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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.16253 |
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| _version_ | 1866929552221011968 |
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| author | Rittler, Nick Chaudhuri, Kamalika |
| author_facet | Rittler, Nick Chaudhuri, Kamalika |
| contents | Generative models at times produce "invalid" outputs, such as images with generation artifacts and unnatural sounds. Validity-constrained distribution learning attempts to address this problem by requiring that the learned distribution have a provably small fraction of its mass in invalid parts of space -- something which standard loss minimization does not always ensure. To this end, a learner in this model can guide the learning via "validity queries", which allow it to ascertain the validity of individual examples. Prior work on this problem takes a worst-case stance, showing that proper learning requires an exponential number of validity queries, and demonstrating an improper algorithm which -- while generating guarantees in a wide-range of settings -- makes an atypical polynomial number of validity queries. In this work, we take a first step towards characterizing regimes where guaranteeing validity is easier than in the worst-case. We show that when the data distribution lies in the model class and the log-loss is minimized, the number of samples required to ensure validity has a weak dependence on the validity requirement. Additionally, we show that when the validity region belongs to a VC-class, a limited number of validity queries are often sufficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16253 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distribution Learning with Valid Outputs Beyond the Worst-Case Rittler, Nick Chaudhuri, Kamalika Machine Learning Generative models at times produce "invalid" outputs, such as images with generation artifacts and unnatural sounds. Validity-constrained distribution learning attempts to address this problem by requiring that the learned distribution have a provably small fraction of its mass in invalid parts of space -- something which standard loss minimization does not always ensure. To this end, a learner in this model can guide the learning via "validity queries", which allow it to ascertain the validity of individual examples. Prior work on this problem takes a worst-case stance, showing that proper learning requires an exponential number of validity queries, and demonstrating an improper algorithm which -- while generating guarantees in a wide-range of settings -- makes an atypical polynomial number of validity queries. In this work, we take a first step towards characterizing regimes where guaranteeing validity is easier than in the worst-case. We show that when the data distribution lies in the model class and the log-loss is minimized, the number of samples required to ensure validity has a weak dependence on the validity requirement. Additionally, we show that when the validity region belongs to a VC-class, a limited number of validity queries are often sufficient. |
| title | Distribution Learning with Valid Outputs Beyond the Worst-Case |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2410.16253 |