  Federated recommender systems have distinct advantages in terms of privacy
protection over traditional recommender systems that are centralized at a data
center. However, previous work on federated recommender systems does not fully
consider the limitations of storage, RAM, energy and communication bandwidth in
a mobile environment. The scales of the models proposed are too large to be
easily run on mobile devices. And existing federated recommender systems need
to fine-tune recommendation models on each device, making it hard to
effectively exploit collaborative filtering information among users/devices.
Our goal in this paper is to design a novel federated learning framework for
rating prediction (RP) for mobile environments. We introduce a federated matrix
factorization (MF) framework, named meta matrix factorization (MetaMF). Given a
user, we first obtain a collaborative vector by collecting useful information
with a collaborative memory module. Then, we employ a meta recommender module
to generate private item embeddings and a RP model based on the collaborative
vector in the server. To address the challenge of generating a large number of
high-dimensional item embeddings, we devise a rise-dimensional generation
strategy that first generates a low-dimensional item embedding matrix and a
rise-dimensional matrix, and then multiply them to obtain high-dimensional
embeddings. We use the generated model to produce private RPs for the given
user on her device. MetaMF shows a high capacity even with a small RP model,
which can adapt to the limitations of a mobile environment. We conduct
extensive experiments on four benchmark datasets to compare MetaMF with
existing MF methods and find that MetaMF can achieve competitive performance.
Moreover, we find MetaMF achieves higher RP performance over existing federated
methods by better exploiting collaborative filtering among users/devices.
