Mr. Pearson, meet Mr. Mandelbrot: Detecting Novel Associations in Large Data Sets
Something you may enjoy along with: Detecting Novel Associations in Large Data Sets.
Jeremy Fox asks what I think about this paper by David N. Reshef, Yakir Reshef, Hilary Finucane, Sharon Grossman, Gilean McVean, Peter Turnbaugh, Eric Lander, Michael Mitzenmacher, and Pardis Sabeti which proposes a new nonlinear R-squared-like measure.
My quick answer is that it looks really cool!
From my quick reading of the paper, it appears that the method reduces on average to the usual R-squared when fit to data of the form y = a + bx + error, and that it also has a similar interpretation when “a + bx” is replaced by other continuous functions.