论文标题
贝叶斯集团在具有连续的尖峰和斜杠的广义线性模型中
Bayesian Group Regularization in Generalized Linear Models with a Continuous Spike-and-Slab Prior
论文作者
论文摘要
我们研究了在连续的尖峰和slab之前，在高维广义线性模型（GLM）中研究了贝叶斯群体调查的估计。我们的框架涵盖了规范和非规范的链接函数，以及对群体稀疏性的物流，泊松，负二项式和高斯回归。我们获得了最大a后验（MAP）估计量和我们先验下的完整后验分布的最小值L2收敛速率。因此，我们的理论结果证明了将后验模式用作点估计器的合理性。后验分布还以与地图估计器相同的速度收缩，这是我们方法的吸引人特征，这对于组的套索并非如此。为了进行计算，我们提出了预期最大化（EM）和马尔可夫链蒙特卡洛（MCMC）算法。我们通过模拟说明了我们的方法，以及预测蛋白质序列中人类免疫缺陷病毒（HIV）耐药性的实际数据应用。
We study Bayesian group-regularized estimation in high-dimensional generalized linear models (GLMs) under a continuous spike-and-slab prior. Our framework covers both canonical and non-canonical link functions and subsumes logistic, Poisson, negative binomial, and Gaussian regression with group sparsity. We obtain the minimax L2 convergence rate for both a maximum a posteriori (MAP) estimator and the full posterior distribution under our prior. Our theoretical results thus justify the use of the posterior mode as a point estimator. The posterior distribution also contracts at the same rate as the MAP estimator, an attractive feature of our approach which is not the case for the group lasso. For computation, we propose expectation-maximization (EM) and Markov chain Monte Carlo (MCMC) algorithms. We illustrate our method through simulations and a real data application on predicting human immunodeficiency virus (HIV) drug resistance from protein sequences.
