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大型稀疏张量的贝叶斯分解AI 解读

It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics. The most common low rank tensor factorization relies on parallel factor analysis (PARAFAC), which expresses a rank k tensor as a sum of rank one tensors. When observations are only available for a tiny subset of the cells of a big tensor,…

融合机理信息的层级高斯过程AI 解读

The statistics literature on functional data analysis focuses primarily on flexible black-box approaches, which are designed to allow individual curves to have essentially any shape while characterizing variability. Such methods typically cannot incorporate mechanistic information, which is commonly expressed in terms of differential equations. Motivated by studies of muscle activation, we propose a nonparametric Bayesian approach that takes into account mechanistic…

预测变量轨迹聚类间响应密度变化的贝叶斯推断AI 解读

In epidemiology, it is often of interest to assess how individuals with different trajectories over time in an environmental exposure or biomarker differ with respect to a continuous response. For ease in interpretation and presentation of results, epidemiologists typically categorize predictors prior to analysis. To extend this approach to time-varying predictors, one can cluster individuals by their predictor trajectory, with the cluster index included as a predictor in a…