  In this paper we explain how to convert discrete invariants into stable ones
via what we call hierarchical stabilization. We illustrate this process by
constructing stable invariants for multi-parameter persistence modules with
respect to the interleaving distance and so called simple noise systems. For
one parameter, we recover the standard barcode information. For more than one
parameter we prove that the constructed invariants are in general NP-hard to
calculate. A consequence is that computing the feature counting function,
proposed by Scolamiero et. al. (2016), is NP-hard.
