arXiv subjects

Yoshikazu Terada

Publications and source records attributed to Yoshikazu Terada.

25 records · Page 2Linked to original sources

arXiv2019

Selective Inference for Testing Trees and Edges in Phylogenetics

Selective inference is considered for testing trees and edges in phylogenetic tree selection from molecular sequences. This improves the previously proposed approximately unbiased test by adjusting the selection bias when testing many trees and edges at the same time. The newly proposed selective inference $p$-value is useful for testing selected edges to claim that they are significantly supported if $p>1-α$, whereas the non-selective $p$-value is still useful for testing candidate trees to claim that they are rejected if $p<α$. The selective $p$-value controls the type-I error conditioned on the selection event, whereas the non-selective $p$-value controls it unconditionally. The selective and non-selective approximately unbiased $p$-values are computed from two geometric quantities called signed distance and mean curvature of the region representing tree or edge of interest in the space of probability distributions. These two geometric quantities are estimated by fitting a model of scaling-law to the non-parametric multiscale bootstrap probabilities. Our general method is applicable to a wider class of problems; phylogenetic tree selection is an example of model selection, and it is interpreted as the variable selection of multiple regression, where each edge corresponds to each predictor. Our method is illustrated in a previously controversial phylogenetic analysis of human, rabbit and mouse.

stat.AP↗

arXiv2018

Simple structure estimation via prenet penalization

We propose a $prenet$ ($pr$oduct $e$lastic $net$), which is a new penalization method for factor analysis models. The penalty is based on the product of a pair of elements in each row of the loading matrix. The prenet not only shrinks some of the factor loadings toward exactly zero, but also enhances the simplicity of the loading matrix, which plays an important role in the interpretation of the common factors. In particular, with a large amount of prenet penalization, the estimated loading matrix possesses a perfect simple structure, which is known as a desirable structure in terms of the simplicity of the loading matrix. Furthermore, the perfect simple structure estimation via the prenet turns out to be a generalization of the $k$-means clustering of variables. On the other hand, a mild amount of the penalization approximates a loading matrix estimated by the quartimin rotation, one of the most commonly used oblique rotation techniques. Thus, the proposed penalty bridges a gap between the perfect simple structure and the quartimin rotation. Monte Carlo simulation is conducted to investigate the performance of the proposed procedure. Three real data analyses are given to illustrate the usefulness of our penalty.

stat.ME↗

arXiv2018

Selective inference for the problem of regions via multiscale bootstrap

A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical clustering where confidence levels of clusters are calculated only for those appeared in the dendrogram, thus subject to heavy selection bias. Our computation is based on a raw confidence measure, called bootstrap probability, which is easily obtained by counting how many times the same cluster appears in bootstrap replicates of the dendrogram. We adjust the bias of the bootstrap probability by utilizing the scaling-law in terms of geometric quantities of the region in the abstract parameter space, namely, signed distance and mean curvature. Although this idea has been used for non-selective inference of hierarchical clustering, its selective inference version has not been discussed in the literature. Our bias-corrected $p$-values are asymptotically second-order accurate in the large sample theory of smooth boundary surfaces of regions, and they are also justified for nonsmooth surfaces such as polyhedral cones. The $p$-values are asymptotically equivalent to those of the iterated bootstrap but with less computation.

math.ST↗

arXiv2014

Strong Consistency of Reduced K-means Clustering

Reduced k-means clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that both clustering of objects and low-dimensional subspace reflecting the cluster structure are simultaneously obtained. In this paper, the relationship between conventional k-means clustering and reduced k-means clustering is discussed. Conditions ensuring almost sure convergence of the estimator of reduced k-means clustering as unboundedly increasing sample size have been presented. The results for a more general model considering conventional k-means clustering and reduced k-means clustering are provided in this paper. Moreover, a new criterion and its consistent estimator are proposed to determine the optimal dimension number of a subspace, given the number of clusters.

math.ST↗

arXiv2014

Strong Consistency of Factorial K-means Clustering

Factorial k-means (FKM) clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that the partition of objects and the low-dimensional subspace reflecting the cluster structure are obtained, simultaneously. Conditions that ensure the almost sure convergence of the estimator of FKM clustering as the sample size increases unboundedly are derived. The result is proved for a more general model including FKM clustering.

math.ST↗

arXiv2014

Functional Factorial K-means Analysis

A new procedure for simultaneously finding the optimal cluster structure of multivariate functional objects and finding the subspace to represent the cluster structure is presented. The method is based on the $k$-means criterion for projected functional objects on a subspace in which a cluster structure exists. An efficient alternating least-squares algorithm is described, and the proposed method is extended to a regularized method for smoothness of weight functions. To deal with the negative effect of the correlation of coefficient matrix of the basis function expansion in the proposed algorithm, a two-step approach to the proposed method is also described. Analyses of artificial and real data demonstrate that the proposed method gives correct and interpretable results compared with existing methods, the functional principal component $k$-means (FPCK) method and tandem clustering approach. It is also shown that the proposed method can be considered complementary to FPCK.

stat.ME↗

arXiv2013

Clustering for high-dimension, low-sample size data using distance vectors

In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that contain information of the cluster structure in high-dimensional space. Based on this fact, we propose an efficient and simple clustering approach, called distance vector clustering, for HDLSS data. Under the assumptions given in the work of Hall et al. (2005), we show the proposed approach provides a true cluster label under milder conditions when the dimension tends to infinity with the sample size fixed. The effectiveness of the distance vector clustering approach is illustrated through a numerical experiment and real data analysis.

stat.ML↗