# Reconstructing the Universe with Variational self-Boosted Sampling

arXiv: https://arxiv.org/abs/2206.15433 · HTML: https://mlsanity.com/paper/2206.15433/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 28 Jun 2022.

## Builds on (most cited first, 11 of 11)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [Reweighted Wake-Sleep](https://mlsanity.com/paper/1406.2751/) (2014)
- [Markovian Score Climbing: Variational Inference with KL(p||q)](https://mlsanity.com/paper/2003.10374/) (2020)
- [Efficient Bayesian Sampling Using Normalizing Flows to Assist Markov Chain Monte Carlo Methods](https://mlsanity.com/paper/2107.08001/) (2021)
- [Geometric variational inference](https://mlsanity.com/paper/2105.10470/) (2021)
- [Translation and Rotation Equivariant Normalizing Flow (TRENF) for Optimal Cosmological Analysis](https://mlsanity.com/paper/2202.05282/) (2022)
- [MUSE: Marginal Unbiased Score Expansion and Application to CMB Lensing](https://mlsanity.com/paper/2112.09354/) (2021)

## Built on by (most cited first, 1 of 1)

- [Amortized Factor Inference Networks for Posterior Inference](https://mlsanity.com/paper/2605.26419/) (2026)

## Abstract (arXiv)

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 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.