Lasso-Type Penalized Maximum Likelihood Factor Analysis

• Activity Number: 498
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Kei Hirose*+ and Michio Yamamoto
• Companies: Graduate School of Engineering Science, Osaka University and Osaka University
• Keywords: Coordinate Descent Algorithm ; Nonconvex Penalty ; Rotation Technique ; Solution Path

Abstract

We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is utilized to find sparse factor loadings. However, the maximum likelihood estimates cannot be obtained when the number of variables is much larger than the number of observations. Furthermore, even if the maximum likelihood estimates are available, the rotation technique does not often produce a sufficiently sparse solution. In the present paper, a penalized likelihood procedure that imposes a nonconvex penalty on the factor loadings is proposed to handle these problems. We show that the penalized likelihood procedure can be viewed as a generalization of the traditional two-step approach, and the proposed methodology can produce sparser solutions than the rotation technique. A new algorithm via the EM algorithm along with coordinate descent is introduced to compute the entire solution path, which permits the application to a wide variety of convex and nonconvex penalties.