Modern analytical techniques provide an unprecedented insight to biomedical samples, allowing an in depth characterization of cells or body fluids, to the level of genes, transcripts, peptides, proteins, metabolites, or metallic ions. The fine grained picture provided by such approaches holds the promise for a better understanding of complex pathologies, and consequently the personalization of diagnosis, prognosis and treatment procedures. In practice however, technical limitations restrict the resolution of the acquired data, and thus of downstream biomedical inference. As a result, the study of complex diseases like leukemia and other types of cancer is impaired by the high heterogeneity of pathologies as well as patient profiles. In this review, we propose an introduction to the general approach of characterizing samples and inferring biomedical results. We highlight the main limitations of the technique with regards to complex and heterogeneous pathologies, and provide ways to overcome these by improving the ability of experiments in discriminating samples.