摘要：AbstractSliced-Normal (SN) distributions enable the characterization of complex multivariate data as both a vector of possibly dependent random variables and as a semi-algebraic, tightly enclosing set. SNs inject the physical space into a higher dimensional (so-called) feature space using a polynomial mapping. Optimization-based strategies for estimating SNs from data in both physical and feature space were recently developed. The formulations in physical space yield non-convex optimization programs whose solutions exhibit the best performance, whereas the formulations in feature space yield either an analytical solution or a convex program thereby facilitating their application to higher dimensional datasets. In both cases, however, the exponential dependency of the number of optimization variables on the dimension of feature space limits their application to moderately sized problems. Two strategies to mend for this deficiency are proposed herein. The first strategy identifies groups of highly interdependent parameters exhibiting a possibly nonlinear dependency using a distribution-free framework. This classification enables estimating a SN for any of such groups independently of the other groups thereby reducing the computational complexity of the estimation process. The second strategy reduces the dimension of feature space by only retaining the monomials of the polynomial mapping that significantly increase the likelihood of the data while leveraging lower dimensional SNs. A system identification example is used for illustration.
