Stochastic Variational Inference for Latent Gaussian Models

在这个项目中，我们将开发一个通用和通用的随机变分推理(SVI)方法，用于不同类型的潜在高斯模型(LGM)的近似贝叶斯推理。将LGM作为底层模型类将使我们能够开发出足够具体的方法，与基于马尔可夫链蒙特卡罗(MCMC)模拟的贝叶斯推理相比，可以实现效率提高，同时保持关于变量族的足够灵活性，例如在通用黑盒变分推理中。多元分布LGM和贝叶斯稀疏回归将被认为是在具有挑战性的案例研究中应用的特例。多变量分布回归中的随机变分推断将使我们能够基于大型医学数据集对多维营养不良和贫困风险以及多变量健康结果进行分析。对于每个协变量效应，贝叶斯稀疏线性回归都需要一个二元潜在包含变量。问题的离散性使得它不仅对于基于MCMC的方法，而且对于最先进的SVI都是低效的。我们将开发一种适用于离散变量的新估计器，并将该估计器应用于人类遗传学预测表达数量性状基因座(EQTL)遗传变异。

In this project, we will develop a generic and versatile stochastic variational inference (SVI) approach for approximate Bayesian inference for different types of Latent Gaussian Models (LGMs). Focusing on LGMs as the underlying model class will enable us to develop approaches that are specific enough to achieve efficiency gains compared to Bayesian inference based on Markov chain Monte Carlo (MCMC) simulations while at the same time maintaining enough flexibility with respect to the variational family such as in generic black box variational inference. Multivariate distributional LGMs and Bayesian sparse regression will be considered as special cases for the application in challenging case studies. Stochastic variational inference in multivariate distributional regression will allow us to perform analyses of multidimensional malnutrition and poverty risks as well as multivariate health outcomes based on large medical data sets. Bayesian sparse linear regression requires a binary latent inclusion variable for each of the covariate effects. The discreteness of the problem renders it inefficient not only for MCMC-based methods but also for state-of-the-art SVI. We will develop a novel estimator that is applicable to discrete variables and apply this estimator in human genetics to predict expression quantitative trait locus (eQTL) genetic variants.