Maintaining balanced growth in a changing environment is a fundamental systems-level challenge for cellular physiology, particularly in microorganisms. While the complete set of regulatory and functional pathways supporting growth and cellular proliferation are not yet known, portions of them are well understood. In particular, cellular proliferation is governed by mechanisms that are highly conserved from unicellular to multicellular organisms, and the disruption of these processes in metazoans is a major factor in the development of cancer. In this paper, we develop statistical methodology to identify quantitative aspects of the regulatory mechanisms underlying cellular proliferation in Saccharomyces cerevisiae. We find that the expression levels of a small set of genes can be exploited to predict the instantaneous growth rate of any cellular culture with high accuracy. The predictions obtained in this fashion are robust to changing biological conditions, experimental methods, and technological platforms. The proposed model is also effective in predicting growth rates for the related yeast Saccharomyces bayanus and the highly diverged yeast Schizosaccharomyces pombe, suggesting that the underlying regulatory signature is conserved across a wide range of unicellular evolution. We investigate the biological significance of the gene expression signature that the predictions are based upon from multiple perspectives: by perturbing the regulatory network through the Ras/PKA pathway, observing strong upregulation of growth rate even in the absence of appropriate nutrients, and discovering putative transcription factor binding sites, observing enrichment in growth-correlated genes. More broadly, the proposed methodology enables biological insights about growth at an instantaneous time scale, inaccessible by direct experimental methods. Data and tools enabling others to apply our methods are available at http://function.princeton.edu/growthrate.