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 cold dark matter 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-max/V-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 per cent level at similar to 10 Mpc h(-1). When an environmental density is measured outside 1Mpc 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 per cent.