linearity testing experiments
This repository contains experiments to test superlinear parsing behavior. The goal is to find a method that is fast, resistant to noise and data efficient.
approach one: linear fit
We sample a number of points and then fit a linear model. The idea is that when the growth is superlinear, the best linear fit will likely intercept the y-axis at some negative y. When it is (sub)linear, the probability of that happening should be no larger than 0.5. So we can do a one-sided hypothesis test of the intercept variable. If it is significantly smaller than zero, we can conclude that the behavior is superlinear. We may want to start with a few samples and keep resampling until we get the required significance (p < 10E-6?). To maintain the speed we want, we'll probably want to abort as soon as the significance drops below some predefined threshold (p > 0.25?).