Summary of Analysing Heavy-tail Properties Of Stochastic Gradient Descent by Means Of Stochastic Recurrence Equations, By Ewa Damek and Sebastian Mentemeier
Analysing heavy-tail properties of Stochastic Gradient Descent by means of Stochastic Recurrence Equations
by Ewa Damek, Sebastian Mentemeier
First submitted to arxiv on: 20 Mar 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC); Probability (math.PR); Statistics Theory (math.ST)
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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 research paper explores the theoretical framework of stochastic recursions to study the heavy tail properties of Stochastic Gradient Descent (SGD). Building on previous work, the authors model iterations of SGD as a multivariate affine stochastic recursion. This setup enables the analysis of linear regression with independent and identically distributed pairs of random matrices and vectors. The paper aims to answer open questions and extend previous results by applying the theory of irreducible-proximal (i-p) matrices. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This study looks at how machine learning works. Researchers are trying to understand how a type of algorithm called Stochastic Gradient Descent (SGD) behaves. They’re using special math tools to see what’s happening inside this algorithm. This can help us make better predictions and learn more about the world. The scientists are answering big questions and making new discoveries by applying these math tools. |
Keywords
* Artificial intelligence * Linear regression * Machine learning * Stochastic gradient descent
