def ridge_regression(matrix_a, matrix_b, lambda_, intercept=False):
#log.print_info(logger, "In Ridge 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 Ridge Regression.
This method use the general formula:
...
to solve the problem:
:math:`X = argmin(||AX - B||_2 + \\lambda||X||_2)`
Args:
matrix_a: input matrix A, of type Matrix
matrix_b: input matrix A, of type Matrix
lambda_: scalar, lambda parameter
intercept: bool. If True intercept is used. Optional, default False.
Returns:
solution X of type Matrix
"""
matrix_a._assert_same_type(matrix_b)
# TODO: check out where to define this assert
assert_same_shape(matrix_a, matrix_b, 0)
matrix_type = type(matrix_a)
dim = matrix_a.shape[1]
if intercept:
matrix_a = matrix_a.hstack(
matrix_type(np.ones((matrix_a.shape[0], 1))))
lambda_diag = (lambda_) * matrix_type.identity(dim)
if intercept:
lambda_diag = padd_matrix(padd_matrix(lambda_diag, 0, 0.0), 1, 0.0)
matrix_a_t = matrix_a.transpose()
try:
tmp_mat = Linalg.pinv(((matrix_a_t * matrix_a) + lambda_diag))
except np.linalg.LinAlgError:
print "Warning! LinAlgError"
tmp_mat = matrix_type.identity(lambda_diag.shape[0])
tmp_res = tmp_mat * matrix_a_t
result = tmp_res * matrix_b
#S: used in generalized cross validation, page 244 7.52 (YZ also used it)
# S is defined in 7.31, page 232
# instead of computing the matrix and then its trace, we can compute
# its trace directly
# NOTE when lambda = 0 we get out trace(S) = rank(matrix_a)
dist = (matrix_a * result - matrix_b).norm()
S_trace = matrix_a_t.multiply(tmp_res).sum()
return result, S_trace, dist
def ridge_regression(matrix_a , matrix_b, lambda_, intercept=False):
#log.print_info(logger, "In Ridge 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 Ridge Regression.
This method use the general formula:
...
to solve the problem:
:math:`X = argmin(||AX - B||_2 + \\lambda||X||_2)`
Args:
matrix_a: input matrix A, of type Matrix
matrix_b: input matrix A, of type Matrix
lambda_: scalar, lambda parameter
intercept: bool. If True intercept is used. Optional, default False.
Returns:
solution X of type Matrix
"""
matrix_a._assert_same_type(matrix_b)
# TODO: check out where to define this assert
assert_same_shape(matrix_a, matrix_b, 0)
matrix_type = type(matrix_a)
dim = matrix_a.shape[1]
if intercept:
matrix_a = matrix_a.hstack(matrix_type(np.ones((matrix_a.shape[0],
1))))
lambda_diag = (lambda_ ) * matrix_type.identity(dim)
if intercept:
lambda_diag = padd_matrix(padd_matrix(lambda_diag, 0, 0.0), 1, 0.0)
matrix_a_t = matrix_a.transpose()
try:
tmp_mat = Linalg.pinv(((matrix_a_t * matrix_a) + lambda_diag))
except np.linalg.LinAlgError:
print "Warning! LinAlgError"
tmp_mat = matrix_type.identity(lambda_diag.shape[0])
tmp_res = tmp_mat * matrix_a_t
result = tmp_res * matrix_b
#S: used in generalized cross validation, page 244 7.52 (YZ also used it)
# S is defined in 7.31, page 232
# instead of computing the matrix and then its trace, we can compute
# its trace directly
# NOTE when lambda = 0 we get out trace(S) = rank(matrix_a)
dist = (matrix_a * result - matrix_b).norm()
S_trace = matrix_a_t.multiply(tmp_res).sum()
return result, S_trace, dist
def _compose(self, arg1_mat, arg2_mat):
#NOTE when we get in this compose arg1 mat and arg2 mat have the same type
[mat_a_t, mat_b_t, arg1_mat
] = resolve_type_conflict([self._mat_a_t, self._mat_b_t, arg1_mat],
type(arg1_mat))
if self._has_intercept:
return arg1_mat * mat_a_t + padd_matrix(arg2_mat, 1) * mat_b_t
else:
return arg1_mat * mat_a_t + arg2_mat * mat_b_t
def _compose(self, arg1_mat, arg2_mat):
#NOTE when we get in this compose arg1 mat and arg2 mat have the same type
[mat_a_t, mat_b_t, arg1_mat] = resolve_type_conflict([self._mat_a_t,
self._mat_b_t,
arg1_mat],
type(arg1_mat))
if self._has_intercept:
return arg1_mat * mat_a_t + padd_matrix(arg2_mat, 1) * mat_b_t
else:
return arg1_mat * mat_a_t + arg2_mat * mat_b_t
def _compose(self, function_arg_vec, arg_vec, function_arg_element_shape):
new_shape = (np.prod(function_arg_element_shape[0:-1]),
function_arg_element_shape[-1])
function_arg_vec.reshape(new_shape)
if self._has_intercept:
comp_el = function_arg_vec * padd_matrix(arg_vec.transpose(), 0)
else:
comp_el = function_arg_vec * arg_vec.transpose()
return comp_el.transpose()
def _compose(self, function_arg_vec, arg_vec, function_arg_element_shape):
new_shape = (np.prod(function_arg_element_shape[0:-1]),
function_arg_element_shape[-1])
function_arg_vec.reshape(new_shape)
if self._has_intercept:
comp_el = function_arg_vec * padd_matrix(arg_vec.transpose(), 0)
else:
comp_el = function_arg_vec * arg_vec.transpose()
return comp_el.transpose()
def test_crossvalidation(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]]))
learner = RidgeRegressionLearner(intercept=True, param_range=[0])
learner2 = LstsqRegressionLearner(intercept=False)
res1 = learner2.train(a, b)
res2 = learner.train(a, b)
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 = padd_matrix(a, 1)
self.assertGreater(((a * res1) - b).norm(), ((new_a * res2) - b).norm())
def test_crossvalidation(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]]))
learner = RidgeRegressionLearner(intercept=True, param_range=[0])
learner2 = LstsqRegressionLearner(intercept=False)
res1 = learner2.train(a, b)
res2 = learner.train(a, b)
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 = padd_matrix(a, 1)
self.assertGreater(((a * res1) - b).norm(),
((new_a * res2) - b).norm())
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")
