潜在空间投影预测推理
Latent space projection predictive inference
摘要：
给定一个包含所有可用变量的参考模型，投影预测推理用仅包含所有变量的子集的约束投影替换其后验。我们扩展投影预测推理，使计算效率的变量和结构选择模型以外的指数家庭。通过采用潜在空间投影预测的观点，我们能够：1）提出一个统一和通用的框架来进行复杂模型中的变量选择，同时充分尊重原始模型结构，2）正确识别相关结构并保留原始模型的后验不确定性，以及3）也为指数族中的非高斯模型提供改进的方法。我们证明了我们的方法的优越性能，通过彻底的测试和比较流行的变量选择方法在广泛的设置，包括现实的数据集。我们的研究结果表明，我们的方法成功地恢复了复杂模型中的相关条款和模型结构，选择的变量比竞争对手的方法更少的现实数据集。
英文摘要：
Given a reference model that includes all the available variables, projection predictive inference replaces its posterior with a constrained projection including only a subset of all variables. We extend projection predictive inference to enable computationally efficient variable and structure selection in models outside the exponential family. By adopting a latent space projection predictive perspective we are able to: 1) propose a unified and general framework to do variable selection in complex models while fully honouring the original model structure, 2) properly identify relevant structure and retain posterior uncertainties from the original model, and 3) provide an improved approach also for non-Gaussian models in the exponential family. We demonstrate the superior performance of our approach by thoroughly testing and comparing it against popular variable selection approaches in a wide range of settings, including realistic data sets. Our results show that our approach successfully recovers relevant terms and model structure in complex models, selecting less variables than competing approaches for realistic datasets.
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