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Random Forest on Small Numbers of Observations

Neil Saunders takes us through an interesting problem:

A recent question on Stack Overflow [r] asked why a random forest model was not working as expected. The questioner was working with data from an experiment in which yeast was grown under conditions where (a) the growth rate could be controlled and (b) one of 6 nutrients was limited. Their dataset consisted of 6 rows – one per nutrient – and several thousand columns, with values representing the activity (expression) of yeast genes. Could the expression values be used to predict the limiting nutrient?

The random forest was not working as expected: not one of the nutrients was correctly classified. I pointed out that with only one case for each outcome, this was to be expected – as the random forest algorithm samples a proportion of the rows, no correct predictions are likely in this case. As sometimes happens the question was promptly deleted, which was unfortunate as we could have further explored the problem.

Neil decided to explore the problem further regardless and came to some interesting conclusions.