The underlying assumption of recent federated learning (FL) paradigms is that local models usually share the same network architecture as the global model, which becomes impractical for mobile and IoT devices with different setups of hardware and infrastructure. A scalable federated learning framework should address heterogeneous clients equipped with different computation and communication capabilities. To this end, this paper proposes FedHM, a novel federated model compression framework that distributes the heterogeneous low-rank models to clients and then aggregates them into a global full-rank model. Our solution enables the training of heterogeneous local models with varying computational complexities and aggregates a single global model. Furthermore, FedHM not only reduces the computational complexity of the device, but also reduces the communication cost by using low-rank models. Extensive experimental results demonstrate that our proposed \system outperforms the current pruning-based FL approaches in terms of test Top-1 accuracy (4.6% accuracy gain on average), with smaller model size (1.5x smaller on average) under various heterogeneous FL settings.

Robots can be used to collect environmental data in regions that are difficult for humans to traverse. However, limitations remain in the size of region that a robot can directly observe per unit time. We introduce a method for selecting a limited number of observation points in a large region, from which we can predict the state of unobserved points in the region. We combine a low rank model of a target attribute with an information-maximizing path planner to predict the state of the attribute throughout a region. Our approach is agnostic to the choice of target attribute and robot monitoring platform. We evaluate our method in simulation on two real-world environment datasets, each containing observations from one to two million possible sampling locations. We compare against a random sampler and four variations of a baseline sampler from the ecology literature. Our method outperforms the baselines in terms of average Fisher information gain per samples taken and performs comparably for average reconstruction error in most trials.

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, $k$-means, $k$-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.