The emerging paradigm of federated learning strives to enable collaborative training of machine learning models on the network edge without centrally aggregating raw data and hence, improving data privacy. This sharply deviates from traditional machine learning and necessitates the design of algorithms robust to various sources of heterogeneity. Specifically, statistical heterogeneity of data across user devices can severely degrade the performance of standard federated averaging for traditional machine learning applications like personalization with deep learning. This paper pro-posesFedPer, a base + personalization layer approach for federated training of deep feedforward neural networks, which can combat the ill-effects of statistical heterogeneity. We demonstrate effectiveness ofFedPerfor non-identical data partitions ofCIFARdatasetsand on a personalized image aesthetics dataset from Flickr.