Least Squares as Random Walks
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909554376179712 |
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| author | Kostinski, Alexander Ierley, Glenn Kostinski, Sarah |
| author_facet | Kostinski, Alexander Ierley, Glenn Kostinski, Sarah |
| contents | Linear least squares (LLS) is perhaps the most common method of data analysis, dating back to Legendre, Gauss and Laplace. Framed as linear regression, LLS is also a backbone of mathematical statistics. Here we report on an unexpected new connection between LLS and random walks. To that end, we introduce the notion of a random walk based on a discrete sequence of data samples (data walk). We show that the slope of a straight line which annuls the net area under a residual data walk equals the one found by LLS. For equidistant data samples this result is exact and holds for an arbitrary distribution of steps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Least Squares as Random Walks Kostinski, Alexander Ierley, Glenn Kostinski, Sarah Methodology Statistical Mechanics Probability Data Analysis, Statistics and Probability Applications Linear least squares (LLS) is perhaps the most common method of data analysis, dating back to Legendre, Gauss and Laplace. Framed as linear regression, LLS is also a backbone of mathematical statistics. Here we report on an unexpected new connection between LLS and random walks. To that end, we introduce the notion of a random walk based on a discrete sequence of data samples (data walk). We show that the slope of a straight line which annuls the net area under a residual data walk equals the one found by LLS. For equidistant data samples this result is exact and holds for an arbitrary distribution of steps. |
| title | Least Squares as Random Walks |
| topic | Methodology Statistical Mechanics Probability Data Analysis, Statistics and Probability Applications |
| url | https://arxiv.org/abs/2503.20965 |