Summary of Asymptotics Of Linear Regression with Linearly Dependent Data, by Behrad Moniri and Hamed Hassani
Asymptotics of Linear Regression with Linearly Dependent Data
by Behrad Moniri, Hamed Hassani
First submitted to arxiv on: 4 Dec 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Systems and Control (eess.SY)
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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 investigates the asymptotics of linear regression when covariates exhibit a non-Gaussian dependency structure, departing from the standard assumption of independence. The authors model these covariates using stochastic processes with spatio-temporal covariance and analyze the performance of ridge regression in the high-dimensional proportional regime. A key finding is that Gaussian universality holds, allowing tools from random matrix theory to be applied. This enables precise characterization of estimation error, which is crucial for understanding dependencies’ influence on estimation and regularization choice. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how linear regression works when there are patterns in the data that aren’t just random. It studies how well a special type of model called ridge regression does when dealing with these patterns. The researchers found that even though the data isn’t normal, they can still use tools from statistics to understand how well the model is doing and why it’s making certain predictions. |
Keywords
» Artificial intelligence » Linear regression » Regression » Regularization
