Monday, February 4th, 2008
Just when I thought I was starting to get my head around the multitudinous uses of convexity in statistics I was thrown by the following definition:
A function f over the interval (a,b) is convex if, for all choices of {x,y,z}
satisfying a < x < y < z < b the [...]
Wednesday, December 19th, 2007
I’ve been attempting to read an interesting NIPS 2007 paper entitled Estimating divergence functionals and the likelihood ratio by convex risk minimzation and realised my knowledge of convex analysis was sketchy at best.
Fortunately, Wikipedia pointed me to an excellent summary of the Legendre-Fenchel transformation by Hugo Touchette. A bit more digging around Hugo’s site led [...]
Wednesday, October 3rd, 2007
Last week I saw an interesting PhD monitoring presentation by Justin Bedo on the
counter-intuitive phenomenon of “anti-learning”. For certain datasets, learning a classifier from a small number of samples and inverting its predictions performs much better than the original classifier. Most of the theoretical results Justin mentioned about are discussed in a recent paper and [...]