  Large-scale machine learning and data mining methods routinely distribute
computations across multiple agents to parallelize processing. The time
required for the computations at the agents is affected by the availability of
local resources and/or poor channel conditions giving rise to the "straggler
problem". As a remedy to this problem, we employ Unequal Error Protection (UEP)
codes to obtain an approximation of the matrix product in the distributed
computation setting to provide higher protection for the blocks with higher
effect on the final result. We characterize the performance of the proposed
approach from a theoretical perspective by bounding the expected reconstruction
error for matrices with uncorrelated entries. We also apply the proposed coding
strategy to the computation of the back-propagation step in the training of a
Deep Neural Network (DNN) for an image classification task in the evaluation of
the gradients. Our numerical experiments show that it is indeed possible to
obtain significant improvements in the overall time required to achieve the DNN
training convergence by producing approximation of matrix products using UEP
codes in the presence of stragglers.
