def log_matrix_diagonal(mat):
assert mat.shape[0] == mat.shape[1]
# make_diagonal() is only defined in the autograd version of numpy
mat_log_diag = np.make_diagonal(
np.log(np.diag(mat)), offset=0, axis1=-1, axis2=-2)
mat_diag = np.make_diagonal(np.diag(mat), offset=0, axis1=-1, axis2=-2)
return mat_log_diag + mat - mat_diag
def test_diagonal():
def fun(D):
return to_scalar(np.diagonal(D, axis1=-1, axis2=-2))
D = np.random.randn(4, 4)
A = np.make_diagonal(D, axis1=-1, axis2=-2)
check_grads(fun, D)
D = np.random.randn(3, 4, 4)
A = np.make_diagonal(D, axis1=-1, axis2=-2)
check_grads(fun, D)
def test_diagonal():
def fun(D):
return to_scalar(np.diagonal(D, axis1=-1, axis2=-2))
D = np.random.randn(4, 4)
A = np.make_diagonal(D, axis1=-1, axis2=-2)
check_grads(fun, D)
D = np.random.randn(3, 4, 4)
A = np.make_diagonal(D, axis1=-1, axis2=-2)
check_grads(fun, D)
def test_make_diagonal():
def fun(D):
return to_scalar(np.make_diagonal(D, axis1=-1, axis2=-2))
D = np.random.randn(4)
A = np.make_diagonal(D, axis1=-1, axis2=-2)
assert np.allclose(np.diag(A), D)
check_grads(fun, D)
D = np.random.randn(3, 4)
A = np.make_diagonal(D, axis1=-1, axis2=-2)
assert all([np.allclose(np.diag(A[i]), D[i]) for i in range(3)])
check_grads(fun, D)
def test_make_diagonal():
def fun(D):
return to_scalar(np.make_diagonal(D, axis1=-1, axis2=-2))
D = np.random.randn(4)
A = np.make_diagonal(D, axis1=-1, axis2=-2)
assert np.allclose(np.diag(A), D)
check_grads(fun, D)
D = np.random.randn(3, 4)
A = np.make_diagonal(D, axis1=-1, axis2=-2)
assert all([np.allclose(np.diag(A[i]), D[i]) for i in range(3)])
check_grads(fun, D)
def _unvectorize_symmetric_matrix(vec_val):
ld_mat = _unvectorize_ld_matrix(vec_val)
mat_val = ld_mat + ld_mat.transpose()
# We have double counted the diagonal. For some reason the autograd
# diagonal functions require axis1=-1 and axis2=-2
mat_val = mat_val - \
np.make_diagonal(np.diagonal(ld_mat, axis1=-1, axis2=-2),
axis1=-1, axis2=-2)
return mat_val
def unpack_params(params):
"""Unpacks parameter vector into the proportions, means and covariances
of each mixture component. The covariance matrices are parametrized by
their Cholesky decompositions."""
log_proportions = parser.get(params, "log proportions")
normalized_log_proportions = log_proportions - logsumexp(log_proportions)
means = parser.get(params, "means")
lower_tris = np.tril(parser.get(params, "lower triangles"), k=-1)
diag_chols = np.exp(parser.get(params, "log diagonals"))
chols = lower_tris + np.make_diagonal(diag_chols, axis1=-1, axis2=-2)
return normalized_log_proportions, means, chols
def unpack_params(params):
"""Unpacks parameter vector into the proportions, means and covariances
of each mixture component. The covariance matrices are parametrized by
their Cholesky decompositions."""
log_proportions = parser.get(params, 'log proportions')
normalized_log_proportions = log_proportions - logsumexp(log_proportions)
means = parser.get(params, 'means')
lower_tris = np.tril(parser.get(params, 'lower triangles'), k=-1)
diag_chols = np.exp( parser.get(params, 'log diagonals'))
chols = lower_tris + np.make_diagonal(diag_chols, axis1=-1, axis2=-2)
return normalized_log_proportions, means, chols
def calculate_b(Ys, X, Us):
total = 0.
count = 0
for i in range(len(Ys)):
Y = Ys[i]
mask_pos = Y == 1
mask_neg = Y == -1
tm = np.sum(mask_pos) / np.sum(mask_pos + mask_neg)
Beta = (mask_pos) * 1 + (mask_neg) * tm
U = np.make_diagonal(Us[D * i:D * (i + 1)], axis1=-1, axis2=-2)
b = np.sum(Beta * (Y - np.dot(np.dot(X, U), (X.T))))
count += np.sum(mask_pos + mask_neg)
total += b
return total / count
def loss_all(Ys, X, Us, b, lambda_x=1., lambda_u=1., sigma_u=0.5):
sum_loss_M = 0
sum_reg_u = 0
num_user = int(Us.size / D)
for i in range(num_user):
Y = Ys[i]
U = np.make_diagonal(Us[D * i:D * (i + 1)], axis1=-1, axis2=-2)
sum_loss_M += loss_M(Y, X, U, b)
diff_U = U - sigma_u * np.eye(U.shape[0])
sum_reg_u += np.linalg.norm(diff_U, ord='fro')**2
Rx = lambda_x * np.sum((np.linalg.norm(X, axis=1)**2))
Ru = lambda_u * sum_reg_u
return Rx + Ru + sum_loss_M
def J(self):
return np.make_diagonal(1 / self.std**2, axis1=-1, axis2=-2)
def fun(D):
return to_scalar(np.make_diagonal(D, axis1=-1, axis2=-2))
def _pack_posdef_matrix(mat, diag_lb=0.0):
k = mat.shape[0]
mat_lb = mat - np.make_diagonal(
np.full(k, diag_lb), offset=0, axis1=-1, axis2=-2)
return _vectorize_ld_matrix(
_log_matrix_diagonal(np.linalg.cholesky(mat_lb)))
def _unpack_posdef_matrix(free_vec, diag_lb=0.0):
mat_chol = _exp_matrix_diagonal(_unvectorize_ld_matrix(free_vec))
mat = np.matmul(mat_chol, mat_chol.T)
k = mat.shape[0]
return mat + np.make_diagonal(
np.full(k, diag_lb), offset=0, axis1=-1, axis2=-2)
def fun(D):
return to_scalar(np.make_diagonal(D, axis1=-1, axis2=-2))
def fun(D):
return np.make_diagonal(D, axis1=-1, axis2=-2)
def sigma(self):
return np.make_diagonal(self.std**2, axis1=-1, axis2=-2)