Sunday, July 15, 2007

von Neumann Symposium at SLC

The von Neumann Symposium on Sparse Representation and High Dimensional Geometry was at Salt Lake City early last week; the background in the group photo looks like a painting.

I could speak about data streams (von Neumann defined computational models) or about game theory for search auctions (von Neumann did game theory too), but instead chose to talk mainly on low rank matrix approximations (I am sure he used matrices in his work). I now have a clean, simple story with proofs starting with approximate l_2 regression and building it to low rank matrix approximation and beyond.

People from math, signal processing, hardware and others, looking at different aspects of sparse representation problems. Rich Baraniuk gave a very engaging talk on using compressed sensing ideas to go from analog singals to information, and spoke about his one pixel camera, camera across large spectrum, etc. Cool! Emmanuel Candes gave a terrific talk, full of intuition on the structure of the LP that arises in compressed sensing. Roman gave a fantastic talk, more on that later. There was one communication theory talk I remember, that studied compressed sensing and quantization. In general, notwithstanding some beautiful math that was talked about, I thought there were a lot of people -- students, scientists and professors -- who did care about algorithms -- designing, implementing and using them---but had very little training in algorithm design techniques, which is interesting! Alas, I left after 2 days, I am sure there were many other great talks.

I planted the idea that we need to do a brainstorming meeting, gathering a few from network coding, communication & information theory, algorithms, and sparse representations, and trying to figure out what are the big open problems in transforming analog signals to information over networks. I have combinatorial versions of stochastic problems communication theorists study and think there is a nice, large problem lurking there, when merged with network coding and sparse representations.

Btw, why runs meetings at the Snowbird resort? It is very expensive and one feels trapped there and has to pay $3 for coffee or bagel (that is, exclusive OR).


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