Joint and adaptive selection of DStMM architecture and skewness complexity

Establish a joint or adaptive selection procedure for the depth, mixture orders, latent dimensions, degrees-of-freedom pooling structure, and skewness active set of the deep skew-$t$ mixture model, extending beyond selection from a finite candidate grid.

Background

The deep skew-$t$ mixture model currently selects architectural and distributional-complexity choices from a finite candidate grid. These choices include the number of latent layers, the number of mixture components at each layer, the latent dimensions, whether degrees of freedom are pooled or component/pathway-specific, and which layers have active skewness parameters.

The paper notes that these quantities are currently not selected jointly or adaptively. A solution would provide a principled model-selection mechanism that accounts simultaneously for hierarchical depth, mixture complexity, latent dimension, tail-parameter pooling, and skewness allocation, potentially improving flexibility while avoiding reliance on manually specified candidate grids.