Which Machine Learning Classifiers are best for small datasets? An empirical study

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Although big data and deep learning are dominant, my own work at the Gates Foundation involves a lot of small (but expensive) datasets, where the number of rows (subjects, samples) is between 100 and 1000. For example, detailed measurements throughout a pregnancy and subsequent neonatal outcomes from pregnant women. A lot of my collaborative investigations involve fitting machine learning models to small datasets like these, and it's not clear what best practices are in this case.