  Models of black hole properties play an important role in the ongoing direct
detection of gravitational waves from black hole binaries. One important aspect
of model based gravitational wave detection, and subsequent estimation of
source parameters, are the low level modeling of information related to
perturbed Kerr black holes. Here, we present new phenomenological methods to
model the analytically understood gravitational wave spectra (quasi-normal mode
frequencies), and harmonic structure of Kerr black holes (mixing coefficients
between spherical and spheroidal harmonics). In particular, we present a
greedy-multivariate-polynomial (GMVP) regression method and
greedy-multivariate-rational (GMVR) regression method for the automated
modeling of polynomial and rational functions respectively. GMVR is a
quasi-linear numerical method for interpolating rational functions. It
therefore represents a solution to Runge's phenomenon. GMVP is used to develop
a model for QNM frequencies that explicitly enforces consistency with the
extremal Kerr limit. GMVR is used to develop a model for harmonic mixing
coefficients that extends previous results to dominant multipoles with $\ell
\le 5$. Both models are the first of their kind to consider black hole spin to
vary between -1 and 1, thus naturally connecting the pro and retrograde modes.
We discuss the potential use of these models in current and future
gravitational wave signal modeling.
