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In this paper, we study the information transmission problem under thedistributed learning framework, where each worker node is merely permitted totransmit a $m$-dimensional statistic to improve learning results of the targetnode. Specifically, we evaluate the corresponding expected population risk(EPR) under the regime of large sample sizes. We prove that the performance canbe enhanced since the transmitted statistics contribute to estimating theunderlying distribution under the mean square error measured by the EPR normmatrix. Accordingly, the transmitted statistics correspond to the eigenvectorsof this matrix, and the desired transmission allocates these eigenvectors amongthe statistics such that the EPR is minimal. Moreover, we provide theanalytical solution of the desired statistics for single-node and two-nodetransmission, where a geometrical interpretation is given to explain theeigenvector selection. For the general case, an efficient algorithm that canoutput the allocation solution is developed based on the node partitions.

An Information-theoretic Method for Collaborative Distributed Learning with Limited Communication