Summary of Combinatorial Optimization Of the Coefficient Of Determination, by Marc Harary
Combinatorial optimization of the coefficient of determination
by Marc Harary
First submitted to arxiv on: 12 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG); Combinatorics (math.CO)
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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 proposes a novel algorithm called the “quadratic sweep” for selecting the k-subset of n points in the plane with the highest coefficient of determination (R2). The method consists of two steps: projectively lifting data points into R5 and then iterating over each linearly separable k-subset. The algorithm leverages combinatorial geometry to find the optimal set of outliers, which is separable from its complement by a conic section in R2 that can be found in O(n^5 log n) time. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper’s main contribution is an efficient method for robust correlation analysis, which is essential in statistics. The quadratic sweep algorithm finds the k-subset of n points with the highest R2 value by lifting data points into R5 and then iterating over each linearly separable k-subset. This approach has been experimentally demonstrated to be optimal up to n=30 without error. |
