Source code for tensorly.regression.tucker_regression

import numpy as np
from ..base import unfold, vec_to_tensor
from ..base import partial_tensor_to_vec, partial_unfold
from ..tenalg import kronecker
from ..tucker_tensor import tucker_to_tensor, tucker_to_vec
from .. import backend as T

# Author: Jean Kossaifi

# License: BSD 3 clause


[docs]class TuckerRegressor(): """Tucker tensor regression Learns a low rank Tucker weight for the regression Parameters ---------- weight_ranks : int list dimension of each mode of the core Tucker weight tol : float convergence value reg_W : int, optional, default is 1 regularisation on the weights n_iter_max : int, optional, default is 100 maximum number of iteration random_state : None, int or RandomState, optional, default is None verbose : int, default is 1 level of verbosity """ def __init__(self, weight_ranks, tol=10e-7, reg_W=1, n_iter_max=100, random_state=None, verbose=1): self.weight_ranks = weight_ranks self.tol = tol self.reg_W = reg_W self.n_iter_max = n_iter_max self.random_state = random_state self.verbose = verbose
[docs] def get_params(self, **kwargs): """Returns a dictionary of parameters """ params = ['weight_ranks', 'tol', 'reg_W', 'n_iter_max', 'random_state', 'verbose'] return {param_name: getattr(self, param_name) for param_name in params}
[docs] def set_params(self, **parameters): """Sets the value of the provided parameters""" for parameter, value in parameters.items(): setattr(self, parameter, value) return self
[docs] def fit(self, X, y): """Fits the model to the data (X, y) Parameters ---------- X : ndarray of shape (n_samples, N1, ..., NS) tensor data y : array of shape (n_samples) labels associated with each sample Returns ------- self """ rng = T.check_random_state(self.random_state) # Initialise randomly the weights G = T.tensor(rng.randn(*self.weight_ranks), **T.context(X)) W = [] for i in range(1, T.ndim(X)): # First dimension of X = number of samples W.append(T.tensor(rng.randn(X.shape[i], G.shape[i - 1]), **T.context(X))) # Norm of the weight tensor at each iteration norm_W = [] for iteration in range(self.n_iter_max): # Optimise modes of W for i in range(len(W)): phi = partial_tensor_to_vec( T.dot(partial_unfold(X, i), T.dot(kronecker(W, skip_matrix=i), T.transpose(unfold(G, i))))) # Regress phi on y: we could call a package here, e.g. scikit-learn inv_term = T.dot(T.transpose(phi), phi) +\ self.reg_W * T.tensor(np.eye(phi.shape[1]), **T.context(X)) W_i = vec_to_tensor(T.solve(inv_term, T.dot(T.transpose(phi), y)), (X.shape[i + 1], G.shape[i])) W[i] = W_i phi = T.dot(partial_tensor_to_vec(X), kronecker(W)) G = vec_to_tensor(T.solve(T.dot(T.transpose(phi), phi) +\ self.reg_W * T.tensor(np.eye(phi.shape[1]), **T.context(X)), T.dot(T.transpose(phi), y)), G.shape) weight_tensor_ = tucker_to_tensor((G, W)) norm_W.append(T.norm(weight_tensor_, 2)) # Convergence check if iteration > 1: weight_evolution = abs(norm_W[-1] - norm_W[-2]) / norm_W[-1] if (weight_evolution <= self.tol): if self.verbose: print('\nConverged in {} iterations'.format(iteration)) break self.weight_tensor_ = weight_tensor_ self.tucker_weight_ = (G, W) self.vec_W_ = tucker_to_vec((G, W)) self.n_iterations_ = iteration + 1 self.norm_W_ = norm_W return self
[docs] def predict(self, X): """Returns the predicted labels for a new data tensor Parameters ---------- X : ndarray tensor data of shape (n_samples, N1, ..., NS) """ return T.dot(partial_tensor_to_vec(X), self.vec_W_)