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Inference is crucial in modern astronomical research, where hiddenastrophysical features and patterns are often estimated from indirect and noisymeasurements. Inferring the posterior of hidden features, conditioned on theobserved measurements, is essential for understanding the uncertainty ofresults and downstream scientific interpretations. Traditional approaches forposterior estimation include sampling-based methods and variational inference.However, sampling-based methods are typically slow for high-dimensional inverseproblems, while variational inference often lacks estimation accuracy. In thispaper, we propose alpha-DPI, a deep learning framework that first learns anapproximate posterior using alpha-divergence variational inference paired witha generative neural network, and then produces more accurate posterior samplesthrough importance re-weighting of the network samples. It inherits strengthsfrom both sampling and variational inference methods: it is fast, accurate, andscalable to high-dimensional problems. We apply our approach to two high-impactastronomical inference problems using real data: exoplanet astrometry and blackhole feature extraction.

alpha-Deep Probabilistic Inference (alpha-DPI): efficient uncertainty quantification from exoplanet astrometry to black hole feature extraction