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Big Model analytics tackles the training of massive models that go beyond theavailable memory of a single computing device, e.g., CPU or GPU. It generalizesBig Data analytics which is targeted at how to train memory-resident modelsover out-of-memory training data. In this paper, we propose an in-databasesolution for Big Model analytics. We identify dot-product as the primaryoperation for training generalized linear models and introduce the firstarray-relation dot-product join database operator between a set of sparsearrays and a dense relation. This is a constrained formulation of theextensively studied sparse matrix vector multiplication (SpMV) kernel. Theparamount challenge in designing the dot-product join operator is how tooptimally schedule access to the dense relation based on the non-contiguousentries in the sparse arrays. We prove that this problem is NP-hard and proposea practical solution characterized by two technical contributions---dynamicbatch processing and array reordering. We devise three heuristics -- LSH,Radix, and K-center -- for array reordering and analyze them thoroughly. Weexecute extensive experiments over synthetic and real data that confirm theminimal overhead the operator incurs when sufficient memory is available andthe graceful degradation it suffers as memory becomes scarce. Moreover,dot-product join achieves an order of magnitude reduction in execution timeover alternative in-database solutions.

Dot-Product Join: An Array-Relation Join Operator for Big Model Analytics