A supervised machine learning estimator for the non-linear matter power
  spectrum - SEMPS
  In this article, we argue that models based on machine learning (ML) can be
very effective in estimating the non-linear matter power spectrum ($P(k)$). We
employ the prediction ability of the supervised ML algorithms to build an
estimator for the $P(k)$. The estimator is trained on a set of cosmological
models, and redshifts for which the $P(k)$ is known, and it learns to predict
$P(k)$ for any other set. We review three ML algorithms -- Random Forest,
Gradient Boosting Machines, and K-Nearest Neighbours -- and investigate their
prime parameters to optimize the prediction accuracy of the estimator. We also
compute an optimal size of the training set, which is realistic enough, and
still yields high accuracy. We find that, employing the optimal values of the
internal parameters, a set of $50-100$ cosmological models is enough to train
the estimator that can predict the $P(k)$ for a wide range of cosmological
models, and redshifts. Using this configuration, we build a blackbox --
Supervised Estimator for Matter Power Spectrum (SEMPS) -- that computes the
$P(k)$ to 5-10$\%$ accuracy up to $k\sim 10 h^{-1}{\rm Mpc}$ with respect to
the reference model (cosmic emulator). We also compare the estimations of SEMPS
to that of the Halofit, and find that for the $k$-range where the cosmic
variance is low, SEMPS estimates are better than that of the Halofit. The
predictions of the SEMPS are instantaneous in the sense that it can evaluate up
to 500 $P(k)$ in less than one second, which makes it ideal for many
applications like visualisations, weak lensing, emulations, likelihood analysis
etc.. As a supplement to this article, we provide a publicly available software
package.
