Shuichi Kawano

Noriaki Sato, Marco Scutari, Shuichi Kawano et al.

Estimating causal networks from biological data is a critical step in systems biology. When evaluating the inferred network, assessing the networks based on their intervention effects is particularly important for downstream probabilistic reasoning and the identification of potential drug targets. In the context of gene regulatory network inference, biological databases are often used as reference sources. These databases typically describe relationships in a qualitative rather than quantitative manner. However, few evaluation metrics have been developed that take this qualitative nature into account. To address this, we developed a metric, the sign-augmented Structural Intervention Distance (sSID), and a weighted sSID that incorporates the net effects of the intervention. Through simulations and analyses of real transcriptomic datasets, we found that our proposed metrics could identify a different algorithm as optimal compared to conventional metrics, and the network selected by sSID had a superior performance in the classification task of clinical covariates using transcriptomic data. This suggests that sSID can distinguish networks that are structurally correct but functionally incorrect, highlighting its potential as a more biologically meaningful and practical evaluation metric.

Akira Okazaki, Shuichi Kawano

Multi-task learning (MTL) aims to improve estimation and prediction performance by sharing common information among related tasks. One natural assumption in MTL is that tasks are classified into clusters based on their characteristics. However, existing MTL methods based on this assumption often ignore outlier tasks that have large task-specific components or no relation to other tasks. To address this issue, we propose a novel MTL method called Multi-Task Learning via Robust Regularized Clustering (MTLRRC). MTLRRC incorporates robust regularization terms inspired by robust convex clustering, which is further extended to handle non-convex and group-sparse penalties. The extension allows MTLRRC to simultaneously perform robust task clustering and outlier task detection. The connection between the extended robust clustering and the multivariate M-estimator is also established. This provides an interpretation of the robustness of MTLRRC against outlier tasks. An efficient algorithm based on a modified alternating direction method of multipliers is developed for the estimation of the parameters. The effectiveness of MTLRRC is demonstrated through simulation studies and application to real data.

Kaito Shimamura, Shuichi Kawano

Network lasso is a method for solving a multi-task learning problem through the regularized maximum likelihood method. A characteristic of network lasso is setting a different model for each sample. The relationships among the models are represented by relational coefficients. A crucial issue in network lasso is to provide appropriate values for these relational coefficients. In this paper, we propose a Bayesian approach to solve multi-task learning problems by network lasso. This approach allows us to objectively determine the relational coefficients by Bayesian estimation. The effectiveness of the proposed method is shown in a simulation study and a real data analysis.

Kohei Yoshikawa, Shuichi Kawano

We consider the problem of extracting a common structure from multiple tensor datasets. For this purpose, we propose multilinear common component analysis (MCCA) based on Kronecker products of mode-wise covariance matrices. MCCA constructs a common basis represented by linear combinations of the original variables which loses as little information of the multiple tensor datasets. We also develop an estimation algorithm for MCCA that guarantees mode-wise global convergence. Numerical studies are conducted to show the effectiveness of MCCA.

Kazuaki. Murayama, Shuichi. Kawano

In the variational relevance vector machine, the gamma distribution is representative as a hyperprior over the noise precision of automatic relevance determination prior. Instead of the gamma hyperprior, we propose to use the inverse gamma hyperprior with a shape parameter close to zero and a scale parameter not necessary close to zero. This hyperprior is associated with the concept of a weakly informative prior. The effect of this hyperprior is investigated through regression to non-homogeneous data. Because it is difficult to capture the structure of such data with a single kernel function, we apply the multiple kernel method, in which multiple kernel functions with different widths are arranged for input data. We confirm that the degrees of freedom in a model is controlled by adjusting the scale parameter and keeping the shape parameter close to zero. A candidate for selecting the scale parameter is the predictive information criterion. However the estimated model using this criterion seems to cause over-fitting. This is because the multiple kernel method makes the model a situation where the dimension of the model is larger than the data size. To select an appropriate scale parameter even in such a situation, we also propose an extended prediction information criterion. It is confirmed that a multiple kernel relevance vector regression model with good predictive accuracy can be obtained by selecting the scale parameter minimizing extended prediction information criterion.

Shengyi Wu, Kaito Shimamura, Kohei Yoshikawa et al.

In linear regression models, fusion of coefficients is used to identify predictors having similar relationships with a response. This is called variable fusion. This paper presents a novel variable fusion method in terms of Bayesian linear regression models. We focus on hierarchical Bayesian models based on a spike-and-slab prior approach. A spike-and-slab prior is tailored to perform variable fusion. To obtain estimates of the parameters, we develop a Gibbs sampler for the parameters. Simulation studies and a real data analysis show that our proposed method achieves better performance than previous methods.

Shuichi Kawano

Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components obtained by the first stage. Since PCA is performed by using only explanatory variables, the principal components have no information about the response variable. To address the problem, we propose a one-stage procedure for PCR in terms of singular value decomposition approach. Our approach is based upon two loss functions, a regression loss and a PCA loss, with sparse regularization. The proposed method enables us to obtain principal component loadings that possess information about both explanatory variables and a response variable. An estimation algorithm is developed by using alternating direction method of multipliers. We conduct numerical studies to show the effectiveness of the proposed method.

Kaito Shimamura, Shuichi Kawano

Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $L_1$ norm is usually employed for the regularization term in sparse convex clustering, its use increases the dependence on the data and reduces the estimation accuracy if the sample size is not sufficient. To tackle these problems, this paper proposes a Bayesian sparse convex clustering method based on the ideas of Bayesian lasso and global-local shrinkage priors. We introduce Gibbs sampling algorithms for our method using scale mixtures of normal distributions. The effectiveness of the proposed methods is shown in simulation studies and a real data analysis.

Kohei Yoshikawa, Shuichi Kawano

We consider the problem of constructing a reduced-rank regression model whose coefficient parameter is represented as a singular value decomposition with sparse singular vectors. The traditional estimation procedure for the coefficient parameter often fails when the true rank of the parameter is high. To overcome this issue, we develop an estimation algorithm with rank and variable selection via sparse regularization and manifold optimization, which enables us to obtain an accurate estimation of the coefficient parameter even if the true rank of the coefficient parameter is high. Using sparse regularization, we can also select an optimal value of the rank. We conduct Monte Carlo experiments and real data analysis to illustrate the effectiveness of our proposed method.

Shuichi Kawano, Hironori Fujisawa, Toyoyuki Takada et al.

Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note that PCA is based only on the explanatory variables, so the principal components are not selected using the information on the response variable. In this paper, we propose a one-stage procedure for PCR in the framework of generalized linear models. The basic loss function is based on a combination of the regression loss and PCA loss. An estimate of the regression parameter is obtained as the minimizer of the basic loss function with a sparse penalty. We call the proposed method sparse principal component regression for generalized linear models (SPCR-glm). Taking the two loss function into consideration simultaneously, SPCR-glm enables us to obtain sparse principal component loadings that are related to a response variable. However, a combination of loss functions may cause a parameter identification problem, but this potential problem is avoided by virtue of the sparse penalty. Thus, the sparse penalty plays two roles in this method. The parameter estimation procedure is proposed using various update algorithms with the coordinate descent algorithm. We apply SPCR-glm to two real datasets, doctor visits data and mouse consomic strain data. SPCR-glm provides more easily interpretable principal component (PC) scores and clearer classification on PC plots than the usual PCA.

Shuichi Kawano, Hironori Fujisawa, Toyoyuki Takada et al.

Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To address this problem, we propose the sparse principal component regression (SPCR) that is a one-stage procedure for PCR. SPCR enables us to adaptively obtain sparse principal component loadings that are related to the response variable and select the number of principal components simultaneously. SPCR can be obtained by the convex optimization problem for each of parameters with the coordinate descent algorithm. Monte Carlo simulations and real data analyses are performed to illustrate the effectiveness of SPCR.