概　 要： データ同化は、数値シミュレーションと観測／計測データを、ベイズ統計学のフレームワークで融合するための手法であり、様々な科学分野に浸透しつつある。本セミナーでは、データ同化の基礎理論について述べた上で、固体地球科学分野への具体的な応用例を紹介する。

概　 要： We study statistical properties of semi-supervised learning, which is considered to be an important problem in the field of machine learning. In standard supervised learning, only labeled data is observed, and classification and regression problems are formalized as supervised learning. On the other hand, in semi-supervised learning, unlabeled data is also obtained in addition to labeled data. Hence, the ability to exploit unlabeled data is important to improve prediction accuracy in semi-supervised learning. This problem is regarded as a semiparametric estimation problem with missing data. Under discriminative probabilistic models, it was considered that the unlabeled data is useless to improve the estimation accuracy. Recently, the weighted estimator using the unlabeled data achieves a better prediction accuracy compared to the learning method using only labeled data, especially when the discriminative probabilistic model is misspecified. That is, the improvement under the semiparametric model with missing data is possible, when the semiparametric model is misspecified. In this paper, we apply the density-ratio estimator to obtain the weight function in semi-supervised learning. Our approach is advantageous because the proposed estimator does not require well-specified probabilistic models for the probability of the unlabeled data. Based on the statistical asymptotic theory, we prove that the estimation accuracy of our method outperforms supervised learning using only the labeled data. Some numerical experiments present the usefulness of our methods.

概　 要： Balanced minimum evolution (BME) is a statistically consistent distance-based method to reconstruct a phylogenetic tree from an alignment of molecular data. In 2000, Pauplin showed that the BME method is equivalent to optimizing a linear functional over the BME polytope, the convex hull of the BME vectors obtained from Pauplin's formula applied to all binary trees. The BME method is related to the Neighbor Joining (NJ) algorithm, now known to be a greedy optimization of the BME principle. Further, the NJ and BME algorithms have been studied previously to understand when the NJ Algorithm returns a BME tree for small numbers of taxa. In this talk we aim to elucidate the structure of the BME polytope and strengthen knowledge of the connection between the BME method and NJ Algorithm. We first prove that any subtree-prune-regraft move from a binary tree to another binary tree corresponds to an edge of the BME polytope. Moreover, we describe an entire family of faces parametrized by disjoint clades. We show that these {\em clade-faces} are smaller dimensional BME polytopes themselves. Finally, we show that for any order of joining nodes to form a tree, there exists an associated distance matrix (i.e., dissimilarity map) for which the NJ Algorithm returns the BME tree. More strongly, we show that the BME cone and every NJ cone associated to a tree $T$ have an intersection of positive measure.

概　 要： Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. In this framework, a set of variables is represented by an undirected graph, where vertices correspond to variables, and an edge connects two vertices if the corresponding pair of variables are dependent, conditional on the remaining ones. Recently, this tool has received a high interest for the discovery of biological networks by l1-penalization of the model likelihood. In this presentation, we introduce various ways of inferring sparse co-expression networks based on partial correlation coefficients from either steady-state or time-course transcriptomic data. All proposals search for a latent structure of the network to drive the selection of edges through an adaptive l1-penalization of the model likelihood. We focus on inference from samples collected in different experimental conditions and therefore not identically distributed.

概　 要： 関数データに基づく回帰，判別手法について報告する．一つの個体に対して，データが時間の経過や位置の変化に伴って複数観測されたとき，これを時間や位置の関数とみなして扱う方法は関数データ解析(FDA;Functional Data Analysis)とよばれている．本研究では，関数データとして与えられた説明変数と，スカラーで与えられた目的変数との関係をモデル化する関数回帰モデリングについて紹介する．特に，説明変数が複数与えられたとき，スパース正則化に基づきモデル推定と変数選択を同時に行う方法について述べる．また，関数データに基づくロジスティック回帰モデルに対してスパース正則化を適用することで，判別に影響を与えている変数の選択を行う方法についても述べる．判別手法を，経時観測された多発性硬化症患者の遺伝子発現データに適用し，遺伝子選択を試みる．

概　 要： Random-graph mixture models are very popular for modelling real data networks. Parameter estimation procedures usually rely on variational approximations, either combined with the expectation?maximization (EM) algorithm or with Bayesian approaches. Despite good results on synthetic data, the validity of the variational approximation is, however, not established. Moreover, these variational approaches aim at approximating the maximum likelihood or the maximum a posteriori estimators, whose behaviour in an asymptotic framework (as the sample size increases to infinity) remains unknown for these models. In this work, we show that, in many different affiliation contexts (for binary or weighted graphs), parameter estimators based either on moment equations or on the maximization of some composite likelihood are strongly consistent and convergent in n square root, when the number n of nodes increases to infinity. As a consequence, our result establishes that the overall structure of an affiliation model can be (asymptotically) caught by the description of the network in terms of its number of triads (order 3 structures) and edges (order 2 structures). Moreover, these parameter estimates are either explicit (as for the moment estimators) or may be approximated by using a simple EM algorithm, whose convergence properties are known. We illustrate the efficiency of our method on simulated data and compare its performances with other existing procedures. A data set of cross-citations among economics journals is also analysed.