Reconstructing the universe with variational self-boosted sampling

Forward modeling approaches in cosmology have made it possible to reconstruct the initial conditions at the beginning of the Universe from the observed survey data. However the high dimensionality of the parameter space still poses a challenge to explore the full posterior, with traditional algorithms such as Hamiltonian Monte Carlo (HMC) being computationally inefficient due to generating correlated samples and the performance of variational inference being highly dependent on the choice of divergence (loss) function. Here we develop a hybrid scheme, called variational self-boosted sampling (VBS) to mitigate the drawbacks of both these algorithms by learning a variational approximation for the proposal distribution of Monte Carlo sampling and combine it with HMC. The variational distribution is parameterized as a normalizing flow and learnt with samples generated on the fly, while proposals drawn from it reduce auto-correlation length in MCMC chains. Our normalizing flow uses Fourier space convolutions and element-wise operations to scale to high dimensions. We show that after a short initial warm-up and training phase, VBS generates better quality of samples than simple VI approaches and in the hybrid sampling phase, reduces the correlation length in the sampling phase by a factor of 10–50 over using only HMC to explore the posterior of initial conditions in 64³ and 128³ dimensional problems, with larger gains for high signal-to-noise data observations. Hybrid sampling with online training of the variational distribution violates Markov property, and to retain the asymptotic guarantees of HMC, in the final phase we use a fixed variational distribution as proposal distribution and propagate these samples to the posterior distribution.