def test_derivatives(self):
print "Testing derivative for p-nested symmetric distribution with radial gamma"
sys.stdout.flush()
myu = 10 * np.random.rand(1)[0]
mys = 10 * np.random.rand(1)[0]
n = 10
L = Auxiliary.LpNestedFunction('(0,0,(1,1:4),4,(1,5:8),8:10)')
p = Distributions.LpNestedSymmetric({
'f':
L,
'n':
n,
'rp':
Distributions.Gamma({
's': mys,
'u': myu
})
})
dat = p.sample(50)
df = p.dldx(dat)
h = 1e-8
df2 = np.array(dat.X * np.Inf)
for k in range(n):
y = np.array(dat.X)
y[k, :] += h
df2[k, :] = (p.loglik(Data(y)) - p.loglik(dat)) / h
self.assertFalse(np.max(np.abs(df-df2).flatten()) > self.llTol,\
'Difference in derivative of log-likelihood for p-nested symmetric greater than ' + str(self.llTol))
def test_RadialFactorizationVsLpNestedNonlinearICA(self):
print "Testing Radial Factorization vs. Lp-nested ICA..."
sys.stdout.flush()
p = np.random.rand() + 1.0
psource = Distributions.LpSphericallySymmetric({
'p':
p,
'rp':
Distributions.Gamma({
'u': 2.0 * np.random.rand() + 1.0,
's': 5.0 * np.random.rand() + 1.0
})
})
F = NonlinearTransformFactory.RadialFactorization(psource)
dat = psource.sample(10)
L = Auxiliary.LpNestedFunction('(0,0:2)', np.array([p]))
psource2 = Distributions.LpNestedSymmetric({
'f':
L,
'n':
2.0,
'rp':
psource.param['rp'].copy()
})
F2 = NonlinearTransformFactory.LpNestedNonLinearICA(psource2)
tol = 1e-6
self.assertTrue(np.max(np.abs(F.logDetJacobian(dat) - F2.logDetJacobian(dat))) < tol,\
'log-determinants of Lp-nestedICA and Radial Factorization are not equal!')
def test_logdeterminantInCombinationWithLinearFilters(self):
print "Testing Log-Determinant of Nonlinear Lp-nested ICA in combination with linear filters..."
sys.stdout.flush()
L = Auxiliary.LpNestedFunction()
p = Distributions.LpNestedSymmetric({'f': L})
dat = p.sample(10)
Flin1 = LinearTransformFactory.oRND(dat)
Flin2 = LinearTransform(
np.random.randn(dat.size(0), dat.size(0)) +
0.1 * np.eye(dat.size(0)))
Fnl = NonlinearTransformFactory.LpNestedNonLinearICA(p)
Fd = {}
Fd['NL'] = Fnl
Fd['L1*L2'] = Flin1 * Flin2
Fd['L1*NL'] = Flin1 * Fnl
Fd['NL*L1'] = Fnl * Flin1
Fd['Nl*L1*L2'] = Fnl * Flin1 * Flin2
Fd['Nl*(L1*L2)'] = Fnl * (Flin1 * Flin2)
Fd['(Nl*L1)*L2'] = (Fnl * Flin1) * Flin2
Fd['L1*Nl*L2'] = Flin1 * Fnl * Flin2
Fd['L1*(Nl*L2)'] = Flin1 * (Fnl * Flin2)
Fd['(L1*Nl)*L2'] = (Flin1 * Fnl) * Flin2
Fd['L2*L1*Nl'] = Flin2 * Flin1 * Fnl
Fd['L2*(L1*Nl)'] = Flin2 * (Flin1 * Fnl)
Fd['(L2*L1)*Nl'] = (Flin2 * Flin1) * Fnl
for (tk, F) in Fd.items():
print "\t ... testing " + tk
sys.stdout.flush()
n, m = dat.size()
h = 5 * 1e-7
logdetJ = F.logDetJacobian(dat)
for i in range(m):
J = np.zeros((n, n))
for j in range(n):
tmp = dat[:, i]
tmp2 = tmp.copy()
tmp2.X[j, :] = tmp2.X[j, :] + h
J[:, j] = ((F * tmp2).X - (F * tmp).X)[:, 0] / h
Q, R = linalg.qr(J)
logdet2 = np.sum(np.log(np.diag(R)))
#print np.abs(logdet2 - logdetJ[i])
self.assertFalse(np.abs(logdet2 - logdetJ[i]) > self.DetTol,\
'Determinant of Jacobian deviates by %.4g which is more than more than %.4g' % (np.abs(logdet2 - logdetJ[i]), self.DetTol))
def test_logdeterminantOfICA(self):
print "Testing Log-Determinant of Nonlinear Lp-nested ICA ..."
sys.stdout.flush()
L = Auxiliary.LpNestedFunction()
p = Distributions.LpNestedSymmetric({'f': L})
dat = p.sample(10)
F = NonlinearTransformFactory.LpNestedNonLinearICA(p)
n, m = dat.size()
h = 1e-7
logdetJ = F.logDetJacobian(dat)
for i in range(m):
J = np.zeros((n, n))
for j in range(n):
tmp = dat[:, i]
tmp2 = tmp.copy()
tmp2.X[j, :] = tmp2.X[j, :] + h
J[:, j] = ((F * tmp2).X - (F * tmp).X)[:, 0] / h
# print np.abs(np.log(linalg.det(J)) - logdetJ[i])
self.assertFalse( np.abs(np.log(linalg.det(J)) - logdetJ[i]) > self.DetTol,\
'Determinant of Jacobian deviates by more than ' + str(self.DetTol) + '!')
def test_estimate(self):
print "Testing parameter estimation for p-nested symmetric distribution with radial gamma"
sys.stdout.flush()
L = Auxiliary.LpNestedFunction('(0,0,(1,1:3),3,(2,4:7))')
L.p = np.random.rand(3) * 1.5 + .5
d = Distributions.LpNestedSymmetric({'f': L, 'n': L.n[()]})
L2 = Auxiliary.LpNestedFunction('(0,0,(1,1:3),3,(2,4:7))')
L2.p = np.random.rand(3) * 1.5 + .5
L.lb = 0.0 * L.p
L.ub = 2.0 * L2.p
rd2 = Distributions.Gamma({
'u': 5 * np.random.rand(),
's': 10 * np.random.rand()
})
# create Distributions object and sample
d2 = Distributions.LpNestedSymmetric({
'f': L2,
'n': L2.n[()],
'rp': rd2
})
print "\t ... checking greedy method"
sys.stdout.flush()
dat = d2.sample(50000)
d.estimate(dat, method="greedy")
self.assertFalse( np.max(np.abs(d.param['f'].p - d2.param['f'].p)) > self.TolParam['p'],\
'Estimated parameter p deviates by more than ' + str(self.TolParam['p']) + '!')
self.assertFalse( np.abs(d.param['rp'].param['u'] - d2.param['rp'].param['u']) > self.TolParam['u'],\
'Estimated parameter u deviates by more than ' + str(self.TolParam['u']) + '!')
self.assertFalse( np.abs(d.param['rp'].param['s'] - d2.param['rp'].param['s']) > self.TolParam['s'],\
'Estimated parameter s deviates by more than ' + str(self.TolParam['s']) + '!')
print "\t ... checking Nelder-Mead method"
sys.stdout.flush()
d = Distributions.LpNestedSymmetric({'f': L, 'n': L.n[()]})
d.estimate(dat, method="neldermead")
self.assertFalse( np.max(np.abs(d.param['f'].p - d2.param['f'].p)) > self.TolParam['p'],\
'Estimated parameter p deviates by more than ' + str(self.TolParam['p']) + '!')
self.assertFalse( np.abs(d.param['rp'].param['u'] - d2.param['rp'].param['u']) > self.TolParam['u'],\
'Estimated parameter u deviates by more than ' + str(self.TolParam['u']) + '!')
self.assertFalse( np.abs(d.param['rp'].param['s'] - d2.param['rp'].param['s']) > self.TolParam['s'],\
'Estimated parameter s deviates by more than ' + str(self.TolParam['s']) + '!')
print "\t ... checking Gradient method"
sys.stdout.flush()
d = Distributions.LpNestedSymmetric({'f': L, 'n': L.n[()]})
d.estimate(dat, method="gradient")
self.assertFalse( np.max(np.abs(d.param['f'].p - d2.param['f'].p)) > self.TolParam['p'],\
'Estimated parameter p deviates by more than ' + str(self.TolParam['p']) + '!')
self.assertFalse( np.abs(d.param['rp'].param['u'] - d2.param['rp'].param['u']) > self.TolParam['u'],\
'Estimated parameter u deviates by more than ' + str(self.TolParam['u']) + '!')
self.assertFalse( np.abs(d.param['rp'].param['s'] - d2.param['rp'].param['s']) > self.TolParam['s'],\
'Estimated parameter s deviates by more than ' + str(self.TolParam['s']) + '!')
print "[Ok]"
