5 ms·
A professor of mine stated it very well. If you can imagine that there is a true model somewhere out in infinitely large model space then ML is just the search
by tel 13y ago
A professor of mine stated it very well. If you can imagine that there is a true model somewhere out in infinitely large model space then ML is just the search for that model.
In order to make it tractable, you pick a finite model space, train it on finite data, and use a finite algorithm to find the best choice inside of that space. That means you can fail in three ways---you can over-constrain your model space so that the true model cannot be found, you can underpower your search so that you have less an ability to discern the best model in your chosen model space, and you can terminate your search early and fail to reach that point entirely.
Almost all error in ML can be seen nicely in this model. In particular here, those who do not remember to optimize validation accuracy are often making their model space so large (overfitting) at the cost of having too little data to power the search within it.
Devroye, Gyorfi, and Lugosi (http://www.amazon.com/Probabilistic-Recognition-Stochastic-Modelling-Probability/dp/0387946187 http://www.amazon.com/Probabilistic-Recognition-Stochastic-M...) have a really great picture of this in their book.
- tedsanders 13y agoI really like that explanation. I've never heard it in those terms before, but it makes a lot of sense. Thanks for sharing.
- dantheman 13y agoThis is a great description, I've tried to explain something like this to novices before -- but this is amazingly eloquent.
- yetanotherphd 13y agoI wouldn't use the term "error" because some people might take that to mean there was a way to avoid these problems. over-constraining your model space means having too few parameters in your model But fixing your data size, the "power" of your search goes down when you increase the number of parameters. So it is no so much an issue of avoiding errors, but of choosing the right number of parameters for your model.
- tel 13y agoI called them errors because that's usually the technical term for them, but the real point, as always, is tradeoffs. The less "finite" a ML setup you want to buy, the less "error".
- joe_the_user 13y agoIn order to make it tractable, you pick a finite model space, train it on finite data, and use a finite algorithm to find the best choice inside of that space. That means you can fail in three ways---you can over-constrain your model space so that the true model cannot be found, you can underpower your search so that you have less an ability to discern the best model in your chosen model space, and you can terminate your search early and fail to reach that point entirely. It seems like you can "mis-power" your model also. For example, the Ptolemaic system could approximate the movement of the planets to any degree if you added enough "wheels within wheels" but since these were "the wrong wheels", the necessary wheels grew without bounds to achieve reasonable approximation over time.
- alok-g 13y agoAwesome example!
- tel 13y agoTotally agree, though I'd call that maybe "picking the wrong shape" for your model space. You can pay a whole lot but if you cannot admit a shape that gets close to the truth then you're spending your data in vain.
- eru 13y agoFunny enough, the wheels within wheels are equivalent to a Fourier transform.
- tel 13y agoAlso, to add, when DGL bring this kind of mental model up they do so to motivate a kind of semi-parametric modeling where the design space changes progressively to move closer to the true model without growing so quickly as to make inference unstable. The problem being, of course, that this causes your algorithm run time to blow out to something cubic, I think, and so you have a beautiful model that loses out on search error.
- rcthompson 13y ago> For example, the Ptolemaic system could approximate the movement of the planets to any degree if you added enough "wheels within wheels" but since these were "the wrong wheels", the necessary wheels grew without bounds to achieve reasonable approximation over time. That would be an example of over-constraining your model (i.e. imposing the arbitrary constraint of a stationary Earth).