The Noisy Quantitative Group Testing Problem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911607383130112 |
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| author | Li, Tenghao Sangwan, Neha Li, Xiaxin Mazumdar, Arya |
| author_facet | Li, Tenghao Sangwan, Neha Li, Xiaxin Mazumdar, Arya |
| contents | In this paper, we study the problem of quantitative group testing (QGT) and analyze the performance of three models: the noiseless model, the additive Gaussian noise model, and the noisy Z-channel model. For each model, we analyze two algorithmic approaches: a linear estimator based on correlation scores, and a least squares estimator (LSE). We derive upper bounds on the number of tests required for exact recovery with vanishing error probability, and complement these results with information-theoretic lower bounds. In the additive Gaussian noise setting, our lower and upper bounds match in order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11797 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Noisy Quantitative Group Testing Problem Li, Tenghao Sangwan, Neha Li, Xiaxin Mazumdar, Arya Information Theory In this paper, we study the problem of quantitative group testing (QGT) and analyze the performance of three models: the noiseless model, the additive Gaussian noise model, and the noisy Z-channel model. For each model, we analyze two algorithmic approaches: a linear estimator based on correlation scores, and a least squares estimator (LSE). We derive upper bounds on the number of tests required for exact recovery with vanishing error probability, and complement these results with information-theoretic lower bounds. In the additive Gaussian noise setting, our lower and upper bounds match in order. |
| title | The Noisy Quantitative Group Testing Problem |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.11797 |