Debiased LASSO under Poisson-Gauss Model
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911784202403840 |
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| author | Abdalla, Pedro Kur, Gil |
| author_facet | Abdalla, Pedro Kur, Gil |
| contents | Quantifying uncertainty in high-dimensional sparse linear regression is a fundamental task in statistics that arises in various applications. One of the most successful methods for quantifying uncertainty is the debiased LASSO, which has a solid theoretical foundation but is restricted to settings where the noise is purely additive. Motivated by real-world applications, we study the so-called Poisson inverse problem with additive Gaussian noise and propose a debiased LASSO algorithm that only requires $n \gg s\log^2p$ samples, which is optimal up to a logarithmic factor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_16764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Debiased LASSO under Poisson-Gauss Model Abdalla, Pedro Kur, Gil Statistics Theory Information Theory Signal Processing Quantifying uncertainty in high-dimensional sparse linear regression is a fundamental task in statistics that arises in various applications. One of the most successful methods for quantifying uncertainty is the debiased LASSO, which has a solid theoretical foundation but is restricted to settings where the noise is purely additive. Motivated by real-world applications, we study the so-called Poisson inverse problem with additive Gaussian noise and propose a debiased LASSO algorithm that only requires $n \gg s\log^2p$ samples, which is optimal up to a logarithmic factor. |
| title | Debiased LASSO under Poisson-Gauss Model |
| topic | Statistics Theory Information Theory Signal Processing |
| url | https://arxiv.org/abs/2402.16764 |