  Inference is crucial in modern astronomical research, where hidden
astrophysical features and patterns are often estimated from indirect and noisy
measurements. Inferring the posterior of hidden features, conditioned on the
observed measurements, is essential for understanding the uncertainty of
results and downstream scientific interpretations. Traditional approaches for
posterior estimation include sampling-based methods and variational inference.
However, sampling-based methods are typically slow for high-dimensional inverse
problems, while variational inference often lacks estimation accuracy. In this
paper, we propose alpha-DPI, a deep learning framework that first learns an
approximate posterior using alpha-divergence variational inference paired with
a generative neural network, and then produces more accurate posterior samples
through importance re-weighting of the network samples. It inherits strengths
from both sampling and variational inference methods: it is fast, accurate, and
scalable to high-dimensional problems. We apply our approach to two high-impact
astronomical inference problems using real data: exoplanet astrometry and black
hole feature extraction.
