LJKProbability & Statistics Seminar

On Thursday September 20 2018 at 14h00 in Room 106  IMAG Building

Seminary of Mr Olivier ZHAM (LJK / AIRSEA)

Certified dimension reduction of the input parameter space of multivariate functions

Summary

Approximation of multivariate functions is a difficult task when the number of input parameters is large. Identifying the directions where the function does not significantly vary is a key preprocessing step to reduce the complexity of the problem we have at hand. We propose a gradient based method that permits to detect such a lowdimensional structure of a function. Our methodology consists in minimizing an upperbound of the approximation error obtained using PoincarĂ©type inequalities, and it generalizes the Active Subspace method. Numerical examples reveals the importance of the choice of the metric to measure errors and compare it with the commonly used truncated KarhunenLoeve decomposition.
We also show that the same methodology can be applied for the reduction of the dimension of Bayesian inverse problems. By seeking an approximation of the likelihood function by a ridge function, the resulting method exploits the fact that the data are not informative over the whole parameter space but only on a lowdimensional subspace.
