On Socially Fair Low-Rank Approximation and Column Subset Selection
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912149171863552 |
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| author | Song, Zhao Vakilian, Ali Woodruff, David P. Zhou, Samson |
| author_facet | Song, Zhao Vakilian, Ali Woodruff, David P. Zhou, Samson |
| contents | Low-rank approximation and column subset selection are two fundamental and related problems that are applied across a wealth of machine learning applications. In this paper, we study the question of socially fair low-rank approximation and socially fair column subset selection, where the goal is to minimize the loss over all sub-populations of the data. We show that surprisingly, even constant-factor approximation to fair low-rank approximation requires exponential time under certain standard complexity hypotheses. On the positive side, we give an algorithm for fair low-rank approximation that, for a constant number of groups and constant-factor accuracy, runs in $2^{\text{poly}(k)}$ time rather than the naïve $n^{\text{poly}(k)}$, which is a substantial improvement when the dataset has a large number $n$ of observations. We then show that there exist bicriteria approximation algorithms for fair low-rank approximation and fair column subset selection that run in polynomial time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_06063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Socially Fair Low-Rank Approximation and Column Subset Selection Song, Zhao Vakilian, Ali Woodruff, David P. Zhou, Samson Machine Learning Data Structures and Algorithms Low-rank approximation and column subset selection are two fundamental and related problems that are applied across a wealth of machine learning applications. In this paper, we study the question of socially fair low-rank approximation and socially fair column subset selection, where the goal is to minimize the loss over all sub-populations of the data. We show that surprisingly, even constant-factor approximation to fair low-rank approximation requires exponential time under certain standard complexity hypotheses. On the positive side, we give an algorithm for fair low-rank approximation that, for a constant number of groups and constant-factor accuracy, runs in $2^{\text{poly}(k)}$ time rather than the naïve $n^{\text{poly}(k)}$, which is a substantial improvement when the dataset has a large number $n$ of observations. We then show that there exist bicriteria approximation algorithms for fair low-rank approximation and fair column subset selection that run in polynomial time. |
| title | On Socially Fair Low-Rank Approximation and Column Subset Selection |
| topic | Machine Learning Data Structures and Algorithms |
| url | https://arxiv.org/abs/2412.06063 |