Inferring absolute counts from proportions by constraining multivariate normal distributions

Biological measurements often result in proportional data, which derive from underlying biological counts. Proportion data are lacking a dimension of information as compared to counts, restricting available analysis methods and separating the data from the biology. We demonstrate a mathematical technique that estimates absolute counts corresponding to proportion data, which we refer to as Mahalanobis Count Inference (MCI). MCI uses information from a population-representative multivariate normal (MVN) distribution of component counts and ultimately outputs an estimated count and a confidence interval per observation proportion vector. We apply MCI to the imputation of white blood cell (WBC) counts, and of total mRNA within single cells. The method performs very well on total mRNA recapitulation (log-space Pearsons R = 0.81), and well enough on WBC counts to outperform proportions at multiple classification tasks. MCI operates with minimal assumptions, and is applicable to many compositional omics.