Summary of Reparameterization Invariance in Approximate Bayesian Inference, by Hrittik Roy et al.
Reparameterization invariance in approximate Bayesian inference
by Hrittik Roy, Marco Miani, Carl Henrik Ek, Philipp Hennig, Marvin Pförtner, Lukas Tatzel, Søren Hauberg
First submitted to arxiv on: 5 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper addresses a fundamental limitation in Bayesian neural networks (BNNs), specifically their inability to maintain invariance under reparameterization. This issue arises when identical functions are parametrized differently, resulting in different posterior densities being assigned by the BNN. The authors investigate this problem in the context of the linearized Laplace approximation, a popular method for alleviating underfitting issues. A new geometric view is developed to explain the success of linearization, and a Riemannian diffusion process is proposed to extend reparameterization invariance properties to the original neural network predictive. The resulting algorithm for approximate posterior sampling empirically improves posterior fit. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Imagine you’re trying to understand something really well, like a picture or a voice. You might want to be sure that your understanding is correct, and that’s where Bayesian neural networks come in. They help us figure out how likely our understanding is to be correct. But sometimes, these networks don’t work very well because they get stuck on how we’re representing the information. This paper helps solve this problem by finding a way to make sure that the network doesn’t get stuck and can understand things correctly no matter how we represent them. |
Keywords
» Artificial intelligence » Diffusion » Neural network » Underfitting
