High Dimensional Estimation and Testing
My work thus far has been split between prediction with sparse multivariate models in high dimensional feature spaces and inference/FDR estimation with marginal models. I would love to (and plan to) work on inference with sparse multivariate models, though I have found honest inference with simple smooth marginal models to be a handful already.
First order methods for non-smooth problems
Distributed optimization (gpu and cloud)
My interest here is really in developing useable algorithms and software for high dimensional statistical methods. I haven't done much with really huge-scale optimization --- most of my datasets fit in memory on our department server (but I wouldn't say no to working on a hadoop implementation of a generalized gradient algorithm). I've also done some recent work with gpu-coding (CUDA), trying to determine where its advantages are more and less pronounced (eg. memory constraints and load times really limit its efficacy for lasso-like problems).