Differentiable Stochastic Halo Occupation Distribution

Benjamin Horowitz, ChangHoon Hahn, Francois Lanusse, Chirag Modi, Simone Ferraro

Submitted on 7 November 2022


In this work, we demonstrate how differentiable stochastic sampling techniques developed in the context of deep Reinforcement Learning can be used to perform efficient parameter inference over stochastic, simulation-based, forward models. As a particular example, we focus on the problem of estimating parameters of Halo Occupancy Distribution (HOD) models which are used to connect galaxies with their dark matter halos. Using a combination of continuous relaxation and gradient parameterization techniques, we can obtain well-defined gradients with respect to HOD parameters through discrete galaxy catalogs realizations. Having access to these gradients allows us to leverage efficient sampling schemes, such as Hamiltonian Monte-Carlo, and greatly speed up parameter inference. We demonstrate our technique on a mock galaxy catalog generated from the Bolshoi simulation using the Zheng et al. 2007 HOD model and find near identical posteriors as standard Markov Chain Monte Carlo techniques with an increase of ~8x in convergence efficiency. Our differentiable HOD model also has broad applications in full forward model approaches to cosmic structure and cosmological analysis.


Comment: 10 pages, 6 figures, comments welcome

Subjects: Astrophysics - Cosmology and Nongalactic Astrophysics; Astrophysics - Astrophysics of Galaxies


Halo occupancy distribution for central (top) and satellite galaxies (bottom) as a function of halo virial mass of our differentiable HOD model (\dhod\ solid). Different colors indicate different temperature values used in the Gumbel-Softmax approximation (see Eq. \ref{eq:softmax}). We include the occupancy distribution from the standard \citet{2007zheng} HOD model for reference (star). In this work, we use \dhod\~with $\tau=0.1$, which is in good agreement with the standard HOD model throughout the full halo mass range. \nblink{Plots_for_Paper}