用于未对齐纵向二元数据的带回归的广义贝叶斯聚类

中文摘要 AI 辅助

受人类癫痫项目的癫痫发作日记数据启发，我们提出了一种用于未对齐纵向二元结局的带回归的广义贝叶斯聚类模型。癫痫发作日记数据稀疏、观测不规则，且患者间差异极大。单一完全指定的生成模型往往要么设定错误，要么计算效率低下。我们通过两种策略应对这一挑战：我们建立一种基于聚类的回归，即使用混合模型的模型基聚类；对于后者，我们采用广义贝叶斯视角，用基于损失的更新替代全似然，该更新使用广义似然。我们结合轨迹相似性损失和回归损失，使聚类同时受轨迹相似性和结局预测的指导。轨迹相似性损失通过将每条轨迹表示为子序列（称为“reads”）的（经验）分布来构建，然后基于这些经验分布之间的切片沃尔什斯坦因距离定义，该损失允许对不规则观测或时间未对齐的序列进行无对齐比较，且其缩放与轨迹长度呈拟线性关系。回归损失为probit回归的负对数似然。我们通过在混合测度上使用狄利克雷过程先验来定义聚类特定参数的先验。

英文摘要

We propose a generalized Bayesian clustering with regression model for unaligned longitudinal binary outcomes, motivated by seizure diary data from the Human Epilepsy Project. Seizure diaries are sparse, irregularly observed, and vary enormously across patients. A single fully-specified generative model tends to be either misspecified or computationally inefficient. We address the challenge by two strategies. We set up a regression by way of clustering as model-based clustering using a mixture model. For the latter, we take a generalized Bayesian perspective which replaces the full likelihood with a loss-based update using a generalized likelihood. We combine a trajectory similarity loss and a regression loss, so that clustering is informed by both trajectory similarity and the prediction of outcomes The trajectory similarity loss is constructed by representing each trajectory as an (empirical) distribution of subsequences, called reads, and then is defined based on the sliced Wasserstein distance between these empirical distributions. This loss allows alignment-free comparison of sequences that are irregularly observed or temporally misaligned, and it scales quasi-linearly in trajectory length. The regression loss is the negative log-likelihood of a probit regression. A prior on the cluster-specific parameters is defined by way of a Dirichlet process prior on the mixing measure.

发表机构

• Texas A&M University（德克萨斯农工大学）
• University of Colorado Anschutz（科罗拉多大学安舒茨分校）
• University of Texas at Austin（德克萨斯大学奥斯汀分校）

机构由 AI 辅助整理，请以论文原文为准。

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29 pages, 6 figures