  Efficient modelling of feature interactions underpins supervised learning for
non-sequential tasks, characterized by a lack of inherent ordering of features
(variables). The brute force approach of learning a parameter for each
interaction of every order comes at an exponential computational and memory
cost (Curse of Dimensionality). To alleviate this issue, it has been proposed
to implicitly represent the model parameters as a tensor, the order of which is
equal to the number of features; for efficiency, it can be further factorized
into a compact Tensor Train (TT) format. However, both TT and other Tensor
Networks (TNs), such as Tensor Ring and Hierarchical Tucker, are sensitive to
the ordering of their indices (and hence to the features). To establish the
desired invariance to feature ordering, we propose to represent the weight
tensor through the Canonical Polyadic (CP) Decomposition (CPD), and introduce
the associated inference and learning algorithms, including suitable
regularization and initialization schemes. It is demonstrated that the proposed
CP-based predictor significantly outperforms other TN-based predictors on
sparse data while exhibiting comparable performance on dense non-sequential
tasks. Furthermore, for enhanced expressiveness, we generalize the framework to
allow feature mapping to arbitrarily high-dimensional feature vectors. In
conjunction with feature vector normalization, this is shown to yield dramatic
improvements in performance for dense non-sequential tasks, matching models
such as fully-connected neural networks.
