Before revision:  We propose two methods in order to build the ellipsoid: one based on principal component analysis and the other on linear programming . We show its performances on highly heterogeneous hyper-rectangles and apply it to a model of the metabolism of the bacterium E.Coli .
After revision:  We propose two methods in order to build the ellipsoid: one based on principal component analysis and the other on linear programming (LP) and finally we employ the Lovazs ellipsoid method (LEM). Our results show that a rounding procedure is mandatory for such inference problems and suggest that a combination of LEM or LP with a subsequent PCA seems to perform the best .