Understanding the transcriptional regulatory code, as well as other types of information encoded within biomolecular sequences, will require learning biophysical models of sequence-function relationships from high-throughput data. Controlling and characterizing the noise in such experiments, however, is notoriously difficult. The unpredictability of such noise creates problems for standard likelihood-based methods in statistical learning, which require that the quantitative form of experimental noise be known precisely. However, when this unpredictability is properly accounted for, important theoretical aspects of statistical learning which remain hidden in standard treatments are revealed. Specifically, one finds a close relationship between the standard inference method, based on likelihood, and an alternative inference method based on mutual information. Here we review and extend this relationship. We also describe its implications for learning sequence-function relationships from real biological data. Finally, we detail an idealized experiment in which these results can be demonstrated analytically.