  We investigate applications of machine learning models to directly infer
physical properties of brown dwarfs from their photometry and spectra using
$\textit{The Cannon}$. We demonstrate that absolute magnitudes, spectral types,
and spectral indices can be determined from low-resolution SpeX prism spectra
of L and T dwarfs without trigonometric parallax measurements and with
precisions competitive with commonly used methods. For T dwarfs with
sufficiently precise spectra and photometry, bolometric luminosities and
effective temperatures can be determined at precisions comparable to methods
that use polynomial relations as a function of absolute magnitudes. We also
provide new and updated polynomial relations for absolute magnitudes as a
function of spectral types L0-T8 in 14 bands spanning Pan-STARRS $r_{P1}$ to
AllWISE $\textit{W3}$, using a volume-limited sample of 256 brown dwarfs
defined entirely by parallaxes. These include the first relations for brown
dwarfs using Pan-STARRS1 photometry and the first for several infrared bands
using a volume-limited sample. We find that our novel method with $\textit{The
Cannon}$ can infer absolute magnitudes with equal or smaller uncertainties than
the polynomial relations that depend on trigonometric parallax measurements.
