MUSE: Marginal Unbiased Score Expansion and Application to CMB Lensing

Abstract

We present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces, yielding Gaussianized asymptotically unbiased and near-optimal constraints on global parameters of interest. It is computationally much cheaper than exact alternatives like Hamiltonian Monte Carlo (HMC), excelling on funnel problems which challenge HMC, and does not require any problem-specific user supervision like other approximate methods such as Variational Inference or many Simulation-Based Inference methods. MUSE makes possible the first joint Bayesian estimation of the delensed Cosmic Microwave Background (CMB) power spectrum and gravitational lensing potential power spectrum, demonstrated here on a simulated data set as large as the upcoming South Pole Telescope 3G 1500 deg${}^2$ survey, corresponding to a latent dimensionality of $\sim 6$ million and of order 100 global bandpower parameters. On a subset of the problem where an exact but more expensive HMC solution is feasible, we verify that MUSE yields nearly optimal results. We also demonstrate that existing spectrum-based forecasting tools which ignore pixel-masking underestimate predicted error bars by only $\sim 10\%$. This method is a promising path forward for fast lensing and delensing analyses which will be necessary for future CMB experiments such as SPT-3G, Simons Observatory, or CMB-S4, and can complement or supersede existing HMC approaches. The success of MUSE on this challenging problem strengthens its case as a generic procedure for a broad class of high-dimensional inference problems.

arXiv comment22 pages, 8 figures

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• Improved cosmic microwave background (de-)lensing using general spherical harmonic transforms
• Lensing power spectrum of the Cosmic Microwave Background with deep polarization experiments
• Joint velocity and density reconstruction of the Universe with nonlinear differentiable forward modeling
• Unified and consistent structure growth measurements from joint ACT, SPT and \textit{Planck} CMB lensing
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• Cosmological Probes of Structure Growth and Tests of Gravity
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• Inference of gravitational lensing and patchy reionization with future CMB data
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• Improving Constraints on Inflation with CMB Delensing
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