> I would say that being scale-invariant and having a fixed range is one of the main benefits of using R^2.
R^2 is upper-bounded by 1, but in held-out data settings it doesn't have a hard lower bound. Being less than 0 means that the predictions was worse than fitting a constant in least squares sense (i.e. predicting the mean). As for scale invariance, this is an interesting aspect and may need to be detailed a little more: R^2 is scale invariant in the sense that you can scale y_true and y_pred by a multiplicative constant and R^2 yields the same result. In Pearson correlation, y_true and y_pred can be scaled with *different* factors and it still yields the same results (you can also add a constant to each of them). An intermediate measure between the two is "explained variance", where var(y_true - y_pred) is considered instead of 1/n ||y_true - y_pred||^2, rendering the measure invariant to addition of a constant, but not to a multiplicative factor. As for the concordance score, I have no idea ;) On Tue, Sep 8, 2015 at 5:15 PM, Andreas Mueller <t3k...@gmail.com> wrote: > I'm also +1 on Pearson, and unsure about concordance ;) > > > > On 09/08/2015 10:43 AM, Mathieu Blondel wrote: > > Maybe I misunderstood Alex's comment but I thought he meant (Pearson) > correlation. > Alex, when you mentioned brain imaging, did you mean Pearson correlation > or concordance correlation? > I can't comment on concordance correlation as I was not familiar with it. > > On Tue, Sep 8, 2015 at 3:12 PM, Andreas Mueller <t3k...@gmail.com> wrote: > >> >> >> On 09/08/2015 06:42 AM, Mathieu Blondel wrote: >> >>> Pearson correlation between y_true and y_pred is also a standard >>> evaluation metric in genomic selection. In a sense, it can be seen as a >>> ranking measure since y_true and y_pred don't need to be equal: they only >>> need to be collinear to achieve perfect correlation. >>> >>> +1 for adding pearson_correlation_score >>> >> I thought we were discussiong the concordance correlation coefficient? >> > > > > > ------------------------------------------------------------------------------ > > _______________________________________________ > Scikit-learn-general mailing list > Scikit-learn-general@lists.sourceforge.net > https://lists.sourceforge.net/lists/listinfo/scikit-learn-general > >
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