  The temperature-dependent behavior of defect densities within a crystalline
structure is intricately linked to the phenomenon of vibrational entropy.
Traditional methods for evaluating vibrational entropy are computationally
intensive, limiting their practical utility. We show that total entropy can be
decomposed into atomic site contributions and rigorously estimate the locality
of site entropy. This analysis suggests that vibrational entropy can be
effectively predicted using a surrogate model for site entropy. We employ
machine learning to develop such a surrogate models employing the Atomic
Cluster Expansion model. We supplement our rigorous analysis with an empirical
convergence study. In addition we demonstrate the performance of our method for
predicting vibrational formation entropy and attempt frequency of the
transition rates, on point defects such as vacancies and interstitials.
