  Most popular dimension reduction (DR) methods like t-SNE and UMAP are based
on minimizing a cost between input and latent pairwise similarities. Though
widely used, these approaches lack clear probabilistic foundations to enable a
full understanding of their properties and limitations. To that extent, we
introduce a unifying statistical framework based on the coupling of hidden
graphs using cross entropy. These graphs induce a Markov random field
dependency structure among the observations in both input and latent spaces. We
show that existing pairwise similarity DR methods can be retrieved from our
framework with particular choices of priors for the graphs. Moreover this
reveals that these methods suffer from a statistical deficiency that explains
poor performances in conserving coarse-grain dependencies. Our model is
leveraged and extended to address this issue while new links are drawn with
Laplacian eigenmaps and PCA.
