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Distributed machine learning (ML) can bring more computational resources to bear than single-machine learning, thus enabling reductions in training time. Distributed learning partitions models and data over many machines, allowing model and dataset sizes beyond the available compute power and memory of a single machine. In practice though, distributed ML is challenging when distribution is mandatory, rather than chosen by the practitioner. In such scenarios, data could unavoidably be separated among workers due to limited memory capacity per worker or even because of data privacy issues. There, existing distributed methods will utterly fail due to dominant transfer costs across workers, or do not even apply. We propose a new approach to distributed fully connected neural network learning, called independent subnet training (IST), to handle these cases. In IST, the original network is decomposed into a set of narrow subnetworks with the same depth. These subnetworks are then trained locally before parameters are exchanged to produce new subnets and the training cycle repeats. Such a naturally "model parallel" approach limits memory usage by storing only a portion of network parameters on each device. Additionally, no requirements exist for sharing data between workers (i.e., subnet training is local and independent) and communication volume and frequency are reduced by decomposing the original network into independent subnets. These properties of IST can cope with issues due to distributed data, slow interconnects, or limited device memory, making IST a suitable approach for cases of mandatory distribution. We show experimentally that IST results in training times that are much lower than common distributed learning approaches. 

When numerical and machine learning (ML) computations are expressed relationally, classical query execution strategies (hash-based joins and aggregations) can do a poor job distributing the computation. In this paper, we propose a two-phase execution strategy for numerical computations that are expressed relationally, as aggregated join trees (that is, expressed as a series of relational joins followed by an aggregation). In a pilot run, lineage information is collected; this lineage is used to optimally plan the computation at the level of individual records. Then, the computation is actually executed. We show experimentally that a relational system making use of this two-phase strategy can be an excellent platform for distributed ML computations.