Summary of Inferring Change Points in High-dimensional Regression Via Approximate Message Passing, by Gabriel Arpino et al.
Inferring Change Points in High-Dimensional Regression via Approximate Message Passing
by Gabriel Arpino, Xiaoqi Liu, Julia Gontarek, Ramji Venkataramanan
First submitted to arxiv on: 11 Apr 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 proposes an efficient algorithm for localizing change points in generalized linear models (GLMs), which covers various statistical learning problems. The Approximate Message Passing (AMP) algorithm estimates both signal values and change point locations. In the high-dimensional limit, where parameters p are proportional to samples n, the algorithm’s performance is characterized by a state evolution recursion. This allows for precise computation of metrics like Hausdorff error and tailoring to prior structural information. The AMP iterates can also be used to compute a Bayesian posterior distribution over change points in the high-dimensional limit. Numerical experiments validate the theory, demonstrating favorable performance on synthetic and real data for linear, logistic, and rectified linear regression. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us better understand how to find changes in patterns when using special types of statistical models called generalized linear models (GLMs). The researchers created a new algorithm that can quickly find both the patterns themselves and where those patterns change. They showed that this algorithm works well even when we have a huge amount of data, which is important for many real-world applications. |
Keywords
» Artificial intelligence » Linear regression
