  Tensor decompositions have proven to be effective in analyzing the structure
of multidimensional data. However, most of these methods require a key
parameter: the number of desired components. In the case of the
CANDECOMP/PARAFAC decomposition (CPD), the ideal value for the number of
components is known as the canonical rank and greatly affects the quality of
the decomposition results. Existing methods use heuristics or Bayesian methods
to estimate this value by repeatedly calculating the CPD, making them extremely
computationally expensive. In this work, we propose FRAPPE, the first method to
estimate the canonical rank of a tensor without having to compute the CPD. This
method is the result of two key ideas. First, it is much cheaper to generate
synthetic data with known rank compared to computing the CPD. Second, we can
greatly improve the generalization ability and speed of our model by generating
synthetic data that matches a given input tensor in terms of size and sparsity.
We can then train a specialized single-use regression model on a synthetic set
of tensors engineered to match a given input tensor and use that to estimate
the canonical rank of the tensor - all without computing the expensive CPD.
FRAPPE is over 24 times faster than the best-performing baseline and exhibits a
10% improvement in MAPE on a synthetic dataset. It also performs as well as or
better than the baselines on real-world datasets.
