A Convex Approximation Framework for Neural Likelihood-Based Bayesian Inverse Problems

2012-11-01 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Engineering & Applied Sciences · Depth: Expert, extended

Summary

A new convex approximation framework addresses challenges in neural likelihood approximation for high-dimensional Bayesian inverse problems, where traditional probabilistic inference methods like Markov chain Monte Carlo are often infeasible due to complex models or high computational costs. This work introduces a method to learn the likelihood function directly from data using un-normalized potentials, folding normalization into the training objective. This approach results in a strictly convex learning problem, ensuring that empirical minimizers converge to the true likelihood as data size increases. Numerical experiments demonstrate its effectiveness in a deblurring problem and a non-linear PDE-based imaging problem, specifically estimating doping profiles in semiconductor devices, showing significant computational acceleration and high accuracy.

Key takeaway

For Research Scientists working on high-dimensional Bayesian inverse problems, this convex neural likelihood approximation offers a robust and computationally efficient alternative to traditional methods. You can achieve accurate posterior sampling, even with unknown observational noise, by leveraging free-form approximations. Consider integrating this framework to significantly reduce computation time for complex models, such as those in semiconductor device analysis, while maintaining high fidelity in your results.

Key insights

A convex framework for neural likelihood approximation improves theoretical foundations and practical efficiency in inverse problems.

Principles

• Un-normalized potentials yield strictly convex learning objectives.
• Empirical minimizers converge to the true likelihood with more data.

Method

Learn likelihoods from data using un-normalized potentials, absorbing normalization into a KL-based objective, then minimize this convex objective.

In practice

• Apply to deblurring problems for accurate posterior estimation.
• Accelerate posterior sampling in PDE-based inverse problems.

Topics

• Neural Likelihood Approximation
• Bayesian Inverse Problems
• Convex Optimization
• Markov Chain Monte Carlo
• Deblurring
• Semiconductor Devices

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.