[in Japanese]

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　The EM algorithm is a popular iterative algorithm for finding maximum likelihood estimates from incomplete data. However, the drawback of the EM algorithm is to converge slowly when the proportion of missing data is large. In order to speed up the convergence of the EM algorithm, we propose the “ε-accelerated EM algorithm” that accelerates the convergence of the EM sequence using the vector ε algorithm. The ε-accelerated EM algorithm only uses the EM estimates to obtain an accelerated sequence for the EM sequence and then does not require the matrix computation such as matrix inversion or evaluation of Hessian and Jacobian matrices, and a line search for step length optimization. Thus the algorithm is successfully extended to the EM algorithm without affecting its stability, flexibility and simplicity. When the accelerated sequence has larger values of the likelihood than the current EM estimate, a re-starting of the EM iterations using the accelerated sequence is more effective to increases its speed of convergence. The re-starting algorithm called the “εR-accelerated EM algorithm” can further improve the EM algorithm and the ε-accelerated EM algorithm in the sense of that it can reduce the number of iterations and computation time. We examine the performance and properties of the ε-accelerated EM and εR-accelerated EM algorithms by using numerical experiments.

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　A multivariate two-sample testing problem is one of the most important topics in nonparametric statistics. Further, a max-type multivariate Baumgartner test is proposed for testing the equality of two continuous distribution functions. In this paper, multivariate two-sample testing problems were examined based on the Jurečková & Kalina's ranks of distances. Simulations were used to investigate the power of the suggested statistic for various population distributions. The results indicate that the proposed test statistic is more suitable than various existing statistics for testing a shift in the location, scale and location-scale parameters. The method is illustrated by the analysis of real data.

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　In network data analysis, visualization of network data plays an important role. The aim of graph embedding (or graph drawing) is to get the geometric representation of graphs by mapping vertices to points in some manifold including Euclidean space. There is a large literature on graph embedding. However, most graph embedding methods mainly focus on the visibility of the geometric representation. Currently, the graph embedding problem has drawn quite some attention in the machine learning community. There are some important results about how to reconstruct the original structure of the network in Euclidean space. In this paper, we introduce four important graph embedding methods that focus on the geometric structure of unweighted graphs.

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　This paper reviews several sparse regularization methods and its algorithms. First, the regression modeling with sparse regularization is described, which includes lasso, group lasso, fused lasso, and generalized lasso. Second, we introduce two algorithms for estimating the parameters in models with sparse regularization; the coordinate descent algorithm and the alternating direction method of multipliers. Simulation results are given to investigate the properties of the two algorithms.

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　This paper outlines the method of structural equation model tree (SEMTree) for longitudinal design, which enables researchers simultaneously to extract the primary patterns of trajectories of changes and to explore independent variables that can explain the group differences in trajectories. More specifically, in SEMTree, relations between longitudinally observed dependent variables are structured through a template model using SEM, and one explores the independent variables that can explain the differences in terms of parameters in template model through decision tree. We also address the issue of the misspecifications of the template model, which can lead to dramatically different estimation results of trees.

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　Human gait analysis is important in health and sport management, medical research, and biometrics. Gait analysis is predominantly based on a motion capture system and video data. Video data-based gait analysis is useful to observe gait motion in a field study. However, many video-based gait analysis methods use lateral-view gait motion. Video data filmed from a frontal view are difficult to analyze, due to the subject being too close to the camera. In this study, we focus on the shape scale-changing in the frontal-view human gait. We estimate scale parameters using statistical registration and modeling with video data. To demonstrate the effectiveness of our method, we apply our model to normal and abnormal gait analysis. Our model performs well in terms of scale estimation and human gait analysis.

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　Bayesian approaches to data analysis have been applied to various empirical problems for its flexibility, built-in mechanism for handling uncertainty, and availability of general-purpose free software. On the other hand, the use of Bayesian approaches in multidimensional scaling is relatively recent movement, one which started only in this century. In this paper, a review of existing Bayesian approaches to multidimensional scaling techniques is provided. The emphasis is given on the interrelationships between various models that have been proposed so far. Some methodological issues in Markov chain Monte Carlo estimation of the parameters are discussed. Then, an individual differences model of Bayesian multidimensional scaling is illustrated with two psychological similarity datasets among multiple exemplars. Finally, future research directions and insights are outlined.

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　This paper reviews bigdata analytics using computational statistics. We explain what bigdata is and introduce the latest computing environment such as databases and Hadoop to handle and analyze it. After that, we discuss about some computationally intensive methods to it, including machine learning. We also refer to some programming languages and software tools, suitable for bigdata.

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