2 research outputs found
Towards Probabilistic Tensor Canonical Polyadic Decomposition 2.0: Automatic Tensor Rank Learning Using Generalized Hyperbolic Prior
Tensor rank learning for canonical polyadic decomposition (CPD) has long been
deemed as an essential but challenging problem. In particular, since the tensor
rank controls the complexity of the CPD model, its inaccurate learning would
cause overfitting to noise or underfitting to the signal sources, and even
destroy the interpretability of model parameters. However, the optimal
determination of a tensor rank is known to be a non-deterministic
polynomial-time hard (NP-hard) task. Rather than exhaustively searching for the
best tensor rank via trial-and-error experiments, Bayesian inference under the
Gaussian-gamma prior was introduced in the context of probabilistic CPD
modeling and it was shown to be an effective strategy for automatic tensor rank
determination. This triggered flourishing research on other structured tensor
CPDs with automatic tensor rank learning. As the other side of the coin, these
research works also reveal that the Gaussian-gamma model does not perform well
for high-rank tensors or/and low signal-to-noise ratios (SNRs). To overcome
these drawbacks, in this paper, we introduce a more advanced generalized
hyperbolic (GH) prior to the probabilistic CPD model, which not only includes
the Gaussian-gamma model as a special case, but also provides more
flexibilities to adapt to different levels of sparsity. Based on this novel
probabilistic model, an algorithm is developed under the framework of
variational inference, where each update is obtained in a closed-form.
Extensive numerical results, using synthetic data and real-world datasets,
demonstrate the excellent performance of the proposed method in learning both
low as well as high tensor ranks even for low SNR cases