  We develop a Bayesian Machine Learning framework called BINGO (Bayesian
INference for Galactic archaeOlogy) centred around a Bayesian neural network.
After being trained on the APOGEE and \emph{Kepler} asteroseismic age data,
BINGO is used to obtain precise relative stellar age estimates with
uncertainties for the APOGEE stars. We carefully construct a training set to
minimise bias and apply BINGO to a stellar population that is similar to our
training set. We then select the 17,305 stars with ages from BINGO and reliable
kinematic properties obtained from \textit{Gaia} DR2. By combining the age and
chemo-kinematical information, we dissect the Galactic disc stars into three
components, namely, the thick disc (old, high-[$\alpha$/Fe], [$\alpha$/Fe]
$\gtrsim$ 0.12), the thin disc (young, low-[$\alpha$/Fe]) and the Bridge, which
is a region between the thick and thin discs. Our results indicate that the
thick disc formed at an early epoch only in the inner region, and the inner
disc smoothly transforms to the thin disc. We found that the outer disc follows
a different chemical evolution pathway from the inner disc. The outer
metal-poor stars only start forming after the compact thick disc phase has
completed and the star-forming gas disc extended outwardly with metal-poor gas
accretion. We found that in the Bridge region the range of [Fe/H] becomes wider
with decreasing age, which suggests that the Bridge region corresponds to the
transition phase from the smaller chemically well-mixed thick to a larger thin
disc with a metallicity gradient.
