The multidimensional dependence of halo bias in the eye of a machine: a
  tale of halo structure, assembly and environment
  We develop a novel approach in exploring the joint dependence of halo bias on
multiple halo properties using Gaussian process regression. Using a
$\Lambda$CDM $N$-body simulation, we carry out a comprehensive study of the
joint bias dependence on halo structure, formation history and environment. We
show that the bias is a multivariate function of halo properties that falls
into three regimes. For massive haloes, halo mass explains the majority of bias
variation. For early-forming haloes, bias depends sensitively on the recent
mass accretion history. For low-mass and late-forming haloes, bias depends more
on the structure of a halo such as its shape and spin. Our framework enables us
to convincingly prove that $V_\mathrm{max}/V_\mathrm{vir}$ is a lossy proxy of
formation time for bias modelling, whereas the mass, spin, shape and formation
time variables are non-redundant with respect to each other. Combining mass and
formation time largely accounts for the mass accretion history dependence of
bias. Combining all the internal halo properties fully accounts for the density
profile dependence inside haloes, and predicts the clustering variation of
individual haloes to a $20\%$ level at $\sim 10\mathrm{Mpc}h^{-1}$. When an
environmental density is measured outside $1\mathrm{Mpc}h^{-1}$ from the halo
centre, it outperforms and largely accounts for the bias dependence on the
internal halo structure, explaining the bias variation above a level of $30\%$.
