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I'm trying to compare a model (random forest) trained on two sets of features. My goal is to compare the performance of the model when I use one set of features vs the other. I only have about 120 samples. The first set of features is about 15 and the second about 8.

I'm using a Monte-Carlo cross validation procedure where I randomly divide the dataset into train and test set 100 times.

I then take the average performances on the test set over the 100 splits for each of the sets of features and compare these averages (using a paired t-test) to see if they are significantly different from each other.

Should I perform hyperparameter optimization in each of the 100 splits, for each of the two sets of features or is it ok to stick to default parameters?

Thank you

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  • $\begingroup$ How many observations do you have? The more you have, the more it makes sense to do hyperparameter optimisation. Also depending on the background you may have a look at how well it goes without optimisation and whether the achieved quality is good enough for you. Not sure what you want to achieve with the t-tests by the way. $\endgroup$ Nov 25 '20 at 15:28
  • $\begingroup$ I only have about 120 samples. Does it mean I do not need to do hyperparameter optimization? $\endgroup$
    – asere
    Nov 25 '20 at 15:39
  • $\begingroup$ In regards to the t-test, my goal is to compare the performance of the model when I use one set of features vs the other. Imagine I get an average (over the 100 splits) accuracy of 75% using the first set of features and and accuracy of 78% using the other set of features. Although 78% is higher than 75%, is this difference significant? That's why I used a paired t-test (I've added this to the question to clarify) $\endgroup$
    – asere
    Nov 25 '20 at 15:41
  • $\begingroup$ Comparing accuracy is suboptimal (see: Why is accuracy not the best measure for assessing classification models?). That said, if you are going to, you should not use a t-test; you want to use McNemar's test (see: Compare classification performance of two heuristics). $\endgroup$ Nov 25 '20 at 15:56
  • $\begingroup$ @asere: I'd assume that you'd like to have an as good result as you can have, and surely I can't tell you what you "need" to do. I can only say that with 120 observations I probably wouldn't do it myself, unless there are good reasons to mistrust the defaults in the specific situation (in which case, also depending on the situation, I may just choose some other parameter values without optimising). Also, as I said before, it may depend on whether what you achieve with the defaults is satisfactory for you. $\endgroup$ Nov 25 '20 at 16:02
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Yes you should perform hyper-parameter optimization even if your only concern is which set of features performs better. By just using the default values you are only getting information that one set of features performs better than the other only on one specific set of hyper-parameters. What if that set of hyper-parameters is the worst possible performing set? Then all you know is that feature set A is better than feature set B on a very bad model. Maybe in reality feature set B outperforms feature set A on the optimal set of hyper-parameters, wouldn’t that be more useful to know?

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  • $\begingroup$ thank you, I think that makes sense and doing hyperparameter optimization was my first instinct as well. However, as I mentioned in a previous comment, because I am doing monte-carlo cross-validation (and therefore, not just 1 split) I was concerned about the "fairness" of comparing 100 models, each with their own set of optimal hyperparameters $\endgroup$
    – asere
    Nov 25 '20 at 16:26

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