def solve_with_moments(m1, M2, M3, K):
"""
Whiten and unwhiten appropriately
"""
assert symmetric_skew(M2) < 1e-2
assert symmetric_skew(M3) < 1e-2
W, Wt = get_whitener( M2, K )
M3_ = sc.einsum( 'ijk,ia,jb,kc->abc', M3, W, W, W )
#print "M3", M3
pi_, M_, _, _ = candecomp(M3_, K)
#print "mu", M_
mu = Wt.dot(M_.dot(diag(pi_)))
return mu
def solve_mixture_model(model, data):
"""
Whiten and unwhiten appropriately
"""
d = model["d"]
# Get moments
moments = model.empirical_moments(data, model.observed_monomials(3))
M2 = zeros((d, d))
M3 = zeros((d, d, d))
for i in xrange(d):
for j in xrange(d):
xij = sp.sympify('x%d * x%d' %(i+1, j+1))
M2[i,j] = moments[xij]
for k in xrange(d):
xijk = sp.sympify('x%d * x%d * x%d' % (i+1, j+1, k+1))
M3[i,j,k] = moments[xijk]
k = model["k"]
# Symmetrize
M2, M3 = symmetrize(M2), symmetrize(M3)
assert symmetric_skew(M2) < 1e-2
assert symmetric_skew(M3) < 1e-2
# Whiten
W, Wt = get_whitener(M2, k)
M3_ = einsum('ijk,ia,jb,kc->abc', M3, W, W, W)
pi_, M_, _, _ = candecomp(M3_, k)
# Unwhiten M
M_ = Wt.dot(M_.dot(diag(pi_)))
pi_ = 1./pi_**2
# "Project" onto simplex
pi_ = make_distribution(abs(pi_))
M_ = array([make_distribution(col) for col in M_.T]).T
return pi_, M_
def solve_mixture_model(model, data):
"""
Whiten and unwhiten appropriately
"""
d = model["d"]
# Get moments
moments = model.empirical_moments(data, model.observed_monomials(3))
M2 = zeros((d, d))
M3 = zeros((d, d, d))
for i in xrange(d):
for j in xrange(d):
xij = sp.sympify('x%d * x%d' % (i + 1, j + 1))
M2[i, j] = moments[xij]
for k in xrange(d):
xijk = sp.sympify('x%d * x%d * x%d' % (i + 1, j + 1, k + 1))
M3[i, j, k] = moments[xijk]
k = model["k"]
# Symmetrize
M2, M3 = symmetrize(M2), symmetrize(M3)
assert symmetric_skew(M2) < 1e-2
assert symmetric_skew(M3) < 1e-2
# Whiten
W, Wt = get_whitener(M2, k)
M3_ = einsum('ijk,ia,jb,kc->abc', M3, W, W, W)
pi_, M_, _, _ = candecomp(M3_, k)
# Unwhiten M
M_ = Wt.dot(M_.dot(diag(pi_)))
pi_ = 1. / pi_**2
# "Project" onto simplex
pi_ = make_distribution(abs(pi_))
M_ = array([make_distribution(col) for col in M_.T]).T
return pi_, M_
def prerequisites( T, K ):
"""
Does the tensor satisfy the prerequisites?
(a) tensor should be symmetric (orthogonal)
"""
if len(T.shape) != 3:
return False
elif not is_square(T):
return False
elif T.shape[0] < K:
return False
elif symmetric_skew(T) > 1e-1:
return False
else:
return True
def prerequisites(T, K):
"""
Does the tensor satisfy the prerequisites?
(a) tensor should be symmetric (orthogonal)
"""
if len(T.shape) != 3:
return False
elif not is_square(T):
return False
elif T.shape[0] < K:
return False
elif symmetric_skew(T) > 1e-1:
return False
else:
return True