论文标题
近似Gibbs采样器，以有效推断分层贝叶斯模型的分组计数数据
Approximate Gibbs Sampler for Efficient Inference of Hierarchical Bayesian Models for Grouped Count Data
论文作者
论文摘要
分层贝叶斯泊松回归模型（HBPRMS）提供了预测变量和计数响应变量之间关系的灵活建模方法。 HBPRMS在大规模数据集中的应用需要有效的推理算法，这是由于基于随机采样的许多模型参数的高计算成本。尽管马尔可夫链蒙特卡洛（MCMC）算法已被广泛用于贝叶斯推断，但使用此类算法进行采样的采样既耗时耗时，用于具有大规模数据和时间敏感决策的应用，部分原因是许多模型的非混合性。为了克服这一局限性，这项研究开发了近似Gibbs采样器（AGS），以有效地学习HBPRMS，同时保持推理准确性。在拟议的采样器中，数据的可能性与高斯分布近似，因此系数的条件后部具有封闭形式的溶液。使用实际和大数量的真实和合成数据集进行的数值实验表明，与最先进的采样算法相比，AG的性能出色，尤其是对于大型数据集。
Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexible modeling approach of the relationship between predictors and count response variables. The applications of HBPRMs to large-scale datasets require efficient inference algorithms due to the high computational cost of inferring many model parameters based on random sampling. Although Markov Chain Monte Carlo (MCMC) algorithms have been widely used for Bayesian inference, sampling using this class of algorithms is time-consuming for applications with large-scale data and time-sensitive decision-making, partially due to the non-conjugacy of many models. To overcome this limitation, this research develops an approximate Gibbs sampler (AGS) to efficiently learn the HBPRMs while maintaining the inference accuracy. In the proposed sampler, the data likelihood is approximated with Gaussian distribution such that the conditional posterior of the coefficients has a closed-form solution. Numerical experiments using real and synthetic datasets with small and large counts demonstrate the superior performance of AGS in comparison to the state-of-the-art sampling algorithm, especially for large datasets.
