Robust Optimization and the Donoho-Tanner Phase Transition

Of interest to this blog on Robust modeling here is an excerpt from Nuit Blanche:

Similarly, Sergey points me to this arxiv preprint which made a passing reference to CS: Theory and Applications of Robust Optimization by Dimitris Bertsimas, David B. Brown, Constantine Caramanis. The abstract reads:

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.

Reading the paper yields to this other paper I had mentioned back in April:

• Robust Regression and Lasso by Huan Xu, Constantine Caramanis, Shie Mannor

which makes a statement about Robust Linear Regression which in our world translates into multiplicative noise. More Rosetta Stone moments....In the meatnime, you might also be interested in the NIPS 2010 Workshop, entitled Robust Statistical learning (robustml): 

Many of these approaches are based on the fact that data are used to learn or fit models. In effect, most of the literature is focused on linear modeling. Quite a few interesting results have come out of these areas including what I have called the Donoho-Tanner phase transition. I will come back to this subject in another blog entry.

Credit: NASA.