Summary of Finite Sample Confidence Regions For Linear Regression Parameters Using Arbitrary Predictors, by Charles Guille-escuret and Eugene Ndiaye
Finite Sample Confidence Regions for Linear Regression Parameters Using Arbitrary Predictors
by Charles Guille-Escuret, Eugene Ndiaye
First submitted to arxiv on: 27 Jan 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); 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 paper presents a novel approach to constructing confidence regions for parameters in linear models using predictions from any arbitrary predictor. The methodology makes minimal assumptions about noise and can accommodate functions that deviate slightly from linearity. The derived confidence regions can be used within a Mixed Integer Linear Programming framework for optimizing linear objectives or extracting confidence intervals for specific parameter coordinates. Unlike previous methods, the new approach can produce empty confidence regions, which can be useful for hypothesis testing. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about finding ways to be more sure when making predictions in linear models. Usually, we make these predictions using a straight line that fits our data well. But sometimes this line isn’t perfect and we need to adjust it a bit. This new method lets us do just that by considering a range of possible lines around the original one. We can use this range to decide if our predictions are good or not, and even test if something is true or not. The results show that this method works well in practice. |
