“Ridiculous stats”

So Johan recently showed me this ridiculous nature article, where they do linear regression on winning olympic 100m sprint times to conclude that by 2150 women will run faster than men. Two responses (here and here) criticize the article, but I thought I should compare to the obvious Bayesian approach: GP regression. I used Carl’s code to perform the regression in Matlab, with squared exponential covariance function, and I optimized the hyperparameters using the minimise function. The two plots below show the results.

Gaussian Process regression for winning Olympic men's 100m sprint.

Figure 1. Gaussian Process regression for winning Olympic men

Gaussian Process regression for winning Olympic men's 100m sprint.

Figure 2. Gaussian Process regression for winning Olympic women

These plots show that GP regression agrees pretty well with intuition: the data tells us nothing about what will happen past about 2030.

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2 Responses to ““Ridiculous stats””

  1. Johan Says:

    Shouldn’t the hyperparameters be optimized simultaneously? The datasets should exhibit the same structure of timescales, no?

    The oscillations of the mean function for men is an interesting artifact of fit. Makes me wonder, if you have data from a true model that is linear but rather noisy, as you progressively obtain more data points in a given interval, how well does automatic hyperparameter optimization transition from a oscillatory low-noise hypothesis to a more linear high-noise hypothesis? I’m trying to get at a more general problem that the apparent problem with the men data: that it should probably have a wider covariance function. Thoughts?

    • explainaway Says:

      I agree the hyperparameters should probably be optimized over both datasets, but I don’t think it would change the result all that much.

      As for fitting the noise in the male data, part of the problem of course is that even type II ML isn’t ideal and is probably why this overfitting occurs.

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