This is an implementation of Exponential Machines from the paper "Tensor Train polynomial models via Riemannian optimization" [1605.03795].

The main idea is to use a full exponentially-large polynomial model with all interactions of every order. To deal with exponential complexity we represent and learn the tensor of parameters in the Tensor Train (TT) format.

• The Python version of the TT-toolbox.
• Scikit-learn
• NumPy
• Numba
• Accelerate is not required, but makes everything faster.

The interface is the same as of Scikit-learn models. To train a model with logistic loss, TT-rank equal 4 using the Riemannian solver for 10 iteration use the following code:

model = TTRegression('all-subsets', 'logistic', rank=4, solver='riemannian-sgd', max_iter=10, verbose=2)
model.fit(X_train, y_train)

The code to reproduce the experiments is in the experiments folder, one Jupyter Notebook per each experiment.