发表机构
University of Calgary（卡尔加里大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对相关预测变量下的稀疏回归，提出自适应混合变分推断，直接联合细化包含指标和系数，在模拟中优于平均场，并建立了理论保证。
AI 中文摘要
相关预测变量可以支持具有相似预测的竞争性稀疏解释，使得关于变量包含的联合不确定性难以通过平均场近似来捕获。我们开发了一种自适应拟合程序，用于高斯回归中具有点质量尖峰-板先验的乘积分布混合。它直接在包含指标和活跃系数上最小化反向Kullback-Leibler散度，随着混合的增长联合细化组件参数和权重。这避免了在独立增广下对未使用的潜在系数的额外散度惩罚。我们的分析将近似精度与混合大小、支持覆盖以及支持内的依赖性联系起来，并在先验、后验浓度和变分误差的显式条件下建立了收缩性、选择一致性和Bernstein-von Mises近似。在所有250个具有精确后验参考的模拟数据集中，混合相对于多起点平均场减少了包含概率、分组支持概率和系数协方差的误差。在固定混合大小和共同初始化下的比较表明，直接联合细化优于增广或受限细化在后验散度上的表现。然而，完整的逐步拟合在接近共线性时可能更准确。结果支持直接联合细化用于后验近似，同时表明局部增益并不能确保完整自适应搜索的优越性。
英文摘要
Correlated predictors can support competing sparse explanations with similar predictions, making joint uncertainty about variable inclusion difficult to capture with mean-field approximations. We develop an adaptive fitting procedure for mixtures of product distributions in Gaussian regression with a point-mass spike-and-slab prior. It minimizes reverse Kullback-Leibler divergence directly on inclusion indicators and active coefficients, jointly refining component parameters and weights as the mixture grows. This avoids an additional divergence penalty on unused latent coefficients under independent augmentation. Our analysis relates approximation accuracy to mixture size, support coverage and dependence within supports, and establishes contraction, selection consistency and a Bernstein-von Mises approximation under explicit conditions on the prior, posterior concentration and variational error. On all 250 simulated datasets with exact posterior references, mixtures reduce errors in inclusion probabilities, grouped support probabilities and coefficient covariance relative to multistart mean field. Comparisons at fixed mixture size and common initialization favor direct joint refinement over augmented or restricted refinement in posterior divergence. Complete stagewise fitting can nevertheless be more accurate near collinearity. The results support direct joint refinement for posterior approximation while showing that local gains do not ensure superiority of the full adaptive search.
Comments25 pages, 3 figures, 7 tables
