Optimum transport (OT) idea focuses, amongst all maps that may morph a likelihood measure onto one other, on these which might be the “thriftiest”, i.e. such that the averaged value between and its picture be as small as potential. Many computational approaches have been proposed to estimate such Monge maps when is the distance, e.g., utilizing entropic maps (Pooladian and Niles-Weed, 2021), or neural networks (Makkuva et al., 2020;
Korotin et al., 2020). We suggest a brand new mannequin for transport maps, constructed on a household of translation invariant prices , the place and is a regularizer. We suggest a generalization of the entropic map appropriate for , and spotlight a stunning hyperlink tying it with the Bregman centroids of the divergence generated by , and the proximal operator of . We present that selecting a sparsity-inducing norm for leads to maps that apply Occam‘s razor to move, within the sense that the displacement vectors they induce are sparse, with a sparsity sample that varies relying on . We showcase the flexibility of our methodology to estimate significant OT maps for high-dimensional single-cell transcription knowledge, within the – area of gene counts for cells, with out utilizing dimensionality discount, thus retaining the flexibility to interpret all displacements on the gene degree.
