Federated Learning of Tensor Generalized Linear Models with low Separation Rank

Biomedical imaging systems often produce multidimensional signals (tensors). The high expense of image acquisition limits sample sizes and privacy regulations can prevent centralizing data from multiple sites. Federated learning can allow researchers to form research consortia to perform joint analyses without centralizing data. Standard analysis approaches for tensors often vectorize the data, resulting in high dimensional models for which the total sample size across a consortium may be insufficient. We propose a federated algorithm for tensor regression using generalized linear models (GLMs) based on a recently proposed centralized method using low separation rank (LSR) tensor decompositions. Our results show that by balancing the ratio of local update steps to rounds of communication, we can achieve results similar to those of a centralized algorithm using the entire data.