论文标题
解决高维参数推断：边际后密度和力矩网络
Solving high-dimensional parameter inference: marginal posterior densities & Moment Networks
论文作者
论文摘要
推理的高维概率密度估计受到“维度的诅咒”。对于许多物理推理问题，全部后验分布笨拙，在实践中很少使用。取而代之的是，我们提出直接估计较低的边缘分布，绕过高维密度估计或高维马尔可夫链蒙特卡洛（MCMC）采样。通过评估二维边缘后期，我们可以揭示全维参数协方差结构。我们还建议构建一个称为Moment Networks的快速神经回归模型的简单层次结构，以计算任何所需的低维度边缘后密度的增加矩；这些重现了分析后期和从掩盖自回归流量获得的重现结果。我们使用高维的LIGO样重力波时间序列估计了边缘后部密度估计，并描述了基本宇宙学问题的应用。
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.
