  We present and discuss a new approach increasing by orders of magnitude the
speed of performing Bayesian inference and parameter estimation within the
framework of slow-roll inflation. The method relies on the determination of an
effective likelihood for inflation which is a function of the primordial
amplitude of the scalar perturbations complemented with the necessary number of
the so-called Hubble flow functions to reach the desired accuracy. Starting
from any cosmological data set, the effective likelihood is obtained by
marginalisation over the standard cosmological parameters, here viewed as
"nuisance" from the early Universe point of view. As being low-dimensional,
basic machine-learning algorithms can be trained to accurately reproduce its
multidimensional shape and then be used as a proxy to perform fast Bayesian
inference on the inflationary models. The robustness and accuracy of the method
are illustrated using the Planck Cosmic Microwave Background (CMB) data to
perform primordial parameter estimation for the large field models of
inflation. In particular, marginalised over all possible reheating history, we
find the power index of the potential to verify p < 2.3 at 95% of confidence.
