I had fun contemplating the math here for a bit. The 1/r proximity metric is quite nasty: integrated over a disc of radius R you get 2pi•R, so it’s not really compact at all.
And it’s not particularly difficult [0] to construct data on a bounded region of the plane where the Pearson correlation between any translation of the 1/r kernel and the data is positive, so “literally everything causes cancer”. (You need to avoid exploding due to the singularity at the center, and I assume that the authors also somehow did something about the singularity, but it’s really unclear what they did.)
I have not come up with a compelling reason why the cancer data in the analysis would have this nasty property. But, of course, the mere existence of the property is a very compelling reminder that correlation should be used with extreme caution.
[0] For discrete data it’s just linear programming.
amluto · · focus · HN ↗
And it’s not particularly difficult [0] to construct data on a bounded region of the plane where the Pearson correlation between any translation of the 1/r kernel and the data is positive, so “literally everything causes cancer”. (You need to avoid exploding due to the singularity at the center, and I assume that the authors also somehow did something about the singularity, but it’s really unclear what they did.)
I have not come up with a compelling reason why the cancer data in the analysis would have this nasty property. But, of course, the mere existence of the property is a very compelling reminder that correlation should be used with extreme caution.
[0] For discrete data it’s just linear programming.