David W. Hogg writes:
If you want to have the flexibility to discover correct structure in your data, you may have to adopt methods that permit variable model complexity.
Context to follow but think about that for a minute.
Do you want to discover structures or confirm what you already believe to be present?
In context:
On day zero of AISTATS, I gave a workshop on machine learning in astronomy, concentrating on the ideas of (a) trusting unreliable data and (b) the necessity of having a likelihood, or probability of the data given the model, making use of a good noise model. Before me, Zoubin Ghahramani gave a very valuable overview of Bayesian non-parametric methods. He emphasized something that was implied to me by Brendon Brewer’s success on my MCMC High Society challenge and mentioned by Rob Fergus when we last talked about image modeling, but which has rarely been explored in astronomy: If you want to have the flexibility to discover correct structure in your data, you may have to adopt methods that permit variable model complexity. The issues are two-fold: For one, a sampler or an optimizer can easily get stuck in a bad local spot if it doesn’t have the freedom to branch more model complexity somewhere else and then later delete the structure that is getting it stuck. For another, if you try to model an image that really does have five stars in it with a model containing only four stars, you are requiring that you will do a bad job! Bayesian non-parametrics is this kind of argument on speed, with all sorts of processes named after different kinds of restaurants. But just working with the simple dictionary of stars and galaxies, we could benefit from the sampling ideas at least. (emphasis added)
Isn’t that awesome? With all the astronomy data that is coming online? (With lots of it already online.)
Not to mention finding structures in other data as well. Maybe even in “big data.”