  The reversible metal-insulator transition in VO$_2$ at $T_\text{C} \approx
340$ K has been closely scrutinized yet its thermodynamic origin remains
ambiguous. We discuss the origin of the transition entropy by calculating the
electron and phonon contributions at $T_\text{C}$ using density functional
theory. The vibration frequencies are obtained from harmonic phonon
calculations, with the soft modes that are imaginary at zero temperature
renormalized to real values at $T_\text{C}$ using experimental information from
diffuse x-ray scattering at high-symmetry wavevectors. Gaussian Process
Regression is used to infer the transformed frequencies for wavevectors across
the whole Brillouin zone, and in turn compute the finite temperature phonon
partition function to predict transition thermodynamics. Using this method, we
predict the phase transition in VO$_2$ is driven five to one by phonon entropy
over electronic entropy, and predict a total transition entropy that accounts
for $95$ % of the calorimetric value.
