Summary of Hessian-free Laplace in Bayesian Deep Learning, by James Mcinerney et al.
Hessian-Free Laplace in Bayesian Deep Learning
by James McInerney, Nathan Kallus
First submitted to arxiv on: 15 Mar 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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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 A novel approach is proposed in this paper, aiming to overcome the computational bottleneck associated with the Laplace approximation (LA) in Bayesian deep learning. The LA is a widely used technique for quantifying uncertainty post-hoc, but it requires calculating and inverting the Hessian matrix of the log posterior, which can be computationally expensive. To address this issue, the authors introduce the Hessian-free Laplace (HFL) approximation, which uses the curvature of both the log posterior and network prediction to estimate its variance. Only two point estimates are required: the standard maximum a posteriori parameter and the optimal parameter under a loss regularized by the network prediction. The authors demonstrate that HFL targets the same variance as LA and can be efficiently amortized in a pre-trained network. Experimental results show comparable performance to exact and approximate Hessians, with excellent coverage for in-between uncertainty. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper proposes a new way to do something called Laplace approximation in deep learning. Currently, this method is used to measure how certain we are about our predictions, but it’s slow because it needs to calculate a big matrix called the Hessian. The authors found a shortcut that doesn’t need the Hessian, which they call the Hessian-free Laplace (HFL) method. This new method uses only two pieces of information: where the best parameters are and what the optimal predictions look like. They tested their method and it worked just as well as the original method, but much faster. |
Keywords
* Artificial intelligence * Deep learning
