5. Tensor regression

TensorLy also allows you to perform Tensor Regression.

5.1. Setting

Tensor regression is available in the module tensorly.regression.

Given a series of N tensor samples/observations, \tilde X_i, i={1, \cdots, N}, and corresponding labels y_i, i={1, \cdots, N}, we want to find the weight tensor \tilde W such that, for each i={1, \cdots, N}:

y_i = \langle \tilde X_i, \tilde W \rangle

We additionally impose that \tilde W be a rank-r CP decomposition (Kruskal regression) or a rank (r_1, \cdots, r_N)-Tucker decomposition (Tucker regression). For a detailed explanation on tensor regression, please refer to [1].

TensorLy implements both types of tensor regression as scikit-learn-like estimators.

For instance, Krusal regression is available through the tensorly.regression.KruskalRegression object. This implements a fit method that takes as parameters X, the data tensor which first dimension is the number of samples, and y, the corresponding vector of labels.

Given a set of testing samples, you can use the predict method to obtain the corresponding predictions from the model.

5.2. References

[1]W. Guo, I. Kotsia, and I. Patras. “Tensor Learning for Regression”, IEEE Transactions on Image Processing 21.2 (2012), pp. 816–827