Sparse Tensor Additive Regression

In such applications, a fundamental statistical tool is tensor regression, a modern high-dimensional regression method that relates a scalar response to tensor covariates. For example, in neuroimaging analysis, an important objective is to predict clinical outcomes using subjects' brain imaging data. This can be formulated as a tensor regression problem by treating the clinical outcomes as the response and the brain images as the tensor covariates. Another example is in the study of how advertisement placement affect users' clicking behavior in online advertising. This again can be formulated as a tensor regression problem by treating the daily overall click-through rate (CTR) as the response and the tensor that summarizes the impressions (i.e., view counts) of different advertisements on different devices (e.g., phone, computer, etc.) as the covariate. In Section 6, we consider such an online advertising application.