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There's an infinite number of functions that can go through two points in cartesian space. What's the simplest? Generally, the simpler the function, the more pl

• xapata 9y ago
  I didn't expect that to get downvoted, since it's a mathematical fact. The more degrees of freedom you have in your hypothesis space, the greater the average distance of any particular hypothesis from the correct one. Curse of dimensionality, Occam's razor, etc.
  • lhorie 9y ago
    I wasn't the one downvoting, but my guess is that it was related to your claim about plausibility. Just because something is simpler or more plausible it doesn't mean it's more likely to be correct. If it were, there would be no reason to be conducting studies like this
    • xapata 9y ago
      In this case, I did indeed mean more plausible in the sense of higher probability of being correct. If I remembered more of my Machine Learning classes I'd be able to quote you the mathematical proof, but it matches the intuition of Occam's Razor -- models with fewer parameters are, in general, better. You're less likely to overfit, etc. > If it were, there would be no reason to be conducting studies like this I don't understand why. The simplest model is to believe there's no relationship (zero parameters). The study gives evidence of a relationship (one parameter). The other commenter was suggesting a parabolic relationship (two parameters), an unnecessary complexity. The best policy is to believe the simplest model that is consistent with the evidence. If a new study observes the behavior at 6 toys and 8 toys that doesn't line up with the previous study, then I might believe a more complex relationship. Or might go back to believing no relationship.