Generalized^2 Linear^2 Models
We introduce the Generalized2 Linear2 Model, a statistical estimator which combines features of nonlinear regression and factor analysis. A (GL)2M approximately decomposes a rectangular matrix X into a simpler representation f(g(A)h(B)). Here A and B are low-rank matrices, while f, g, and h arc link functions. (GL)2Ms include many useful models as special cases, including principal components analysis, exponential-family PCA, the infomax formulation of independent components analysis, linear regression, and generalized linear models. They also include new and interesting special cases, one of which we describe below. We also present an iterative procedure which optimizes the parameters of a (GL)2M. This procedure reduces to well-known algorithms for some of the special cases listed above; for other special cases, it is new.