TY - JOUR
T1 - On principal graphical models with application to gene network
AU - Kim, Kyongwon
N1 - Funding Information:
We are grateful to the Editor, the Associate Editor, and two referees for their insightful and constructive review, which contains useful comments and suggestions that have helped us to significantly improve this paper. This work is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIT ) (No. 2021R1F1A1046976 ) and Ewha Womans University Research Grant of 2021.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2022/2
Y1 - 2022/2
N2 - The principal graphical model is introduced by incorporating the ideas from the linear sufficient dimension reduction (SDR) methods such as the sliced inverse regression and sliced average variance estimation to a nonparametric graphical model. A nonparametric graphical model is a widely used method to investigate undirected graphs. However, when the number of nodes is large, a nonparametric graphical model suffers from the ‘curse of dimensionality’ because they contain intrinsic high dimensional kernels. The parametric graphical models such as the Gaussian or copula Gaussian graphical models are also well known for their intuitive structure and interpretability. However, they hinge on strong parametric model assumptions. The principal graphical model applies well-known linear SDR techniques to the nonparametric graphical models to enhance performance in high dimensional networks, avoid model assumptions, and maintain interpretability. We use components of linear SDR as modules and implement them in the (p2) pairs of variables in the network to evaluate conditional independence. In the numerical experiment, our methods have competitive accuracy in both low and high-dimensional settings. Our methods are applied to the DREAM 4 challenge gene network dataset and they work well in high dimensional settings with a limited number of observations.
AB - The principal graphical model is introduced by incorporating the ideas from the linear sufficient dimension reduction (SDR) methods such as the sliced inverse regression and sliced average variance estimation to a nonparametric graphical model. A nonparametric graphical model is a widely used method to investigate undirected graphs. However, when the number of nodes is large, a nonparametric graphical model suffers from the ‘curse of dimensionality’ because they contain intrinsic high dimensional kernels. The parametric graphical models such as the Gaussian or copula Gaussian graphical models are also well known for their intuitive structure and interpretability. However, they hinge on strong parametric model assumptions. The principal graphical model applies well-known linear SDR techniques to the nonparametric graphical models to enhance performance in high dimensional networks, avoid model assumptions, and maintain interpretability. We use components of linear SDR as modules and implement them in the (p2) pairs of variables in the network to evaluate conditional independence. In the numerical experiment, our methods have competitive accuracy in both low and high-dimensional settings. Our methods are applied to the DREAM 4 challenge gene network dataset and they work well in high dimensional settings with a limited number of observations.
KW - Conjoined conditional covariance operator
KW - Reproducing Kernel Hilbert space
KW - Sliced average variance estimation
KW - Sliced inverse regression
KW - Statistical graphical model
UR - http://www.scopus.com/inward/record.url?scp=85114779147&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2021.107344
DO - 10.1016/j.csda.2021.107344
M3 - Article
AN - SCOPUS:85114779147
VL - 166
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
SN - 0167-9473
M1 - 107344
ER -