def test_train_intercept(self):
a1_mat = DenseMatrix(np.mat([[3,4],[5,6]]))
a2_mat = DenseMatrix(np.mat([[1,2],[3,4]]))
train_data = [("a1", "man", "a1_man"),
("a2", "car", "a2_car"),
("a1", "boy", "a1_boy"),
("a2", "boy", "a2_boy")
]
n_mat = DenseMatrix(np.mat([[13,21],[3,4],[5,6]]))
n_space = Space(n_mat, ["man", "car", "boy"], self.ft)
an1_mat = (a1_mat * n_mat.transpose()).transpose()
an2_mat = (a2_mat * n_mat.transpose()).transpose()
an_mat = an1_mat.vstack(an2_mat)
an_space = Space(an_mat, ["a1_man","a1_car","a1_boy","a2_man","a2_car","a2_boy"], self.ft)
#test train
model = LexicalFunction(learner=LstsqRegressionLearner(intercept=True))
model._MIN_SAMPLES = 1
model.train(train_data, n_space, an_space)
a_space = model.function_space
a1_mat.reshape((1,4))
#np.testing.assert_array_almost_equal(a1_mat.mat,
# a_space.cooccurrence_matrix.mat[0])
a2_mat.reshape((1,4))
#np.testing.assert_array_almost_equal(a2_mat.mat,
# a_space.cooccurrence_matrix.mat[1])
self.assertListEqual(a_space.id2row, ["a1", "a2"])
self.assertTupleEqual(a_space.element_shape, (2,3))
#test compose
a1_mat = DenseMatrix(np.mat([[3,4,5,6]]))
a2_mat = DenseMatrix(np.mat([[1,2,3,4]]))
a_mat = a_space.cooccurrence_matrix
a_space = Space(a_mat, ["a1", "a2"], [], element_shape=(2,3))
model = LexicalFunction(function_space=a_space, intercept=True)
model._MIN_SAMPLES = 1
comp_space = model.compose(train_data, n_space)
self.assertListEqual(comp_space.id2row, ["a1_man", "a2_car", "a1_boy", "a2_boy"])
self.assertListEqual(comp_space.id2column, [])
self.assertEqual(comp_space.element_shape, (2,))
np.testing.assert_array_almost_equal(comp_space.cooccurrence_matrix.mat,
an_mat[[0,4,2,5]].mat, 8)
def test_train_intercept(self):
a1_mat = DenseMatrix(np.mat([[3, 4], [5, 6]]))
a2_mat = DenseMatrix(np.mat([[1, 2], [3, 4]]))
train_data = [("a1", "man", "a1_man"),
("a2", "car", "a2_car"),
("a1", "boy", "a1_boy"),
("a2", "boy", "a2_boy")
]
n_mat = DenseMatrix(np.mat([[13, 21], [3, 4], [5, 6]]))
n_space = Space(n_mat, ["man", "car", "boy"], self.ft)
an1_mat = (a1_mat * n_mat.transpose()).transpose()
an2_mat = (a2_mat * n_mat.transpose()).transpose()
an_mat = an1_mat.vstack(an2_mat)
an_space = Space(an_mat, ["a1_man", "a1_car", "a1_boy", "a2_man", "a2_car", "a2_boy"], self.ft)
#test train
model = LexicalFunction(learner=LstsqRegressionLearner(intercept=True))
model.train(train_data, n_space, an_space)
a_space = model.function_space
a1_mat.reshape((1, 4))
#np.testing.assert_array_almost_equal(a1_mat.mat,
# a_space.cooccurrence_matrix.mat[0])
a2_mat.reshape((1, 4))
#np.testing.assert_array_almost_equal(a2_mat.mat,
# a_space.cooccurrence_matrix.mat[1])
self.assertListEqual(a_space.id2row, ["a1", "a2"])
self.assertTupleEqual(a_space.element_shape, (2, 3))
#test compose
a1_mat = DenseMatrix(np.mat([[3, 4, 5, 6]]))
a2_mat = DenseMatrix(np.mat([[1, 2, 3, 4]]))
a_mat = a_space.cooccurrence_matrix
a_space = Space(a_mat, ["a1", "a2"], [], element_shape=(2, 3))
model = LexicalFunction(function_space=a_space, intercept=True)
comp_space = model.compose(train_data, n_space)
self.assertListEqual(comp_space.id2row, ["a1_man", "a2_car", "a1_boy", "a2_boy"])
self.assertListEqual(comp_space.id2column, [])
self.assertEqual(comp_space.element_shape, (2,))
np.testing.assert_array_almost_equal(comp_space.cooccurrence_matrix.mat,
an_mat[[0, 4, 2, 5]].mat, 8)
def test_3d(self):
# setting up
v_mat = DenseMatrix(np.mat([[0,0,1,1,2,2,3,3],#hate
[0,1,2,4,5,6,8,9]])) #love
vo11_mat = DenseMatrix(np.mat([[0,11],[22,33]])) #hate boy
vo12_mat = DenseMatrix(np.mat([[0,7],[14,21]])) #hate man
vo21_mat = DenseMatrix(np.mat([[6,34],[61,94]])) #love boy
vo22_mat = DenseMatrix(np.mat([[2,10],[17,26]])) #love car
train_vo_data = [("hate_boy", "man", "man_hate_boy"),
("hate_man", "man", "man_hate_man"),
("hate_boy", "boy", "boy_hate_boy"),
("hate_man", "boy", "boy_hate_man"),
("love_car", "boy", "boy_love_car"),
("love_boy", "man", "man_love_boy"),
("love_boy", "boy", "boy_love_boy"),
("love_car", "man", "man_love_car")
]
# if do not find a phrase
# what to do?
train_v_data = [("love", "boy", "love_boy"),
("hate", "man", "hate_man"),
("hate", "boy", "hate_boy"),
("love", "car", "love_car")]
sentences = ["man_hate_boy", "car_hate_boy", "boy_hate_boy",
"man_hate_man", "car_hate_man", "boy_hate_man",
"man_love_boy", "car_love_boy", "boy_love_boy",
"man_love_car", "car_love_car", "boy_love_car" ]
n_mat = DenseMatrix(np.mat([[3,4],[1,2],[5,6]]))
n_space = Space(n_mat, ["man", "car", "boy"], self.ft)
s1_mat = (vo11_mat * n_mat.transpose()).transpose()
s2_mat = (vo12_mat * n_mat.transpose()).transpose()
s3_mat = (vo21_mat * n_mat.transpose()).transpose()
s4_mat = (vo22_mat * n_mat.transpose()).transpose()
s_mat = vo11_mat.nary_vstack([s1_mat,s2_mat,s3_mat,s4_mat])
s_space = Space(s_mat, sentences, self.ft)
#test train 2d
model = LexicalFunction(learner=LstsqRegressionLearner(intercept=False))
model._MIN_SAMPLES = 1
model.train(train_vo_data, n_space, s_space)
vo_space = model.function_space
self.assertListEqual(vo_space.id2row, ["hate_boy", "hate_man","love_boy", "love_car"])
self.assertTupleEqual(vo_space.element_shape, (2,2))
vo11_mat.reshape((1,4))
np.testing.assert_array_almost_equal(vo11_mat.mat,
vo_space.cooccurrence_matrix.mat[0])
vo12_mat.reshape((1,4))
np.testing.assert_array_almost_equal(vo12_mat.mat,
vo_space.cooccurrence_matrix.mat[1])
vo21_mat.reshape((1,4))
np.testing.assert_array_almost_equal(vo21_mat.mat,
vo_space.cooccurrence_matrix.mat[2])
vo22_mat.reshape((1,4))
np.testing.assert_array_almost_equal(vo22_mat.mat,
vo_space.cooccurrence_matrix.mat[3])
# test train 3d
model2 = LexicalFunction(learner=LstsqRegressionLearner(intercept=False))
model2._MIN_SAMPLES = 1
model2.train(train_v_data, n_space, vo_space)
v_space = model2.function_space
np.testing.assert_array_almost_equal(v_mat.mat,
v_space.cooccurrence_matrix.mat)
self.assertListEqual(v_space.id2row, ["hate","love"])
self.assertTupleEqual(v_space.element_shape, (2,2,2))
# test compose 3d
vo_space2 = model2.compose(train_v_data, n_space)
id2row1 = list(vo_space.id2row)
id2row2 = list(vo_space2.id2row)
id2row2.sort()
self.assertListEqual(id2row1, id2row2)
row_list = vo_space.id2row
vo_rows1 = vo_space.get_rows(row_list)
vo_rows2 = vo_space2.get_rows(row_list)
np.testing.assert_array_almost_equal(vo_rows1.mat, vo_rows2.mat,7)
self.assertTupleEqual(vo_space.element_shape, vo_space2.element_shape)
def test_3d(self):
# setting up
v_mat = DenseMatrix(np.mat([[0, 0, 1, 1, 2, 2, 3, 3], #hate
[0, 1, 2, 4, 5, 6, 8, 9]])) #love
vo11_mat = DenseMatrix(np.mat([[0, 11], [22, 33]])) #hate boy
vo12_mat = DenseMatrix(np.mat([[0, 7], [14, 21]])) #hate man
vo21_mat = DenseMatrix(np.mat([[6, 34], [61, 94]])) #love boy
vo22_mat = DenseMatrix(np.mat([[2, 10], [17, 26]])) #love car
train_vo_data = [("hate_boy", "man", "man_hate_boy"),
("hate_man", "man", "man_hate_man"),
("hate_boy", "boy", "boy_hate_boy"),
("hate_man", "boy", "boy_hate_man"),
("love_car", "boy", "boy_love_car"),
("love_boy", "man", "man_love_boy"),
("love_boy", "boy", "boy_love_boy"),
("love_car", "man", "man_love_car")
]
# if do not find a phrase
# what to do?
train_v_data = [("love", "boy", "love_boy"),
("hate", "man", "hate_man"),
("hate", "boy", "hate_boy"),
("love", "car", "love_car")]
sentences = ["man_hate_boy", "car_hate_boy", "boy_hate_boy",
"man_hate_man", "car_hate_man", "boy_hate_man",
"man_love_boy", "car_love_boy", "boy_love_boy",
"man_love_car", "car_love_car", "boy_love_car"]
n_mat = DenseMatrix(np.mat([[3, 4], [1, 2], [5, 6]]))
n_space = Space(n_mat, ["man", "car", "boy"], self.ft)
s1_mat = (vo11_mat * n_mat.transpose()).transpose()
s2_mat = (vo12_mat * n_mat.transpose()).transpose()
s3_mat = (vo21_mat * n_mat.transpose()).transpose()
s4_mat = (vo22_mat * n_mat.transpose()).transpose()
s_mat = vo11_mat.nary_vstack([s1_mat, s2_mat, s3_mat, s4_mat])
s_space = Space(s_mat, sentences, self.ft)
#test train 2d
model = LexicalFunction(learner=LstsqRegressionLearner(intercept=False))
model.train(train_vo_data, n_space, s_space)
vo_space = model.function_space
self.assertListEqual(vo_space.id2row, ["hate_boy", "hate_man", "love_boy", "love_car"])
self.assertTupleEqual(vo_space.element_shape, (2, 2))
vo11_mat.reshape((1, 4))
np.testing.assert_array_almost_equal(vo11_mat.mat,
vo_space.cooccurrence_matrix.mat[0])
vo12_mat.reshape((1, 4))
np.testing.assert_array_almost_equal(vo12_mat.mat,
vo_space.cooccurrence_matrix.mat[1])
vo21_mat.reshape((1, 4))
np.testing.assert_array_almost_equal(vo21_mat.mat,
vo_space.cooccurrence_matrix.mat[2])
vo22_mat.reshape((1, 4))
np.testing.assert_array_almost_equal(vo22_mat.mat,
vo_space.cooccurrence_matrix.mat[3])
# test train 3d
model2 = LexicalFunction(learner=LstsqRegressionLearner(intercept=False))
model2.train(train_v_data, n_space, vo_space)
v_space = model2.function_space
np.testing.assert_array_almost_equal(v_mat.mat,
v_space.cooccurrence_matrix.mat)
self.assertListEqual(v_space.id2row, ["hate", "love"])
self.assertTupleEqual(v_space.element_shape, (2, 2, 2))
# test compose 3d
vo_space2 = model2.compose(train_v_data, n_space)
id2row1 = list(vo_space.id2row)
id2row2 = list(vo_space2.id2row)
id2row2.sort()
self.assertListEqual(id2row1, id2row2)
row_list = vo_space.id2row
vo_rows1 = vo_space.get_rows(row_list)
vo_rows2 = vo_space2.get_rows(row_list)
np.testing.assert_array_almost_equal(vo_rows1.mat, vo_rows2.mat, 7)
self.assertTupleEqual(vo_space.element_shape, vo_space2.element_shape)
def tracenorm_regression(matrix_a , matrix_b, lmbd, iterations, intercept=False):
#log.print_info(logger, "In Tracenorm regression..", 4)
#log.print_matrix_info(logger, matrix_a, 5, "Input matrix A:")
#log.print_matrix_info(logger, matrix_b, 5, "Input matrix B:")
"""
Performs Trace Norm Regression.
This method uses approximate gradient descent
to solve the problem:
:math:`X = argmin(||AX - B||_2 + \\lambda||X||_*)`
where :math:`||X||_*` is the trace norm of :math:`X`, the sum of its
singular values.
It is implemented for dense matrices only.
The algorithm is the Extended Gradient Algorithm from (Ji and Ye, 2009).
Args:
matrix_a: input matrix A, of type Matrix
matrix_b: input matrix A, of type Matrix. If None, it is defined as matrix_a
lambda_: scalar, lambda parameter
intercept: bool. If True intercept is used. Optional, default False.
Returns:
solution X of type Matrix
"""
if intercept:
matrix_a = matrix_a.hstack(matrix_type(np.ones((matrix_a.shape[0],
1))))
if matrix_b == None:
matrix_b = matrix_a
# TODO remove this
matrix_a = DenseMatrix(matrix_a).mat
matrix_b = DenseMatrix(matrix_b).mat
# Matrix shapes
p = matrix_a.shape[0]
q = matrix_a.shape[1]
assert_same_shape(matrix_a, matrix_b, 0)
# Initialization of the algorithm
W = (1.0/p)* Linalg._kronecker_product(matrix_a)
# Sub-expressions reused at various places in the code
matrix_a_t = matrix_a.transpose()
at_times_a = np.dot(matrix_a_t, matrix_a)
# Epsilon: to ensure that our bound on the Lipschitz constant is large enough
epsilon_lbound = 0.05
# Expression of the bound of the Lipschitz constant of the cost function
L_bound = (1+epsilon_lbound)*2*Linalg._frobenius_norm_squared(at_times_a)
# Current "guess" of the local Lipschitz constant
L = 1.0
# Factor by which L should be increased when it happens to be too small
gamma = 1.2
# Epsilon to ensure that mu is increased when the inequality hold tightly
epsilon_cost = 0.00001
# Real lambda: resized according to the number of training samples (?)
lambda_ = lmbd*p
# Variables used for the accelerated algorithm (check the original paper)
Z = W
alpha = 1.0
# Halting condition
epsilon = 0.00001
last_cost = 1
current_cost = -1
linalg_error_caught = False
costs = []
iter_counter = 0
while iter_counter < iterations and (abs((current_cost - last_cost)/last_cost)>epsilon) and not linalg_error_caught:
sys.stdout.flush()
# Cost tracking
try:
next_W, tracenorm = Linalg._next_tracenorm_guess(matrix_a, matrix_b, lambda_, L, Z, at_times_a)
except LinAlgError:
print "LinAlgError caught in trace norm regression"
linalg_error_caught = True
break
last_cost = current_cost
current_fitness = Linalg._fitness(matrix_a, matrix_b, next_W)
current_cost = current_fitness + lambda_ * tracenorm
if iter_counter > 0: # The first scores are messy
cost_list = [L, L_bound, current_fitness, current_cost]
costs.append(cost_list)
while (current_fitness + epsilon_cost >=
Linalg._intermediate_cost(matrix_a, matrix_b, next_W, Z, L)):
if L > L_bound:
print "Trace Norm Regression: numerical error detected at iteration "+str(iter_counter)
break
L = gamma * L
try:
next_W, tracenorm = Linalg._next_tracenorm_guess(matrix_a, matrix_b, lambda_, L, Z, at_times_a)
except LinAlgError:
print "LinAlgError caught in trace norm regression"
linalg_error_caught = True
break
last_cost = current_cost
current_fitness = Linalg._fitness(matrix_a, matrix_a, next_W)
current_cost = current_fitness + lambda_*tracenorm
if linalg_error_caught:
break
previous_W = W
W = next_W
previous_alpha = alpha
alpha = (1.0 + sqrt(1.0 + 4.0*alpha*alpha))/2.0
Z = W
# Z = W + ((alpha - 1)/alpha)*(W - previous_W)
iter_counter += 1
sys.stdout.flush()
W = np.real(W)
return DenseMatrix(W), costs