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(f"\nConverged in {iteration} iterations")
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_)