Measurements of $H_0$ and reconstruction of the dark energy properties
  from a model-independent joint analysis
  Gaussian processes (GP) provide an elegant and model-independent method for
extracting cosmological information from the observational data. In this work,
we employ GP to perform a joint analysis by using the geometrical cosmological
probes such as Supernova Type Ia (SN), Cosmic chronometers (CC), Baryon
Acoustic Oscillations (BAO), and the H0LiCOW lenses sample to constrain the
Hubble constant $H_0$, and reconstruct some properties of dark energy (DE),
viz., the equation of state parameter $w$, the sound speed of DE perturbations
$c^2_s$, and the ratio of DE density evolution $X = \rho_{\rm de}/\rho_{\rm
de,0}$. From the joint analysis SN+CC+BAO+H0LiCOW, we find that $H_0$ is
constrained at 1.1\% precision with $H_0 = 73.78 \pm 0.84$ km
s$^{-1}$Mpc$^{-1}$, which is in agreement with SH0ES and H0LiCOW estimates, but
in $\sim$6.2$\sigma$ tension with the current CMB measurements of $H_0$. With
regard to the DE parameters, we find $c^2_s < 0$ at $\sim$2$\sigma$ at high
$z$, and the possibility of $X$ to become negative for $z > 1.5$. We compare
our results with the ones obtained in the literature, and discuss the
consequences of our main results on the DE theoretical framework.
