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We propose the extit{linear barycentric coding model (LBCM)} that utilizes the linear optimal transport (LOT) metric for analysis and synthesis of probability measures. We provide a closed-form solution to the variational problem characterizing the probability measures in the LBCM and establish equivalence of the LBCM to the set of Wasserstein-2 barycenters in the special case of compatible measures. Computational methods for synthesizing and analyzing measures in the LBCM are developed with finite sample guarantees. One of our main theoretical contributions is to identify an LBCM, expressed in terms of a simple family, which is sufficient to express all probability measures on the interval [0,1]. We show that a natural analogous construction of an LBCM in ℝ2 fails, and we leave it as an open problem to identify the proper extension in more than one dimension. We conclude by demonstrating the utility of LBCM for covariance estimation and data imputation. 

Abstract Motivation Leveraging cross-species information in protein function prediction can add significant power to network-based protein function prediction methods, because so much functional information is conserved across at least close scales of evolution. We introduce MUNDO, a new cross-species co-embedding method that combines a single-network embedding method with a co-embedding method to predict functional annotations in a target species, leveraging also functional annotations in a model species network. Results Across a wide range of parameter choices, MUNDO performs best at predicting annotations in the mouse network, when trained on mouse and human protein–protein interaction (PPI) networks, in the human network, when trained on human and mouse PPIs, and in Baker’s yeast, when trained on Fission and Baker’s yeast, as compared to competitor methods. MUNDO also outperforms all the cross-species methods when predicting in Fission yeast when trained on Fission and Baker’s yeast; however, in this single case, discarding the information from the other species and using annotations from the Fission yeast network alone usually performs best. Availability and implementation All code is available and can be accessed here: github.com/v0rtex20k/MUNDO. Supplementary information Supplementary data are available at Bioinformatics Advances online. Additional experimental results are on our github site.