Efficient Parametric Projection Pursuit Density Estimation

Product models of low dimensional experts are a powerful way to avoid the curse of dimensionality. We present the "under­ complete product of experts" (UPoE), where each expert models a one dimensional pro­ jection of the data. The UPoE may be inter­ preted as a parametric probabilistic model for projection pursuit. Its ML learning rules are identical to the approximate learning rules proposed before for under-complete ICA. We also derive an efficient sequential learning al­ gorithm and discuss its relationship to pro­ jection pursuit density estimation and fea­ ture induction algorithms for additive ran­ dom field models.