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
# License: BSD 3 clause
[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(f"\nConverged in {iteration} iterations")
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)