It's quite simply, the stuff of Life...

As I was watching the excellent video presentation on Path coding penalties for directed acyclic graphs by Julien Mairal who uses SPAMS for metabolic network detection ( SPAMS -SPArse Modeling Software- by Julien Mairal, Francis Bach, Jean Ponce,Guillermo Sapiro is listed on the Matrix Factorization Jungle Page). I was reminded of the fact that, at some point, there needs to be a serious discussion on the connection between regularization techniques, structured sparsity and their roots in the physical world. I wrote two entries on the subject a month ago:

• Multiple Regularizers For the Reconstruction of Natural Objects ?
• Can I tell you my secret now ?....I see dead reconstructions

This is not the first time that metabolic networks have been mentioned here:( Instances of Null Spaces: Can Compressive Sensing Help Study Non Steady State Metabolic Networks ? ). But what really triggered this entry is a salient question by an audience member at the very end of the talk. At that point, Julien has to explain if somehow his structured sparsity would remove loops. It turns out that, in metabolic systems like the ones Julien explores, loops are quite simply the stuff of Life. Take for instance the Krebs cycle:

In other words, choosing an ad-hoc regularization will impact your discovery process. TV regularization may be fine for getting good looking pictures and so we are OK with the fact that it is ad-hoc, but if we are to venture outside of that "image processing" garden of Lena and her sisters, we need to think hard about the connection between regularization and its connection to physical world. As mentioned in the entries listed above, Adrian Bejan's work seems to be a worthwhile, if empirical, path in that direction. I am sure there are others, but that discussion needs to occur.

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