Conditional Probability Tensor Decompositions for Multivariate Categorical Response Regression
提出一种新方法，通过功能概率张量分解对多个分类响应变量的联合概率质量函数建模，适用于响应变量多、类别多、预测变量维度高的场景，并给出可扩展的惩罚期望最大化算法。
In many modern regression applications, the response consists of multiple categorical random variables whose probability mass is a function of a common set of predictors. In this article, we propose a new method for modeling such a probability mass function in settings where the number of response variables, the number of categories per response, and the dimension of the predictor are large. Our method relies on a functional probability tensor decomposition: a decomposition of a tensor-valued function such that its range is a restricted set of low-rank probability tensors. This decomposition is motivated by the connection between the conditional independence of responses, or lack thereof, and their probability tensor rank. We show that the model implied by such a low-rank functional probability tensor decomposition can be interpreted in terms of a mixture of regressions and can thus be fit using maximum likelihood. We derive an efficient and scalable penalized expectation maximization algorithm to fit this model and examine its statistical properties. We demonstrate the encouraging performance of our method through both simulation studies and an application to modeling the functional classes of genes.