Summary of Data Subsampling For Poisson Regression with Pth-root-link, by Han Cheng Lie and Alexander Munteanu
Data subsampling for Poisson regression with pth-root-link
by Han Cheng Lie, Alexander Munteanu
First submitted to arxiv on: 30 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Data Structures and Algorithms (cs.DS); Machine Learning (stat.ML)
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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 innovative data subsampling techniques for Poisson regression, a crucial model for count data. Specifically, the authors focus on the generalized linear model with ID- and square root-link functions. They explore the method of coresets, which are small weighted subsets that approximate the loss function of Poisson regression up to a factor of 1±ε. The paper shows lower bounds against coresets for Poisson regression, demonstrating the existence of sublinear coresets with 1±ε approximation guarantees when the complexity parameter is small. The authors also analyze the dependence on input parameters, revealing that the square root-link has an O(log(y_max)) dependence and the ID-link requires a Θ(√y_max/ log(y_max)) dependence. Additionally, they establish an improved bound on the principal branch of the Lambert W0 function, which may be of independent interest. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about making it easier to work with count data using Poisson regression. The authors develop new ways to reduce big datasets without losing important information. They show that these techniques can be used for different types of data and explain how they work. The results are useful because they help us understand the limitations of our current methods. |
Keywords
* Artificial intelligence * Loss function * Regression
