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On a tangential note, "The robust beauty of improper linear models in decision making"[1] is probably one of my favorite papers on modeling and decision researc
by nhf 10y ago
On a tangential note, "The robust beauty of improper linear models in decision making"[1] is probably one of my favorite papers on modeling and decision research.
> Improper linear models are those in which the weights of the predictor variables are obtained by some nonoptimal method; for example, they may be obtained on the basis of intuition, derived from simulating a clinical judge's predictions, or set to be equal. This article presents evidence that even such improper linear models are superior to clinical intuition when predicting a numerical criterion from numerical predictors.
[1] http://www.niaoren.info/pdf/Beauty/9.pdf http://www.niaoren.info/pdf/Beauty/9.pdf
- yummyfajitas 10y agoI studied this a couple of years back. You can even prove error bounds. For example, using Jensen's inequality, I was able to prove that a unit weighted linear model will get the same result as the optimal linear model 75% of the time on average, provided the features are independent normally distributed gaussians. https://www.chrisstucchio.com/blog/2014/equal_weights.html https://www.chrisstucchio.com/blog/2014/equal_weights.html I haven't figured out how to prove the same result for binary features, but simulations suggest that will work also.
- deleted 10y ago[deleted]
- dxbydt 10y ago> prove that a unit weighted linear model will get the same result as the optimal linear model 75% of the time on average This is such an important result & yet doesn't seem to be a widely known result. Your proof is very well done. You should consider publishing it in CMJ. Or if you don't mind, I'd be happy to rework it & send it in :) Thanks for writing it up.
- yummyfajitas 10y agoI'm not familiar with CMJ but happy to discuss the idea. Write to me, email is in my profile. As a paper it would be significantly stronger if it did the binary case, though.
- dxbydt 10y agoHey thanks! I prefer the CMJ (http://www.maa.org/press/periodicals/college-mathematics-journal/the-college-mathematics-journal http://www.maa.org/press/periodicals/college-mathematics-jou...) to AMM etc. because your proof is ultimately undergrad math - some calculus, complex analysis, change of coords and inequalities. It's a pity the CMJ is not as well known. My professor used to circulate copies in class and we learnt more from it than from the grad journals which went out of the way to make things abstract. You also have a fantastic blog on Harris Benedict equation, which I have combined with an ML approach on WeightGreat - truth be told, this was one of those miracles that happen when you read Hacker News regularly. You find someone has worked on the exact same problem you are interested in, using a different approach, and you can combine that with your own insight to come up with a very promising idea.
- yummyfajitas 10y agoI'll take a look. And send me an email, what you are doing sounds interesting, would love to learn more.
- gwern 10y agoThat is surprising. I wouldn't've guessed 75%. I would've guessed it could be arbitrarily close to 50%.
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- addicted 10y agoI haven't read the paper but based on your extract are such improper models more susceptible to black swan events? I'd suspect a more clinical model might actually be even more susceptible (more variables means a greater chance of some variables being wrong and/or missing correlations between variables which would amplify a wing variable to a greater degree) but I'm curious if this aspect had been explored.