Accurate Coresets for Latent Variable Models and Regularized Regression
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912171745607680 |
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| author | Ranjan, Sanskar Shit, Supratim |
| author_facet | Ranjan, Sanskar Shit, Supratim |
| contents | Accurate coresets are a weighted subset of the original dataset, ensuring a model trained on the accurate coreset maintains the same level of accuracy as a model trained on the full dataset. Primarily, these coresets have been studied for a limited range of machine learning models. In this paper, we introduce a unified framework for constructing accurate coresets. Using this framework, we present accurate coreset construction algorithms for general problems, including a wide range of latent variable model problems and $\ell_p$-regularized $\ell_p$-regression. For latent variable models, our coreset size is $O\left(\mathrm{poly}(k)\right)$, where $k$ is the number of latent variables. For $\ell_p$-regularized $\ell_p$-regression, our algorithm captures the reduction of model complexity due to regularization, resulting in a coreset whose size is always smaller than $d^{p}$ for a regularization parameter $λ> 0$. Here, $d$ is the dimension of the input points. This inherently improves the size of the accurate coreset for ridge regression. We substantiate our theoretical findings with extensive experimental evaluations on real datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20189 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Accurate Coresets for Latent Variable Models and Regularized Regression Ranjan, Sanskar Shit, Supratim Machine Learning Accurate coresets are a weighted subset of the original dataset, ensuring a model trained on the accurate coreset maintains the same level of accuracy as a model trained on the full dataset. Primarily, these coresets have been studied for a limited range of machine learning models. In this paper, we introduce a unified framework for constructing accurate coresets. Using this framework, we present accurate coreset construction algorithms for general problems, including a wide range of latent variable model problems and $\ell_p$-regularized $\ell_p$-regression. For latent variable models, our coreset size is $O\left(\mathrm{poly}(k)\right)$, where $k$ is the number of latent variables. For $\ell_p$-regularized $\ell_p$-regression, our algorithm captures the reduction of model complexity due to regularization, resulting in a coreset whose size is always smaller than $d^{p}$ for a regularization parameter $λ> 0$. Here, $d$ is the dimension of the input points. This inherently improves the size of the accurate coreset for ridge regression. We substantiate our theoretical findings with extensive experimental evaluations on real datasets. |
| title | Accurate Coresets for Latent Variable Models and Regularized Regression |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2412.20189 |