Solving high-dimensional parameter inference: marginal posterior densities & Moment Networks
This addresses computational bottlenecks in physical inference problems like cosmology and gravitational wave analysis, though it appears incremental as an alternative to existing density estimation methods.
The paper tackles the curse of dimensionality in high-dimensional probability density estimation for inference by proposing direct estimation of lower-dimensional marginal distributions, bypassing full posterior estimation or MCMC sampling. The result includes Moment Networks that compute moments of marginal posteriors, reproducing exact results from analytic posteriors and Masked Autoregressive Flows, demonstrated on LIGO-like gravitational wave data.
High-dimensional probability density estimation for inference suffers from the "curse of dimensionality". For many physical inference problems, the full posterior distribution is unwieldy and seldom used in practice. Instead, we propose direct estimation of lower-dimensional marginal distributions, bypassing high-dimensional density estimation or high-dimensional Markov chain Monte Carlo (MCMC) sampling. By evaluating the two-dimensional marginal posteriors we can unveil the full-dimensional parameter covariance structure. We additionally propose constructing a simple hierarchy of fast neural regression models, called Moment Networks, that compute increasing moments of any desired lower-dimensional marginal posterior density; these reproduce exact results from analytic posteriors and those obtained from Masked Autoregressive Flows. We demonstrate marginal posterior density estimation using high-dimensional LIGO-like gravitational wave time series and describe applications for problems of fundamental cosmology.