  The physical processes which make a galaxy a Lyman Alpha Emitter have been
extensively studied for the past 25 years. However, the correlations between
physical and morphological properties of galaxies and the strength of the
Ly$\alpha$ emission line are still highly debated. Therefore, we investigate
the correlations between the rest-frame Ly$\alpha$ equivalent width and stellar
mass, star formation rate, dust reddening, metallicity, age, half-light
semi-major axis, S\'ersic index and projected axis ratio in a sample of 1578
galaxies in the redshift range $2 \leq z \leq 7.9$ from the GOODS-S, UDS and
COSMOS fields. From the large sample of Ly$\alpha$ emitters (LAEs) in the
dataset we find that LAEs are typically common main sequence star forming
galaxies which show stellar mass $ \leq 10^9 \text{M}_{\odot}$, star formation
rate $ \leq 10^{0.5} \text{M}_{\odot}/\text{yr}$, $E(B-V) \leq 0.2$ and
half-light semi-major axis $\leq 1 \text{kpc}$. Building on these findings we
develop a new method based on Random Forest (i.e. a Machine Learning
classifier) in order to select galaxies which have the highest probability of
being Ly$\alpha$ emitters. When applied to a population in the redshift range
$z \in [2.5, 4.5]$, our classifier holds a $(80 \pm 2)\%$ accuracy and $(73 \pm
4)\%$ precision. At higher redshifts ($z \in [4.5, 6]$), we obtain a $73\%$
accuracy and a $80\%$ precision. These results highlight it is possible to
overcome the current limitations in assembling large samples of LAEs by making
informed predictions that can be used for planning future large scale
spectroscopic surveys.
