  We investigate the higher-order correlation properties of the VIMOS Public
Extragalactic Redshift Survey (VIPERS) to test the hierarchical scaling
hypothesis at z~1 and the dependence on galaxy luminosity, stellar mass, and
redshift. We also aim to assess deviations from the linearity of galaxy bias
independently from a previously performed analysis of our survey (Di Porto et
al. 2014). We have measured the count probability distribution function in
cells of radii 3 < R < 10 Mpc/h, deriving $\sigma_{8g}$, the volume-averaged
two-,three-,and four-point correlation functions and the normalized skewness
$S_{3g}$ and kurtosis $S_{4g}$ for volume-limited subsamples covering the
ranges $-19.5 \le M_B(z=1.1)-5log(h) \le -21.0$, $9.0 < log(M*/M_{\odot}
h^{-2}) \le 11.0$, $0.5 \le z < 1.1$. We have thus performed the first
measurement of high-order correlations at z~1 in a spectroscopic redshift
survey. Our main results are the following. 1) The hierarchical scaling holds
throughout the whole range of scale and z. 2) We do not find a significant
dependence of $S_{3g}$ on luminosity (below z=0.9 $S_{3g}$ decreases with
luminosity but only at 1{\sigma}-level). 3) We do not detect a significant
dependence of $S_{3g}$ and $S_{4g}$ on scale, except beyond z~0.9, where the
dependence can be explained as a consequence of sample variance. 4) We do not
detect an evolution of $S_{3g}$ and $S_{4g}$ with z. 5) The linear bias factor
$b=\sigma_{8g}/\sigma_{8m}$ increases with z, in agreement with previous
results. 6) We quantify deviations from the linear bias by means of the Taylor
expansion parameter $b_2$. Our results are compatible with a null non-linear
bias term, but taking into account other available data we argue that there is
evidence for a small non-linear bias term.
