Summary of Variational Inference For Uncertainty Quantification: An Analysis Of Trade-offs, by Charles C. Margossian et al.
Variational Inference for Uncertainty Quantification: an Analysis of Trade-offs
by Charles C. Margossian, Loucas Pillaud-Vivien, Lawrence K. Saul
First submitted to arxiv on: 20 Mar 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Computation (stat.CO)
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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 In a machine learning subfield paper, researchers tackle the issue of variational inference (VI) in scenarios where the true distribution p does not factorize. They show that using a factorized family Q for approximation leads to an impossibility theorem: any factorized approximation q can only accurately estimate one measure of uncertainty among marginal variances, precisions, or generalized variance (related to entropy). The team explores how choosing different divergences between distributions D(q,p) affects which measure is correctly estimated. They analyze classic Kullback-Leibler and Rényi divergences as well as a score-based divergence. In the case of Gaussian p and factorized Gaussian q, they demonstrate that all considered divergences can be ordered based on uncertainty estimates from VI. Finally, they empirically validate this ordering when p is not Gaussian. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Variational inference (VI) is a way to find an approximate distribution q that’s close to the real distribution p. But what happens if p doesn’t have a special property called factorization? The researchers show that using factorized distributions for approximation leads to problems. They explore how choosing different ways to measure distance between distributions affects which uncertainty measures are accurately estimated. For example, they look at classic methods and a new score-based method. They test these methods when the real distribution p is a special type called Gaussian, but they also show that their findings apply more broadly. |
Keywords
* Artificial intelligence * Inference * Machine learning
