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Hmm, so gaussian distributions are easy to use and ubiquitous and all (they're the basis functions used in SVM), except that I don't see any reason for them to
by pjin 14y ago
Hmm, so gaussian distributions are easy to use and ubiquitous and all (they're the basis functions used in SVM), except that I don't see any reason for them to be priors here. But since 2012 > 2008 I feel like I'm obligated (and I'm semi-trolling) to point out the obvious about lazy assumptions based on "flexibility and tractability", which is that they can implode hilariously in your face. C.f. the financial crisis.
[1] http://econometricsense.blogspot.com/2011/03/copula-functions-r-and-financial-crisis.html http://econometricsense.blogspot.com/2011/03/copula-function...
- bayesregressor 14y agoI think you're confusing the Gaussian "process" used in Bayesian optimization with a standard Gaussian distribution. They are very different things - as are Gaussian copulas and what is referred to as the 'Gaussian kernel' (which is not actually a distribution at all) in the SVM. The Gaussian process is a distribution over functions, the properties of which are governed by the covariance function - so the prior over the function, or the assumption about its complexity and form, is determined by the choice of covariance function. Of course it is very important to choose a prior that corresponds to the functional form you are interested in, which is actually discussed and empirically validated in the literature referred to in that post. It's a bit ironic that you are claiming to point out the dangers of making lazy assumptions by doing exactly that.