Efficient Parametric Projection Pursuit Density Estimation
This work provides an efficient method for high-dimensional density estimation, though it appears incremental as it builds on existing ICA and projection pursuit techniques.
The paper tackles the curse of dimensionality in density estimation by introducing the under-complete product of experts (UPoE), a fully tractable parametric model for projection pursuit, and shows that its maximum likelihood learning rules match those of under-complete ICA.
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 projection of the data. The UPoE is fully tractable and may be interpreted 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 algorithm and discuss its relationship to projection pursuit density estimation and feature induction algorithms for additive random field models.