Generalized² Linear² Models

Part of Advances in Neural Information Processing Systems 15 (NIPS 2002)

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Geoffrey J. Gordon


We introduce the Generalized2 Linear2 Model, a statistical estima(cid:173) tor which combines features of nonlinear regression and factor anal(cid:173) ysis. A (GL)2M approximately decomposes a rectangular matrix X into a simpler representation j(g(A)h(B)). Here A and Bare low-rank matrices, while j, g, and h are link functions. (GL)2Ms include many useful models as special cases, including principal components analysis, exponential-family peA, the infomax formu(cid:173) lation 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.