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_intercept_lstsq_regression(self):
a = DenseMatrix(np.matrix([[1, 1],[2, 3],[4, 6]]))
b = DenseMatrix(np.matrix([[12, 15, 18],[21, 27, 33],[35, 46, 57]]))
res = DenseMatrix(np.matrix([[1, 2, 3],[4, 5, 6],[7, 8, 9]]))
res1 = Linalg.lstsq_regression(a, b)
res2 = Linalg.lstsq_regression(a, b, intercept=True)
np.testing.assert_array_almost_equal(res2.mat[:-1,:], res[0:2,:].mat, 6)
np.testing.assert_array_almost_equal(res2.mat[-1,:], res[2:3,:].mat, 6)
new_a = a.hstack(DenseMatrix(np.ones((a.shape[0], 1))))
self.assertGreater(((a * res1) - b).norm(), ((new_a * res2) - b).norm())
def _dense_svd(matrix_, reduced_dimension):
print "Running dense svd"
u, s, vt = np.linalg.svd(matrix_.mat, False, True)
rank = len(s[s > Linalg._SVD_TOL])
no_cols = min(u.shape[1], reduced_dimension, rank)
u = DenseMatrix(u[:,0:no_cols])
s = s[0:no_cols]
v = DenseMatrix(vt[0:no_cols,:].transpose())
Linalg._check_reduced_dim(matrix_.shape[1], u.shape[1], reduced_dimension)
if not u.is_mostly_positive():
u = -u
v = -v
return u, s, v
def test_dense_lstsq_regression(self):
test_cases = self.pinv_test_cases
for m, m_inv in test_cases:
m1 = DenseMatrix(m)
id_ = DenseMatrix.identity(m1.shape[0])
res = Linalg.lstsq_regression(m1, id_)
np.testing.assert_array_almost_equal(res.mat, m_inv, 7)
def test_space_compose_dense(self):
test_cases = [([("a","b","a_b")], self.space4, self.space5, DenseMatrix.identity(2), DenseMatrix.identity(2)),
([("a","b","a_b")], self.space4, self.space6, np.mat([[0,0],[0,0]]), np.mat([[0,0],[0,0]])),
([("a","b","a_b"),("a","b","a_a")], self.space4, self.space7, DenseMatrix.identity(2), DenseMatrix.identity(2)),
]
for in_data, arg_space, phrase_space, mat_a, mat_b in test_cases:
comp_model = FullAdditive(A=mat_a, B=mat_b)
comp_space = comp_model.compose(in_data, arg_space)
np.testing.assert_array_almost_equal(comp_space.cooccurrence_matrix.mat,
phrase_space.cooccurrence_matrix.mat, 10)
self.assertListEqual(comp_space.id2column, [])
self.assertDictEqual(comp_space.column2id, {})
self.assertListEqual(comp_space.id2row, phrase_space.id2row)
self.assertDictEqual(comp_space.row2id, phrase_space.row2id)
self.assertFalse(comp_model._has_intercept)
def test_space_compose_sparse(self):
#WHAT TO DO HERE???
#PARAMTERS ARE GIVEN AS DENSE MATRICES, INPUT DATA AS SPARSE??
test_cases = [([("a","b","a_b")], self.space1, self.space2, DenseMatrix.identity(2), DenseMatrix.identity(2)),
([("a","b","a_b")], self.space1, self.space3, np.mat([[0,0],[0,0]]), np.mat([[0,0],[0,0]]))
]
for in_data, arg_space, phrase_space, mat_a, mat_b in test_cases:
comp_model = FullAdditive(A=mat_a, B=mat_b)
comp_space = comp_model.compose(in_data, arg_space)
np.testing.assert_array_almost_equal(comp_space.cooccurrence_matrix.mat.todense(),
phrase_space.cooccurrence_matrix.mat.todense(), 10)
def setUp(self):
self.a = np.array([[1, 2, 3], [4, 0, 5]])
self.b = np.array([[0, 0, 0], [0, 0, 0]])
self.c = np.array([[0, 0], [0, 0], [0, 0]])
self.d = np.array([[1, 0], [0, 1]])
self.e = np.array([1, 10])
self.f = np.array([1, 10, 100])
self.matrix_a = DenseMatrix(self.a)
self.matrix_b = DenseMatrix(self.b)
self.matrix_c = DenseMatrix(self.c)
self.matrix_d = DenseMatrix(self.d)
def test_dense_ridge_regression(self):
test_cases = self.pinv_test_cases
for m, m_inv in test_cases:
m1 = DenseMatrix(m)
id_ = DenseMatrix.identity(m1.shape[0])
res1 = Linalg.lstsq_regression(m1, id_)
np.testing.assert_array_almost_equal(res1.mat, m_inv, 7)
res2 = Linalg.ridge_regression(m1, id_, 1)[0]
error1 = (m1 * res1 - DenseMatrix(m_inv)).norm()
error2 = (m1 * res2 - DenseMatrix(m_inv)).norm()
#print "err", error1, error2
norm1 = error1 + res1.norm()
norm2 = error2 + res2.norm()
#print "norm", norm1, norm2
#THIS SHOULD HOLD, BUT DOES NOT, MAYBE ROUNDING ERROR?
#self.assertGreaterEqual(error2, error1)
self.assertGreaterEqual(norm1, norm2)
def train(self, matrix_a, matrix_b=None):
"""
matrix_b is ignored
"""
W = DenseMatrix.identity(matrix_a.shape[1])
return W
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)
class TestDenseMatrix(unittest.TestCase):
def setUp(self):
self.a = np.array([[1, 2, 3], [4, 0, 5]])
self.b = np.array([[0, 0, 0], [0, 0, 0]])
self.c = np.array([[0, 0], [0, 0], [0, 0]])
self.d = np.array([[1, 0], [0, 1]])
self.e = np.array([1, 10])
self.f = np.array([1, 10, 100])
self.matrix_a = DenseMatrix(self.a)
self.matrix_b = DenseMatrix(self.b)
self.matrix_c = DenseMatrix(self.c)
self.matrix_d = DenseMatrix(self.d)
def tearDown(self):
pass
def test_init(self):
nparr = self.a
test_cases = [nparr, np.mat(nparr), csr_matrix(nparr), csc_matrix(nparr), SparseMatrix(nparr)]
for inmat in test_cases:
outmat = DenseMatrix(inmat)
self.assertIsInstance(outmat.mat, np.matrix)
numpy.testing.assert_array_equal(nparr, np.array(outmat.mat))
def test_add(self):
test_cases = [
(self.matrix_a, self.matrix_a, np.mat([[2, 4, 6], [8, 0, 10]])),
(self.matrix_a, self.matrix_b, self.matrix_a.mat),
]
for (term1, term2, expected) in test_cases:
sum_ = term1 + term2
numpy.testing.assert_array_equal(sum_.mat, expected)
self.assertIsInstance(sum_, type(term1))
def test_add_raises(self):
test_cases = [(self.matrix_a, self.a), (self.matrix_a, SparseMatrix(self.a))]
for (term1, term2) in test_cases:
self.assertRaises(TypeError, term1.__add__, term2)
def test_div(self):
test_cases = [
(self.matrix_a, 2, np.mat([[0.5, 1.0, 1.5], [2.0, 0.0, 2.5]])),
(self.matrix_c, 2, np.mat(self.c)),
]
for (term1, term2, expected) in test_cases:
sum_ = term1 / term2
numpy.testing.assert_array_equal(sum_.mat, expected)
self.assertIsInstance(sum_, DenseMatrix)
def test_div_raises(self):
test_cases = [
(self.matrix_a, self.a, TypeError),
(self.matrix_a, SparseMatrix(self.a), TypeError),
(self.matrix_a, "3", TypeError),
(self.matrix_a, 0, ZeroDivisionError),
]
for (term1, term2, error_type) in test_cases:
self.assertRaises(error_type, term1.__div__, term2)
def test_mul(self):
test_cases = [
(self.matrix_a, self.matrix_c, np.mat([[0, 0], [0, 0]])),
(self.matrix_d, self.matrix_a, self.matrix_a.mat),
(self.matrix_a, 2, np.mat([[2, 4, 6], [8, 0, 10]])),
(2, self.matrix_a, np.mat([[2, 4, 6], [8, 0, 10]])),
(self.matrix_a, np.int64(2), np.mat([[2, 4, 6], [8, 0, 10]])),
(np.int64(2), self.matrix_a, np.mat([[2, 4, 6], [8, 0, 10]])),
]
for (term1, term2, expected) in test_cases:
sum_ = term1 * term2
numpy.testing.assert_array_equal(sum_.mat, expected)
self.assertIsInstance(sum_, DenseMatrix)
def test_mul_raises(self):
test_cases = [
(self.matrix_a, self.a),
(self.matrix_a, SparseMatrix(self.a)),
(self.matrix_a, "3"),
("3", self.matrix_a),
]
for (term1, term2) in test_cases:
self.assertRaises(TypeError, term1.__mul__, term2)
def test_multiply(self):
test_cases = [
(self.matrix_a, self.matrix_a, np.mat([[1, 4, 9], [16, 0, 25]])),
(self.matrix_a, self.matrix_b, np.mat(self.b)),
]
for (term1, term2, expected) in test_cases:
mult1 = term1.multiply(term2)
mult2 = term2.multiply(term1)
numpy.testing.assert_array_equal(mult1.mat, expected)
numpy.testing.assert_array_equal(mult2.mat, expected)
self.assertIsInstance(mult1, DenseMatrix)
self.assertIsInstance(mult2, DenseMatrix)
def test_multiply_raises(self):
test_cases = [
(self.matrix_a, self.matrix_d, ValueError),
(self.matrix_a, self.a, TypeError),
(self.matrix_a, SparseMatrix(self.a), TypeError),
]
for (term1, term2, error_type) in test_cases:
self.assertRaises(error_type, term1.multiply, term2)
def test_scale_rows(self):
outcome = np.mat([[1, 2, 3], [40, 0, 50]])
test_cases = [(self.matrix_a, self.e, outcome), (self.matrix_a, np.mat(self.e).T, outcome)]
for (term1, term2, expected) in test_cases:
term1 = term1.scale_rows(term2)
numpy.testing.assert_array_equal(term1.mat, expected)
def test_scale_columns(self):
test_cases = [(self.matrix_a, self.f, np.mat([[1, 20, 300], [4, 0, 500]]))]
for (term1, term2, expected) in test_cases:
term1 = term1.scale_columns(term2)
numpy.testing.assert_array_equal(term1.mat, expected)
def test_scale_raises(self):
test_cases = [
(self.matrix_a, self.f, ValueError, self.matrix_a.scale_rows),
(self.matrix_a, self.e, ValueError, self.matrix_a.scale_columns),
(self.matrix_a, self.b, ValueError, self.matrix_a.scale_rows),
(self.matrix_a, self.b, ValueError, self.matrix_a.scale_columns),
(self.matrix_a, "3", TypeError, self.matrix_a.scale_rows),
]
for (term1, term2, error_type, function) in test_cases:
self.assertRaises(error_type, function, term2)
def test_plog(self):
m = DenseMatrix(np.mat([[0.5, 1.0, 1.5], [2.0, 0.0, 2.5]]))
m_expected = np.mat([[0.0, 0.0, 0.4054], [0.6931, 0.0, 0.9162]])
a_expected = np.mat([[0.0, 0.6931, 1.0986], [1.3862, 0.0, 1.6094]])
test_cases = [(self.matrix_a.copy(), a_expected), (m, m_expected)]
for (term, expected) in test_cases:
term.plog()
numpy.testing.assert_array_almost_equal(term.mat, expected, 3)
def compute_matreps(self,vecspace,matspace,multiply_matrices=False):
'''
This method computes symbolic and numeric matrix representations od a
papfunc node, taking as input a vector space, a matrix space. An optional Boolean argument, if set to True, makes matrices to be multiplied rather than summed when both subconstituents have arity greater than 0.
'''
# for terminal nodes call insert_terminal_node_representation
if self.is_terminal():
matrep,temp_numrep=self.insert_terminal_node_representation(vecspace,matspace)
self._matrep = matrep
if temp_numrep[0] == "empty":
numrep = []
else:
numrep = [temp_numrep[0].transpose()]
dimensionality=(temp_numrep[0].shape[1])
if len(temp_numrep)>1:
# all matrices are stored flattened, as long vectors. We need to
# reshape them before we use them in computations
for x in range(1, (len(temp_numrep))):
y = DenseMatrix(temp_numrep[x])
y.reshape((dimensionality,(y.shape[1]/dimensionality)))
numrep.append(y)
self._numrep = numrep
#raise an exception for a non-terminal node without children
elif len(self._children) == 0:
raise ValueError("Non-terminal non-branching node!")
# inherit the value of the single daughter in case of unary branching
if len(self._children) == 1:
self._matrep = self.get_child(0)._matrep
self._numrep = self.get_child(0)._numrep
#apply composition for binary branching nodes
if len(self._children) == 2 and self._matrep == []:
matrep1=self.get_child(0)._matrep
#ignore 'empty' nodes
if not matrep1:
raise ValueError("Empty matrix representation for node %s!" %self.get_child(0))
matrep2=self.get_child(1)._matrep
if not matrep2:
raise ValueError("Empty matrix representation for node %s!" %self.get_child(1))
arity1=len(matrep1)-1
arity2=len(matrep2)-1
# first, compute symbolic matrix representation
# default to componentwise addition for daughters of equal arity
if arity1-arity2 == 0:
for x in range(0, arity1+1):
self._matrep.append('(' + matrep1[x] + '+' + matrep2[x] + ')')
# left function application
if arity1 < arity2 and not re.search('empty$',matrep2[0]) and not re.search('empty$',matrep1[0]):
for x in range(0, arity2):
if x == 0: #compute the vector
self._matrep.append('(' + matrep2[x] + '+' + matrep2[arity2] + '*' + matrep1[x] + ')')
# compute a matrix
# If both daughters have matrices in the xth position in
# their vector-matrix structures, add or multiply those
# matrices according to the multiply_matrices parameter
elif x < len(matrep1):
if multiply_matrices: self._matrep.append('(' + matrep2[x] + '*' + matrep1[x] + ')')
else: self._matrep.append('(' + matrep2[x] + '+' + matrep1[x] + ')')
# inherit the function's extra lexical matrix
else:
self._matrep.append(matrep2[x])
# right function application
if arity1 > arity2 and not re.search('empty$',matrep2[0]) and not re.search('empty$',matrep1[0]):
for x in range(0, arity1):
if x == 0:
self._matrep.append('(' + matrep1[x] + '+' + matrep1[arity1] + '*' + matrep2[x] + ')')
# compute a matrix
# If both daughters have matrices in the xth position in
# their vector-matrix structures, add or multiply those
# matrices according to the multiply_matrices parameter
elif x < len(matrep2):
if multiply_matrices: self._matrep.append('(' + matrep1[x] + '*' + matrep2[x] + ')')
else: self._matrep.append('(' + matrep1[x] + '+' + matrep2[x] + ')')
else:
self._matrep.append(matrep1[x])
# ignore 'empty' elements
if re.search('empty$',matrep1[0]):
self._matrep = matrep2
if re.search('empty$',matrep2[0]):
self._matrep = matrep1
# computing numeric matrix representation of a node from those of its two daughters
numrep1=self.get_child(0)._numrep
numrep2=self.get_child(1)._numrep
if arity1-arity2 == 0 and numrep1 and numrep2:
for x in range(0, arity1+1):
self._numrep.append(numrep1[x].__add__(numrep2[x]))
# left function application
if arity1 < arity2 and not numrep1==[] and not numrep2==[]:
for x in range(0, arity2):
if x == 0: #compute the vector
self._numrep.append(numrep2[x].__add__(numrep2[arity2] * padd_matrix(numrep1[x],0)))
elif x < len(numrep1):
if multiply_matrices:
self._numrep.append(numrep2[x] * numrep1[x])
else:
self._numrep.append(numrep1[x].__add__(numrep2[x]))
else:
self._numrep.append(numrep2[x])
# right function application
if arity1 > arity2 and not numrep1==[] and not numrep2==[]:
for x in range(0, arity1):
if x == 0: # compute the vector
self._numrep.append(numrep1[x].__add__(numrep1[arity1] * padd_matrix(numrep2[x],0)))
elif x < len(numrep2):
if multiply_matrices:
self._numrep.append(numrep2[x] * numrep1[x])
else:
self._numrep.append(numrep1[x].__add__(numrep2[x]))
else:
self._numrep.append(numrep1[x])
# ignore 'empty' elements
if (numrep1 == []):
self._numrep = numrep2
if (numrep2 == []):
self._numrep = numrep1
# end of numrep computation
# Raise an exception for non-binary branching - we don't want to handle those structures
if len(self._children)>2:
raise ValueError("Matrix representations are not defined for trees with more than binary branching")
def compute_matreps(self,vecspace,matspace,multiply_matrices=False):
'''
This method computes symbolic and numeric matrix representations od a
papfunc node, taking as input a vector space, a matrix space. An optional Boolean argument, if set to True, makes matrices to be multiplied rather than summed when both subconstituents have arity greater than 0.
'''
# for terminal nodes do lexical insertions by calling
#insert_terminal_node_representation
if self.is_terminal():
matrep,temp_numrep=self.insert_terminal_node_representation(vecspace,matspace)
self._matrep = matrep
if temp_numrep[0] == "empty":
numrep = [] #default semantic representation for syntactic elements we ignore
else:
numrep = [temp_numrep[0].transpose()]
dimensionality=(temp_numrep[0].shape[1])
if len(temp_numrep)>1:
# Matrices are "flattened", stored as vectors.
# We reshape each matrix to a normal shape (usually square)
for x in range(1, (len(temp_numrep))):
y = DenseMatrix(temp_numrep[x])
y.reshape((dimensionality,(y.shape[1]/dimensionality)))
numrep.append(y)
self._numrep = numrep
#raise an exception for a non-terminal node without children
elif len(self._children) == 0:
raise ValueError("Non-terminal non-branching node!")
# inherit the value of the single daughter in case of unary branching
if len(self._children) == 1:
self._matrep = self.get_child(0)._matrep
self._numrep = self.get_child(0)._numrep
#apply composition for binary branching nodes
if len(self._children) == 2 and self._matrep == []:
matrep1=self.get_child(0)._matrep
if not matrep1:
raise ValueError("Empty matrix representation for node %s!" %self.get_child(0))
matrep2=self.get_child(1)._matrep
if not matrep2:
raise ValueError("Empty matrix representation for node %s!" %self.get_child(1))
#get the arity of two daughter nodes in order to determine which of
#them is the function and which is the argument
arity1=len(matrep1)-1
arity2=len(matrep2)-1
# first, compute symbolic matrix representation
if arity1-arity2 == 0:
for x in range(0, arity1+1):
self._matrep.append('(' + matrep1[x] + '+' + matrep2[x] + ')')
#left application
if arity1 < arity2 and not re.search('empty$',matrep2[0]) and not re.search('empty$',matrep1[0]):
for x in range(0, arity2):
if x == 0: # compute vector of the mother node
self._matrep.append('(' + matrep2[x] + '+' + matrep2[arity2] + '*' + matrep1[x] + ')')
elif x < len(matrep1): # compute matrices of the mother node
if multiply_matrices: self._matrep.append('(' + matrep2[x] + '*' + matrep1[x] + ')')
else: self._matrep.append('(' + matrep2[x] + '+' + matrep1[x] + ')')
else:
self._matrep.append(matrep2[x])
#right application
if arity1 > arity2 and not re.search('empty$',matrep2[0]) and not re.search('empty$',matrep1[0]):
for x in range(0, arity1):
if x == 0:
self._matrep.append('(' + matrep1[x] + '+' + matrep1[arity1] + '*' + matrep2[x] + ')')
elif x < len(matrep2):
if multiply_matrices: self._matrep.append('(' + matrep1[x] + '*' + matrep2[x] + ')')
else: self._matrep.append('(' + matrep1[x] + '+' + matrep2[x] + ')')
else:
self._matrep.append(matrep1[x])
#if one of the daughters is 'empty' (marked to be ignored), ignore it
if re.search('empty$',matrep1[0]):
self._matrep = matrep2
if re.search('empty$',matrep2[0]):
self._matrep = matrep1
# computing numeric matrix representation of a node from those of
# its two daughters.
# First, get arity of the daughters to establish the directionality
# of function application
numrep1=self.get_child(0)._numrep
numrep2=self.get_child(1)._numrep
if arity1-arity2 == 0 and numrep1 and numrep2:
for x in range(0, arity1+1):
self._numrep.append(numrep1[x].__add__(numrep2[x]))
#left application
if arity1 < arity2 and not numrep1==[] and not numrep2==[]:
for x in range(0, arity2):
# compute the vector
if x == 0:
self._numrep.append(numrep2[x].__add__(numrep2[arity2] * numrep1[x]))
# compute a matrix
elif x < len(numrep1):
if multiply_matrices:
self._numrep.append(numrep2[x] * numrep1[x])
else:
self._numrep.append(numrep1[x].__add__(numrep2[x]))
else:
self._numrep.append(numrep2[x])
#right aplication
if arity1 > arity2 and not numrep1==[] and not numrep2==[]:
for x in range(0, arity1):
if x == 0:
self._numrep.append(numrep1[x].__add__(numrep1[arity1]*numrep2[x]))
elif x < len(numrep2):
if multiply_matrices:
self._numrep.append(numrep2[x] * numrep1[x])
else:
self._numrep.append(numrep1[x].__add__(numrep2[x]))
else:
self._numrep.append(numrep1[x])
# ignore 'empty' elements in composition
if (numrep1 == []):
self._numrep = numrep2
if (numrep2 == []):
self._numrep = numrep1
# end of numrep computation
# Raise an exception for non-binary branching - we don't want to handle those structures
if len(self._children)>2:
raise ValueError("Matrix representations are not defined for trees with more than binary branching")
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
