Summary of Overparameterized Multiple Linear Regression As Hyper-curve Fitting, by E. Atza et al.
Overparameterized Multiple Linear Regression as Hyper-Curve Fitting
by E. Atza, N. Budko
First submitted to arxiv on: 11 Apr 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 The paper demonstrates an equivalence between a fixed-effect multiple linear regression model and fitting data with a hyper-curve parameterized by a single scalar. This allows for a predictor-focused approach, where each predictor is described by a function of this chosen parameter. The study shows that a linear model can produce exact predictions even in the presence of nonlinear dependencies violating model assumptions. Applications include regularization of problems with noisy predictors and removing “improper” predictors from models. The paper uses synthetic and experimental data to demonstrate its findings, including parameterization based on the dependent variable and monomial basis. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper shows that a special type of math problem can be solved using a simple formula. This helps us make predictions even when there are things in the data that don’t follow the rules we thought were important. The research uses fake and real data to test this idea and shows that it works well. It’s useful for fixing problems with noisy or bad data. |
Keywords
* Artificial intelligence * Linear regression * Regularization
