Are galactic star formation and quenching governed by local, global or
  environmental phenomena?
  We present an analysis of star formation and quenching in the SDSS-IV
MaNGA-DR15, utilising over 5 million spaxels from $\sim$3500 local galaxies. We
estimate star formation rate surface densities ($\Sigma_{\rm SFR}$) via dust
corrected $H\alpha$ flux where possible, and via an empirical relationship
between specific star formation rate (sSFR) and the strength of the 4000
Angstrom break (D4000) in all other cases. We train a multi-layered artificial
neural network (ANN) and a random forest (RF) to classify spaxels into `star
forming' and `quenched' categories given various individual (and groups of)
parameters. We find that global parameters (pertaining to the galaxy as a
whole) perform collectively the best at predicting when spaxels will be
quenched, and are substantially superior to local/ spatially resolved and
environmental parameters. Central velocity dispersion is the best single
parameter for predicting quenching in central galaxies. We interpret this
observational fact as a probable consequence of the total integrated energy
from AGN feedback being traced by the mass of the black hole, which is well
known to correlate strongly with central velocity dispersion. Additionally, we
train both an ANN and RF to estimate $\Sigma_{\rm SFR}$ values directly via
regression in star forming regions. Local/ spatially resolved parameters are
collectively the most predictive at estimating $\Sigma_{\rm SFR}$ in these
analyses, with stellar mass surface density at the spaxel location ($\Sigma_*$)
being by far the best single parameter. Thus, quenching is fundamentally a
global process but star formation is governed locally by processes within each
spaxel.
