AI 中文总结
针对高维计数数据回归难题，开发变分贝叶斯框架，用马蹄形和连续收缩先验实现稀疏负二项回归，相比MCMC方法计算量大幅减少，在过度离散和泊松数据中都有良好表现，为高维稀疏计数回归提供实用工具。
AI 中文摘要
在现代应用中，具有过度离散和高维预测变量的计数数据带来了重大挑战。虽然负二项回归提供了一个灵活的建模框架，但现有的贝叶斯方法依赖于计算成本高昂的MCMC方法，在高维环境中变得不切实际。本文使用马蹄形和连续收缩先验开发了一个用于稀疏负二项回归的变分贝叶斯框架。我们提出的方法在实现估计精度和变量选择性能方面可与MCMC基准相媲美，同时所需计算时间不到1%。大量模拟表明，负二项分布规范对于过度离散数据至关重要，基于泊松的方法在过度离散情况下表现出显著的性能下降。相反，当数据为泊松分布时，我们的方法仍然稳健，使其成为更安全的默认选择。对实际基准数据集的应用进一步证实了我们方法的实用性。所提出的框架为高维环境中的稀疏计数回归提供了一种计算高效且可靠的工具。
英文摘要
Count data with overdispersion and high-dimensional predictors pose significant challenges in modern applications. While negative binomial regression offers a flexible modeling framework, existing Bayesian approaches rely on computationally expensive MCMC methods that become impractical in high-dimensional settings. This paper develops a variational Bayesian framework for sparse negative binomial regression using horseshoe and continuous spike-and-slab priors. Our proposed methods achieve estimation accuracy and variable selection performance comparable to MCMC benchmarks while offering substantial computational savings over MCMC. Extensive simulations demonstrate that the negative binomial specification is essential for overdispersed data, as Poisson-based approaches exhibit substantial performance degradation under overdispersion. Conversely, our methods remain robust when the data are Poisson, making them a safer default choice. Applications to real benchmark datasets further confirm the practical utility of our approach.
CommentsThe second paper of the PhD thesis of Miss Kharabati
