What is the current thinking on performing power analyses when using a random forest model? For hypothesis test-bases statistical inference, one must ensure that the sample size is large enough to achieve sufficient power to reject the null hypothesis assuming that it is false. This is a critical consideration when designing studies, as there is no point in performing a study if there is only a small chance that an effect of interest can be detected.
The typical use case for random forest (RF) models does not involve hypothesis testing. Typically one's objective is either to maximize classification accuracy or minimize prediction error. For this reason, a power analysis as typically conceived is not meaningful in the case of an RF based analysis, as there is no null to reject. However, the principle of power still applies, namely, what guarantee do we have that our sample size is large enough so we can detect some signal of interest, assuming it's there?
I'll note that this is a very broad question, and that as I've phrased it there isn't a straightforward or even well defined answer. What I'm hoping to find here is a body of literature addressing this topic. I'm looking for guidance about how to think about the problem, or some papers where a power-analysis-like procedure has been performed for an RF model, or really any statistical procedure where sample size is relevant and that doesn't involve hypothesis testing. The answer may be as simple as a googleable term that I just don't know so I can research the question.
Thank you in advance!

I'm lazy, and by lazy I mean greedy, and by lazy or greedy I mean that I have so much to do and so little time that "good enough" is "best".
For a problem like this a "cheap-shot" is to say "would a classic linear model work here", and if there is enough power that a linear model could do the job then I can infer that a more capable learner also has sufficient samples.
I also like to think about binomial confidence intervals, and if I have enough samples such that the CI size for a binomial "weighted coin" is smaller than my acceptable uncertainty, I like to use that.
I'm a bit of a glutton, and when I can get more data, I generally try to start with more and then start trimming.
