"What is your main domain of expertise?"

I'll be starting grad school in math in the fall. I'm interested in the areas of applied math that deal with getting information from data -- when it's noisy, when it's high-dimensional, when it's uncertain. Way down the line, this is related to machine learning and image processing.

"What issues in your domain call most critically for sharp thinking?"

I think -- and I'm getting this impression not only from my own opinion but from professors I admire -- that we need to think more about philosophy of science and ask ourselves what, exactly, we're doing.

For example, consider an interdisciplinary problem about interpreting some biological data with computational techniques. A computer scientist will tend to look for solutions that treat the data as arbitrary strings, and "throw away" any physical significance, which means that he can only prove modest claims. A biologist will tend to use techniques that assume a lot of a priori knowledge about the specific experiment, and thus aren't generally applicable. Both extremes lack a nice quality of explanatory efficiency.

Especially when we're looking at data, and models to explain data, we're going to need to face the question "What makes an explanation good?" And my personal opinion is that philosophers of the LW variety can help.

"What do you know that could be of interest to the LessWrong community?"

Some mathematical concepts that I know are good metaphors or explanations for how we develop knowledge from data. Some are already familiar here (Bayesianism), and some possibly less so (PCA; diffusion geometry; entropy, in the information-theoretic sense; K-means clustering; random matrix theory.)

"What might you learn from other experts that might be useful in yours?"

Oh, god, where to begin. People who actually know how computers see/define/categorize would be invaluable (I'm only recently learning that I'm interested in questions posed in CS or EE, but I don't have much of a prior programming background.) Philosophers know what questions to ask. Statisticians know a lot about updating knowledge. Physics is where all the examples come from, and I don't know any physics. People in any line of work who have insights about how their own minds work can come up with ideas on how to make an algorithmic "mind" work.