5. 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 $i=1,\cdots ,N$:

We additionally impose that $\tilde{W}$ be a rank-r CP decomposition (CP 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.CPRegression object. This implements a fit method that takes as parameters X, the data tensor whose 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