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We propose a nonparametric factorization approach for sparsely observedtensors. The sparsity does not mean zero-valued entries are massive ordominated. Rather, it implies the observed entries are very few, and even fewerwith the growth of the tensor; this is ubiquitous in practice. Compared withthe existent works, our model not only leverages the structural informationunderlying the observed entry indices, but also provides extra interpretabilityand flexibility -- it can simultaneously estimate a set of location factorsabout the intrinsic properties of the tensor nodes, and another set ofsociability factors reflecting their extrovert activity in interacting withothers; users are free to choose a trade-off between the two types of factors.Specifically, we use hierarchical Gamma processes and Poisson random measuresto construct a tensor-valued process, which can freely sample the two types offactors to generate tensors and always guarantees an asymptotic sparsity. Wethen normalize the tensor process to obtain hierarchical Dirichlet processes tosample each observed entry index, and use a Gaussian process to sample theentry value as a nonlinear function of the factors, so as to capture both thesparse structure properties and complex node relationships. For efficientinference, we use Dirichlet process properties over finite sample partitions,density transformations, and random features to develop a stochasticvariational estimation algorithm. We demonstrate the advantage of our method inseveral benchmark datasets.

Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes