Mathematics Colloquium

WHEN:
Thursday, February 5, 2009 at 2:30 PM

WHERE:
Durham Science Center 115

WHAT:

ABSTRACT:
Screening experiments (SE) deal with finding a small number s of significant factors out of a vast total number t of inputs in a regression model. Of special interest in the SE theory is finding the so-called maximal rate ( capacity ) defined as log t/N(s,t, gamma ) such that a (N,t) -design matrix with N< N(s,t,gamma) enables identifying s randomly chosen significant variables out of t with the probability exceeding 1-gamma. The capacity was found asymptotically as t approaches to infinity in a very general setting for the brute force analysis of experiments in (Malyutov(1979)) and its relation to the capacity region of Multiple Access Communication Channel was outlined. In this paper, we use a simple tractable linear programming relaxation instead of the brute force analysis, and we use simulations to approximate the quantity N*(s,t,gamma) such that the same property as above holds, if N< N*(s,t,gamma) for analysis of experiments using linear programming relaxation. We find that the linear programming relaxation is often successful in finding the significant variables, but the hypothesis N*(s,t,gamma)=N(s,t,gamma) is not supported by our simulation, i.e. it turns out that the capacity of screening under this practical method of analysis is less than that for the brute force analysis.

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