We address the identification of optimal biomarkers for the rapid diagnosis of neonatal sepsis. We employ both canonical correlation analysis (CCA) and sparse support vector machine (SSVM) classifiers to select the best subset of biomarkers from a large hematological data set collected from infants with suspected sepsis from Yale-New Haven Hospital's Neonatal Intensive Care Unit (NICU). CCA is used to select sets of biomarkers of increasing size that are most highly correlated with infection. The effectiveness of these biomarkers is then validated by constructing a sparse support vector machine diagnostic classifier. We find that the following set of five biomarkers capture the essential diagnostic information (in order of importance): Bands, Platelets, neutrophil CD64, White Blood Cells, and Segs. Further, the diagnostic performance of the optimal set of biomarkers is significantly higher than that of isolated individual biomarkers. These results suggest an enhanced sepsis scoring system for neonatal sepsis that includes these five biomarkers. We demonstrate the robustness of our analysis by comparing CCA with the Forward Selection method and SSVM with LASSO Logistic Regression.