Neuronized Priors for Bayesian Sparse Linear Regression
Neuronized Priors for Bayesian Sparse Linear Regression
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DOI：
10.1080/01621459.2021.1876710
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发表时间：
2018-09
影响因子：
3.7
通讯作者：
Minsuk Shin;Jun S. Liu
中科院分区：
文献类型：
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作者：
Minsuk Shin;Jun S. Liu
摘要 尽管贝叶斯变量选择方法已得到深入研究，但其在实践中的日常使用尚未赶上 Lasso 等非贝叶斯变量选择方法，这可能是由于计算困难和先验选择的灵活性所致。为了缓解这些挑战，我们提出神经元化先验来统一和扩展一些流行的收缩先验，例如拉普拉斯、柯西、马蹄形和尖峰和平板先验。神经化先验可以写为高斯权重变量和通过激活函数从高斯变换而来的尺度变量的乘积。与经典的尖峰和平板先验相比，神经元化先验在不使用任何潜在指示变量的情况下实现了相同的显式变量选择，从而实现了更高效和灵活的后验采样以及更有效的后验模态估计。理论上，我们在神经元化公式上提供了实现最佳后收缩率的特定条件，并表明广泛适用的 MCMC 算法在神经元化公式下实现了指数级快速收敛速度。我们还检查了各种模拟和真实数据示例，并证明在所有众所周知的情况下，使用神经元化表示在计算上比其标准对应物更有效或相当有效。提供了 R 包 NPrior，用于在贝叶斯线性回归中使用神经化先验。
Abstract Although Bayesian variable selection methods have been intensively studied, their routine use in practice has not caught up with their non-Bayesian counterparts such as Lasso, likely due to difficulties in both computations and flexibilities of prior choices. To ease these challenges, we propose the neuronized priors to unify and extend some popular shrinkage priors, such as Laplace, Cauchy, horseshoe, and spike-and-slab priors. A neuronized prior can be written as the product of a Gaussian weight variable and a scale variable transformed from Gaussian via an activation function. Compared with classic spike-and-slab priors, the neuronized priors achieve the same explicit variable selection without employing any latent indicator variables, which results in both more efficient and flexible posterior sampling and more effective posterior modal estimation. Theoretically, we provide specific conditions on the neuronized formulation to achieve the optimal posterior contraction rate, and show that a broadly applicable MCMC algorithm achieves an exponentially fast convergence rate under the neuronized formulation. We also examine various simulated and real data examples and demonstrate that using the neuronization representation is computationally more or comparably efficient than its standard counterpart in all well-known cases. An R package NPrior is provided for using neuronized priors in Bayesian linear regression.