Summary of Posterior Concentrations Of Fully-connected Bayesian Neural Networks with General Priors on the Weights, by Insung Kong and Yongdai Kim
Posterior concentrations of fully-connected Bayesian neural networks with general priors on the weights
by Insung Kong, Yongdai Kim
First submitted to arxiv on: 21 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 Bayesian approaches for training deep neural networks (BNNs) have garnered significant interest and been effectively utilized in various applications. While several studies have explored the properties of posterior concentrations of BNNs, these investigations primarily focused on models with sparse or heavy-tailed priors. Notably, no theoretical results currently exist for BNNs using Gaussian priors, which are the most commonly employed type. The lack of theory stems from the absence of approximation results for Deep Neural Networks (DNNs) that are non-sparse and have bounded parameters. This paper presents a novel approximation theory for non-sparse DNNs with bounded parameters, and, based on this theory, demonstrates that BNNs with general priors can achieve near-minimax optimal posterior concentration rates to the true model. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Bayesian neural networks are special kinds of artificial intelligence models that use probability to make decisions. In this paper, researchers want to understand how these models work when they’re given a lot of information about what the answers should look like. They found that most studies only looked at cases where the model has very little information or very extreme information. But in real life, we usually have a mix of both. So, the researchers came up with a new way to understand how these models work when they’re given average amounts of information. This is important because it can help us make better predictions and decisions. |
Keywords
* Artificial intelligence * Probability
