Predicting Ly$\alpha$ Emission from Galaxies via Empirical Markers of
  Production and Escape in the KBSS
  Ly$\alpha$ emission is widely used to detect and confirm high-redshift
galaxies and characterize the evolution of the intergalactic medium. However,
many galaxies do not display Ly$\alpha$ emission in typical spectroscopic
observations, and intrinsic Ly$\alpha$-emitters represent a potentially biased
set of high-redshift galaxies. In this work, we analyze a set of 703 galaxies
at $2\lesssim z\lesssim3$ with both Ly$\alpha$ spectroscopy and measurements of
other rest-frame ultraviolet and optical properties in order to develop an
empirical model for Ly$\alpha$ emission from galaxies and understand how the
probability of Ly$\alpha$ emission depends on other observables. We consider
several empirical proxies for the efficiency of Ly$\alpha$ photon production as
well as the subsequent escape of these photons through their local interstellar
medium. We find that the equivalent width of metal-line absorption and the O3
ratio of rest-frame optical nebular lines are advantageous empirical proxies
for Ly$\alpha$ escape and production, respectively. We develop a new quantity,
$X_\mathrm{LIS}^\mathrm{O3}$, that combines these two properties into a single
predictor of net Ly$\alpha$ emission, which we find describes $\sim$90% of the
observed variance in Ly$\alpha$ equivalent width when accounting for our
observational uncertainties. We also construct conditional probability
distributions demonstrating that galaxy selection based on measurements of
galaxy properties yield samples of galaxies with widely varying probabilities
of net Ly$\alpha$ emission. The application of the empirical models and
probability distributions described here may be used to infer the selection
biases of current galaxy surveys and evaluate the significance of high-redshift
Ly$\alpha$ (non-)detections in studies of reionization and the intergalactic
medium.
