MCMC-Net: Accelerating Markov Chain Monte Carlo with Neural Networks for Inverse Problems
| Autor: | Majee, Sudeb, Abhishek, Anuj, Strauss, Thilo, Khan, Taufiquar |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In many computational problems, using the Markov Chain Monte Carlo (MCMC) can be prohibitively time-consuming. We propose MCMC-Net, a simple yet efficient way to accelerate MCMC via neural networks. The key idea of our approach is to substitute the likelihood function of the MCMC method with a neural operator. We extensively evaluate the accuracy and speedup of our method on three different PDE-based inverse problems where likelihood computations are computationally expensive, namely electrical impedance tomography, diffuse optical tomography, and quantitative photoacoustic tomography. MCMC-Net performs similar to the classical likelihood counterpart but with a significant, up to twelvefold, speedup. We conjecture that the method can be applied to any problem with a sufficiently expensive likelihood function. We also analyze MCMC-Net in a theoretical setting for the different use cases. We prove a universal approximation theorem-type result to show that the proposed network can approximate the mapping resulting from forward model evaluations to a desired accuracy. Furthermore, we establish convergence of the surrogate posterior to the true posterior under Hellinger distance. Comment: 30 pages, 6 figures, 3 tables |
| Databáze: | arXiv |
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