Products of Gaussians

Recently Hinton (1999) has introduced the Products of Experts (PoE) model in which several individual probabilistic models for data are combined to provide an overall model of the data. Be(cid:173) low we consider PoE models in which each expert is a Gaussian. Although the product of Gaussians is also a Gaussian, if each Gaus(cid:173) sian has a simple structure the product can have a richer structure. We examine (1) Products of Gaussian pancakes which give rise to probabilistic Minor Components Analysis, (2) products of I-factor PPCA models and (3) a products of experts construction for an AR(l) process. Recently Hinton (1999) has introduced the Products of Experts (PoE) model in which several individual probabilistic models for data are combined to provide an overall model of the data.