On Mon, Jan 02, 2012 at 04:24:50PM +0100, Andreas wrote:
> 1)
> The narrative docs say that max_features=n_features is a good value for 
> RandomForests.
> As far as I know, Breiman 2001 suggests max_features = 
> log_2(n_features). I also
> saw a claim that Breiman 2001 suggests max_features = sqrt(n_features) but I
> couldn't find that in the paper.
> I just tried "digits" and max_features = log_2(n_features) works better than
> max_featurs = n_features. Of course that is definitely no conclusive 
> evidence ;)
> Is there any reference that says max_features = n_features is good?

Actually, I believe consistency can be shown for random forest greedily
grown (as they are in the standard implementations) if they are many
samples per leaf:
http://jmlr.csail.mit.edu/papers/volume9/biau08a/biau08a.pdf, 
theorem 9: the number of leafs k goes as k = o(sqrt(n/log(n)))

For me, this makes sens intuitively: overfit is prevented by some sort of
averaging. This averaging works better is each leaf has more than one
sample.

Now for better rules of thumb, I have no references :).

Thanks for the discussion, Andreas and Gilles, having different people
hammering on the code and the docs definitely helps making it accessible
to everybody.

Gael

PS: happy new year.

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