Summary of Learning a Gaussian Mixture For Sparsity Regularization in Inverse Problems, by Giovanni S. Alberti et al.
Learning a Gaussian Mixture for Sparsity Regularization in Inverse Problems
by Giovanni S. Alberti, Luca Ratti, Matteo Santacesaria, Silvia Sciutto
First submitted to arxiv on: 29 Jan 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 This paper proposes a novel probabilistic sparsity prior for linear inverse problems, which can be used to regularize solutions. The approach is based on a mixture of degenerate Gaussians and can model sparsity with respect to any basis. A neural network is designed as the Bayes estimator for these problems, and both supervised and unsupervised training strategies are presented to estimate the network’s parameters. The effectiveness of this method is evaluated through numerical comparisons with LASSO, group LASSO, iterative hard thresholding, and sparse coding/dictionary learning on 1D datasets. Results show that our approach consistently produces lower mean square error values across all datasets, even when they deviate from a Gaussian mixture model. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper creates a new way to solve inverse problems by adding an extra layer of information about how the solution should look. This helps by making the answer more accurate and easier to find. The idea is based on mixing together different types of probability distributions, which can represent how some answers are mostly zero with only a few important parts. A special type of computer program called a neural network is designed to solve these problems in the best way possible. To make sure this works well, two ways are suggested to train the program: one that uses labeled data and one that doesn’t. The results show that our method does better than some other popular methods on certain types of data. |
Keywords
* Artificial intelligence * Mixture model * Neural network * Probability * Supervised * Unsupervised
