High-dimensional prediction for count response via sparse exponential weights
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916447585828864 |
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| author | Mai, The Tien |
| author_facet | Mai, The Tien |
| contents | Count data is prevalent in various fields like ecology, medical research, and genomics. In high-dimensional settings, where the number of features exceeds the sample size, feature selection becomes essential. While frequentist methods like Lasso have advanced in handling high-dimensional count data, Bayesian approaches remain under-explored with no theoretical results on prediction performance. This paper introduces a novel probabilistic machine learning framework for high-dimensional count data prediction. We propose a pseudo-Bayesian method that integrates a scaled Student prior to promote sparsity and uses an exponential weight aggregation procedure. A key contribution is a novel risk measure tailored to count data prediction, with theoretical guarantees for prediction risk using PAC-Bayesian bounds. Our results include non-asymptotic oracle inequalities, demonstrating rate-optimal prediction error without prior knowledge of sparsity. We implement this approach efficiently using Langevin Monte Carlo method. Simulations and a real data application highlight the strong performance of our method compared to the Lasso in various settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-dimensional prediction for count response via sparse exponential weights Mai, The Tien Methodology Statistics Theory Machine Learning Count data is prevalent in various fields like ecology, medical research, and genomics. In high-dimensional settings, where the number of features exceeds the sample size, feature selection becomes essential. While frequentist methods like Lasso have advanced in handling high-dimensional count data, Bayesian approaches remain under-explored with no theoretical results on prediction performance. This paper introduces a novel probabilistic machine learning framework for high-dimensional count data prediction. We propose a pseudo-Bayesian method that integrates a scaled Student prior to promote sparsity and uses an exponential weight aggregation procedure. A key contribution is a novel risk measure tailored to count data prediction, with theoretical guarantees for prediction risk using PAC-Bayesian bounds. Our results include non-asymptotic oracle inequalities, demonstrating rate-optimal prediction error without prior knowledge of sparsity. We implement this approach efficiently using Langevin Monte Carlo method. Simulations and a real data application highlight the strong performance of our method compared to the Lasso in various settings. |
| title | High-dimensional prediction for count response via sparse exponential weights |
| topic | Methodology Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2410.15381 |