Robustly Learning Monotone Generalized Linear Models via Data Augmentation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915424543703040 |
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| author | Zarifis, Nikos Wang, Puqian Diakonikolas, Ilias Diakonikolas, Jelena |
| author_facet | Zarifis, Nikos Wang, Puqian Diakonikolas, Ilias Diakonikolas, Jelena |
| contents | We study the task of learning Generalized Linear models (GLMs) in the agnostic model under the Gaussian distribution. We give the first polynomial-time algorithm that achieves a constant-factor approximation for \textit{any} monotone Lipschitz activation. Prior constant-factor GLM learners succeed for a substantially smaller class of activations. Our work resolves a well-known open problem, by developing a robust counterpart to the classical GLMtron algorithm (Kakade et al., 2011). Our robust learner applies more generally, encompassing all monotone activations with bounded $(2+ζ)$-moments, for any fixed $ζ>0$ -- a condition that is essentially necessary. To obtain our results, we leverage a novel data augmentation technique with decreasing Gaussian noise injection and prove a number of structural results that may be useful in other settings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_08611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robustly Learning Monotone Generalized Linear Models via Data Augmentation Zarifis, Nikos Wang, Puqian Diakonikolas, Ilias Diakonikolas, Jelena Machine Learning Optimization and Control Statistics Theory We study the task of learning Generalized Linear models (GLMs) in the agnostic model under the Gaussian distribution. We give the first polynomial-time algorithm that achieves a constant-factor approximation for \textit{any} monotone Lipschitz activation. Prior constant-factor GLM learners succeed for a substantially smaller class of activations. Our work resolves a well-known open problem, by developing a robust counterpart to the classical GLMtron algorithm (Kakade et al., 2011). Our robust learner applies more generally, encompassing all monotone activations with bounded $(2+ζ)$-moments, for any fixed $ζ>0$ -- a condition that is essentially necessary. To obtain our results, we leverage a novel data augmentation technique with decreasing Gaussian noise injection and prove a number of structural results that may be useful in other settings. |
| title | Robustly Learning Monotone Generalized Linear Models via Data Augmentation |
| topic | Machine Learning Optimization and Control Statistics Theory |
| url | https://arxiv.org/abs/2502.08611 |