Solving Bayesian Inverse Problems via Variational Autoencoders
December 05, 2019 ยท Declared Dead ยท ๐ Mathematical and Scientific Machine Learning
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Authors
Hwan Goh, Sheroze Sheriffdeen, Jonathan Wittmer, Tan Bui-Thanh
arXiv ID
1912.04212
Category
stat.ML: Machine Learning (Stat)
Cross-listed
cs.LG,
eess.IV
Citations
49
Venue
Mathematical and Scientific Machine Learning
Last Checked
3 months ago
Abstract
In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a small shift in perspective, we leverage and adapt VAEs for a different purpose: uncertainty quantification in scientific inverse problems. We introduce UQ-VAE: a flexible, adaptive, hybrid data/model-informed framework for training neural networks capable of rapid modelling of the posterior distribution representing the unknown parameter of interest. Specifically, from divergence-based variational inference, our framework is derived such that most of the information usually present in scientific inverse problems is fully utilized in the training procedure. Additionally, this framework includes an adjustable hyperparameter that allows selection of the notion of distance between the posterior model and the target distribution. This introduces more flexibility in controlling how optimization directs the learning of the posterior model. Further, this framework possesses an inherent adaptive optimization property that emerges through the learning of the posterior uncertainty.
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