about the individual attributes which are sometimes very important. In this paper, we proposed a modelling based on the single index models embedded with homogeneity for panel data analysis, which builds the individual attributes in the model and is parsimonious at the same time. We develop a data driven approach to identify the structure of homogeneity, and estimate the unknown parameters and functions based on the identified structure. Asymptotic properties of the resulting estimators are established. Intensive simulation studies conducted in this paper also show the resulting estimators work very well when sample size is finite. Finally, the proposed modelling is applied to a public financial dataset and a UK climate dataset, the results reveal some interesting findings.

Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid of points contaminated by i.i.d. measurement errors. In practice, however, the dynamical dependence across different curves may exist and the parametric assumption on the error covariance structure could be unrealistic. In this paper, we consider functional linear regression with serially dependent observations of the functional predictor, when the contamination of the predictor by the white noise is genuinely functional with fully nonparametric covariance structure. Inspired by the fact that the autocovariance function of observed functional predictors automatically filters out the impact from the unobservable noise term, we propose a novel autocovariance-based generalized method-of-moments estimate of the slope function. We also develop a nonparametric smoothing approach to handle the scenario of partially observed functional predictors. The asymptotic properties of the resulting estimators under different scenarios are established. Finally, we demonstrate that our proposed method significantly outperforms possible competing methods through an extensive set of simulations and an analysis of a public financial dataset.

Using semantic information can help to accurately find suitable services from a variety of available (different semantics) services, and the semantic information of Web services can be described in detail in a Web service knowledge graph. In this paper, a Web service recommendation algorithm based on knowledge graph representation learning (kg-WSR) is proposed. The algorithm embeds the entities and relationships of the knowledge graph into the low-dimensional vector space. By calculating the distance between service entities in low-dimensional space, the relationship information of services which is not considered in recommendation approaches using a collaborative filtering algorithm is incorporated into the recommendation algorithm to enhance the accurateness of the result. The experimental results show that this algorithm can not only effectively improve the accuracy rate, recall rate, and coverage rate of recommendation but also solve the cold start problem to some extent.