Revision **1295ccb09626f89f20d0c0183d618f96b4833bf1** authored by Jean Kossaifi on **08 May 2018, 21:04:53 UTC**, committed by Jean Kossaifi on **08 May 2018, 22:15:23 UTC**

kruskal_regression.py

```
import numpy as np
from ..base import partial_tensor_to_vec, partial_unfold
from ..tenalg import khatri_rao
from ..kruskal_tensor import kruskal_to_tensor, kruskal_to_vec
from ..random import check_random_state
from .. import backend as T
# Author: Jean Kossaifi
# License: BSD 3 clause
class KruskalRegressor():
"""Kruskal 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
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}
def set_params(self, **parameters):
"""Sets the value of the provided parameters"""
for parameter, value in parameters.items():
setattr(self, parameter, value)
return self
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 = 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 = []
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_ = kruskal_to_tensor(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.kruskal_weight_ = W
self.vec_W_ = kruskal_to_vec(W)
self.n_iterations_ = iteration + 1
self.norm_W_ = norm_W
return self
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_)
```

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