# Source code for tensorly.regression.cp_regression

```import numpy as np
from ..base import partial_tensor_to_vec, partial_unfold
from ..tenalg import khatri_rao
from ..cp_tensor import cp_to_tensor, cp_to_vec
from .. import backend as T
from ..utils import DefineDeprecated

# Author: Jean Kossaifi

[docs]class CPRegressor():
"""CP tensor regression

Learns a low rank CP tensor weight

Parameters
----------
weight_rank : int
rank of the CP decomposition of the regression weights
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_rank, tol=10e-7, reg_W=1, n_iter_max=100, random_state=None, verbose=1):
self.weight_rank = weight_rank
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_rank', '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
tensor data of shape (n_samples, N1, ..., NS)
y : 1D-array of shape (n_samples, )
labels associated with each sample

Returns
-------
self
"""
rng = T.check_random_state(self.random_state)

# Initialise randomly the weights
W = []
for i in range(1, T.ndim(X)):  # The first dimension of X is the number of samples
W.append(T.tensor(rng.randn(X.shape[i], self.weight_rank), **T.context(X)))

# Norm of the weight tensor at each iteration
norm_W = []
weights = T.ones(self.weight_rank, **T.context(X))

for iteration in range(self.n_iter_max):

# Optimise each factor of W
for i in range(len(W)):
phi = T.reshape(
T.dot(partial_unfold(X, i, skip_begin=1),
khatri_rao(W, skip_matrix=i)),
(X.shape[0], -1))
inv_term = T.dot(T.transpose(phi), phi) + self.reg_W*T.tensor(np.eye(phi.shape[1]), **T.context(X))
W[i] = T.reshape(T.solve(inv_term, T.dot(T.transpose(phi), y)), (X.shape[i + 1], self.weight_rank))

weight_tensor_ = cp_to_tensor((weights, 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.cp_weight_ = (weights, W)

self.vec_W_ = cp_to_vec((weights, 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_)

KruskalRegressor = DefineDeprecated('KruskalRegressor', CPRegressor)
```