Comparison to Ranksim, ConR, etc.

[panmianzhi]

I notice that several existing regression methods apply similar principles to the representation space to make it topologically similar to the target space, e.g. ranksim, conr. Can you provide some insights about the similarity between PH-Reg and these methods? Maybe PH-Reg is a more general framework?

[needylove]

Thanks for your question. The main focus of ranksim and conr is ordinality, while ours focuses on the topology (shape) of the feature manifold which does not necessarily preserve the ordinality. However, we empirically observed (also can be observed in their visualization) that ranksim encourages a lower intrinsic dimension feature manifold that is topologically similar to the target space. Thus, I guess preserving ordinality has a similar effect to PH-Reg (a similarity). By the way, preserving ordinality, of course, is important, however, why it is important is still not clear.