  Partial-wave analysis of meson and photon-induced reactions is needed to
enable the comparison of many theoretical approaches to data. In both
energy-dependent and independent parametrizations of partial waves, the
selection of the model amplitude is crucial. Principles of the $S$-matrix are
implemented to different degree in different approaches, but a many times
overlooked aspect concerns the selection of undetermined coefficients and
functional forms for fitting, leading to a minimal yet sufficient
parametrization. We present an analysis of low-energy neutral pion
photoproduction using the Least Absolute Shrinkage and Selection Operator
(LASSO) in combination with criteria from information theory and $K$-fold cross
validation. These methods are not yet widely known in the analysis of excited
hadrons but will become relevant in the era of precision spectroscopy. The
principle is first illustrated with synthetic data, then, its feasibility for
real data is demonstrated by analyzing the latest available measurements of
differential cross sections ($d\sigma/d\Omega$), photon-beam asymmetries
($\Sigma$), and target asymmetry differential cross sections
($d\sigma_T/d\Omega$) in the low energy regime.
