def test_lower_bound(self):
"""
Test the Wishart VB lower bound
"""
#
# By having the Wishart node as the only latent node, VB will give exact
# results, thus the VB lower bound is the true marginal log likelihood.
# Thus, check that they are equal. The true marginal likelihood is the
# multivariate Student-t distribution.
#
np.random.seed(42)
D = 3
n = (D-1) + np.random.uniform(0.1, 0.5)
V = random.covariance(D)
Lambda = Wishart(n, V)
mu = np.random.randn(D)
Y = Gaussian(mu, Lambda)
y = np.random.randn(D)
Y.observe(y)
Lambda.update()
L = Y.lower_bound_contribution() + Lambda.lower_bound_contribution()
mu = mu
nu = n + 1 - D
Cov = V / nu
self.assertAllClose(L,
_student_logpdf(y,
mu,
Cov,
nu))
pass
def test_lower_bound(self):
"""
Test the Wishart VB lower bound
"""
#
# By having the Wishart node as the only latent node, VB will give exact
# results, thus the VB lower bound is the true marginal log likelihood.
# Thus, check that they are equal. The true marginal likelihood is the
# multivariate Student-t distribution.
#
np.random.seed(42)
D = 3
n = (D-1) + np.random.uniform(0.1, 0.5)
V = random.covariance(D)
Lambda = Wishart(n, V)
mu = np.random.randn(D)
Y = Gaussian(mu, Lambda)
y = np.random.randn(D)
Y.observe(y)
Lambda.update()
L = Y.lower_bound_contribution() + Lambda.lower_bound_contribution()
mu = mu
nu = n + 1 - D
Cov = V / nu
self.assertAllClose(L,
_student_logpdf(y,
mu,
Cov,
nu))
pass
def test_moments(self):
"""
Test the moments of Wishart node
"""
np.random.seed(42)
# Test prior moments
D = 3
n = (D-1) + np.random.uniform(0.1,2)
V = random.covariance(D)
Lambda = Wishart(n, V)
Lambda.update()
u = Lambda.get_moments()
self.assertAllClose(u[0],
n*np.linalg.inv(V),
msg='Mean incorrect')
self.assertAllClose(u[1],
(np.sum(special.digamma((n - np.arange(D))/2))
+ D*np.log(2)
- np.linalg.slogdet(V)[1]),
msg='Log determinant incorrect')
# Test posterior moments
D = 3
n = (D-1) + np.random.uniform(0.1,2)
V = random.covariance(D)
Lambda = Wishart(n, V)
mu = np.random.randn(D)
Y = Gaussian(mu, Lambda)
y = np.random.randn(D)
Y.observe(y)
Lambda.update()
u = Lambda.get_moments()
n = n + 1
V = V + np.outer(y-mu, y-mu)
self.assertAllClose(u[0],
n*np.linalg.inv(V),
msg='Mean incorrect')
self.assertAllClose(u[1],
(np.sum(special.digamma((n - np.arange(D))/2))
+ D*np.log(2)
- np.linalg.slogdet(V)[1]),
msg='Log determinant incorrect')
pass
def test_gaussian_mixture_plot():
"""
Test the gaussian_mixture plotting function.
The code is from http://www.bayespy.org/examples/gmm.html
"""
np.random.seed(1)
y0 = np.random.multivariate_normal([0, 0], [[1, 0], [0, 0.02]], size=50)
y1 = np.random.multivariate_normal([0, 0], [[0.02, 0], [0, 1]], size=50)
y2 = np.random.multivariate_normal([2, 2], [[1, -0.9], [-0.9, 1]], size=50)
y3 = np.random.multivariate_normal([-2, -2], [[0.1, 0], [0, 0.1]], size=50)
y = np.vstack([y0, y1, y2, y3])
bpplt.pyplot.plot(y[:, 0], y[:, 1], 'rx')
N = 200
D = 2
K = 10
alpha = Dirichlet(1e-5 * np.ones(K), name='alpha')
Z = Categorical(alpha, plates=(N, ), name='z')
mu = Gaussian(np.zeros(D), 1e-5 * np.identity(D), plates=(K, ), name='mu')
Lambda = Wishart(D, 1e-5 * np.identity(D), plates=(K, ), name='Lambda')
Y = Mixture(Z, Gaussian, mu, Lambda, name='Y')
Z.initialize_from_random()
Q = VB(Y, mu, Lambda, Z, alpha)
Y.observe(y)
Q.update(repeat=1000)
bpplt.gaussian_mixture_2d(Y, scale=2)
def test_moments(self):
"""
Test the moments of Wishart node
"""
np.random.seed(42)
# Test prior moments
D = 3
n = (D-1) + np.random.uniform(0.1,2)
V = random.covariance(D)
Lambda = Wishart(n, V)
Lambda.update()
u = Lambda.get_moments()
self.assertAllClose(u[0],
n*np.linalg.inv(V),
msg='Mean incorrect')
self.assertAllClose(u[1],
(np.sum(special.digamma((n - np.arange(D))/2))
+ D*np.log(2)
- np.linalg.slogdet(V)[1]),
msg='Log determinant incorrect')
# Test posterior moments
D = 3
n = (D-1) + np.random.uniform(0.1,2)
V = random.covariance(D)
Lambda = Wishart(n, V)
mu = np.random.randn(D)
Y = Gaussian(mu, Lambda)
y = np.random.randn(D)
Y.observe(y)
Lambda.update()
u = Lambda.get_moments()
n = n + 1
V = V + np.outer(y-mu, y-mu)
self.assertAllClose(u[0],
n*np.linalg.inv(V),
msg='Mean incorrect')
self.assertAllClose(u[1],
(np.sum(special.digamma((n - np.arange(D))/2))
+ D*np.log(2)
- np.linalg.slogdet(V)[1]),
msg='Log determinant incorrect')
pass
def test_message_to_parents(self):
""" Check gradient passed to inputs parent node """
D = 3
X = Gaussian(np.random.randn(D), random.covariance(D))
V = Wishart(D + np.random.rand(), random.covariance(D))
Y = Gaussian(X, V)
self.assert_moments(
Y,
lambda u: [u[0], u[1] + u[1].T]
)
Y.observe(np.random.randn(D))
self.assert_message_to_parent(Y, X)
#self.assert_message_to_parent(Y, V)
pass
from bayespy.nodes import Dirichlet, Categorical from bayespy.nodes import Gaussian, Wishart from bayespy.nodes import Mixture from bayespy.inference import VB y0 = np.random.multivariate_normal([0, 0], [[2, 0], [0, 0.1]], size=50) y1 = np.random.multivariate_normal([0, 0], [[0.1, 0], [0, 2]], size=50) y2 = np.random.multivariate_normal([2, 2], [[2, -1.5], [-1.5, 2]], size=50) y3 = np.random.multivariate_normal([-2, -2], [[0.5, 0], [0, 0.5]], size=50) y = np.vstack([y0, y1, y2, y3]) N = 200 D = 2 K = 10 alpha = Dirichlet(1e-5*np.ones(K), name='alpha') Z = Categorical(alpha, plates=(N,),name='z') mu = Gaussian(np.zeros(D),1e-5*np.identity(D),plates=(K,),name='mu') Lambda = Wishart(D,1e-5*np.identity(D),plates=(K,),name='Lambda') Y = Mixture(Z, Gaussian, mu, Lambda, name='Y') Z.initialize_from_random() Q = VB(Y, mu, Lambda, Z, alpha) Y.observe(y) Q.update(repeat=1000) bpplt.gaussian_mixture_2d(Y, alpha=alpha, scale=2)
def test_message_to_child(self):
"""
Test the message to child of GaussianGammaISO node.
"""
# Simple test
mu = np.array([1, 2, 3])
Lambda = np.identity(3)
a = 2
b = 10
X_alpha = GaussianGammaISO(mu, Lambda, a, b)
u = X_alpha._message_to_child()
self.assertEqual(len(u), 4)
tau = np.array(a / b)
self.assertAllClose(u[0], tau[..., None] * mu)
self.assertAllClose(
u[1],
(linalg.inv(Lambda) + tau[..., None, None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2], tau)
self.assertAllClose(u[3], -np.log(b) + special.psi(a))
# Test with unknown parents
mu = Gaussian(np.arange(3), 10 * np.identity(3))
Lambda = Wishart(10, np.identity(3))
a = 2
b = Gamma(3, 15)
X_alpha = GaussianGammaISO(mu, Lambda, a, b)
u = X_alpha._message_to_child()
(mu, mumu) = mu._message_to_child()
Cov_mu = mumu - linalg.outer(mu, mu)
(Lambda, _) = Lambda._message_to_child()
(b, _) = b._message_to_child()
(tau, logtau) = Gamma(
a, b + 0.5 * np.sum(Lambda * Cov_mu))._message_to_child()
self.assertAllClose(u[0], tau[..., None] * mu)
self.assertAllClose(
u[1],
(linalg.inv(Lambda) + tau[..., None, None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2], tau)
self.assertAllClose(u[3], logtau)
# Test with plates
mu = Gaussian(np.reshape(np.arange(3 * 4), (4, 3)),
10 * np.identity(3),
plates=(4, ))
Lambda = Wishart(10, np.identity(3))
a = 2
b = Gamma(3, 15)
X_alpha = GaussianGammaISO(mu, Lambda, a, b, plates=(4, ))
u = X_alpha._message_to_child()
(mu, mumu) = mu._message_to_child()
Cov_mu = mumu - linalg.outer(mu, mu)
(Lambda, _) = Lambda._message_to_child()
(b, _) = b._message_to_child()
(tau, logtau) = Gamma(
a, b +
0.5 * np.sum(Lambda * Cov_mu, axis=(-1, -2)))._message_to_child()
self.assertAllClose(u[0] * np.ones((4, 1)),
np.ones((4, 1)) * tau[..., None] * mu)
self.assertAllClose(
u[1] * np.ones((4, 1, 1)),
np.ones((4, 1, 1)) *
(linalg.inv(Lambda) + tau[..., None, None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2] * np.ones(4), np.ones(4) * tau)
self.assertAllClose(u[3] * np.ones(4), np.ones(4) * logtau)
pass
def test_init(self):
"""
Test the creation of GaussianGammaISO node
"""
# Simple construction
X_alpha = GaussianGammaISO([1, 2, 3], np.identity(3), 2, 10)
self.assertEqual(X_alpha.plates, ())
self.assertEqual(X_alpha.dims, ((3, ), (3, 3), (), ()))
# Plates
X_alpha = GaussianGammaISO([1, 2, 3],
np.identity(3),
2,
10,
plates=(4, ))
self.assertEqual(X_alpha.plates, (4, ))
self.assertEqual(X_alpha.dims, ((3, ), (3, 3), (), ()))
# Plates in mu
X_alpha = GaussianGammaISO(np.ones((4, 3)), np.identity(3), 2, 10)
self.assertEqual(X_alpha.plates, (4, ))
self.assertEqual(X_alpha.dims, ((3, ), (3, 3), (), ()))
# Plates in Lambda
X_alpha = GaussianGammaISO(np.ones(3),
np.ones((4, 3, 3)) * np.identity(3), 2, 10)
self.assertEqual(X_alpha.plates, (4, ))
self.assertEqual(X_alpha.dims, ((3, ), (3, 3), (), ()))
# Plates in a
X_alpha = GaussianGammaISO(np.ones(3), np.identity(3), np.ones(4), 10)
self.assertEqual(X_alpha.plates, (4, ))
self.assertEqual(X_alpha.dims, ((3, ), (3, 3), (), ()))
# Plates in Lambda
X_alpha = GaussianGammaISO(np.ones(3), np.identity(3), 2, np.ones(4))
self.assertEqual(X_alpha.plates, (4, ))
self.assertEqual(X_alpha.dims, ((3, ), (3, 3), (), ()))
# Inconsistent plates
self.assertRaises(ValueError,
GaussianGammaISO,
np.ones((4, 3)),
np.identity(3),
2,
10,
plates=())
# Inconsistent plates
self.assertRaises(ValueError,
GaussianGammaISO,
np.ones((4, 3)),
np.identity(3),
2,
10,
plates=(5, ))
# Unknown parameters
mu = Gaussian(np.zeros(3), np.identity(3))
Lambda = Wishart(10, np.identity(3))
b = Gamma(1, 1)
X_alpha = GaussianGammaISO(mu, Lambda, 2, b)
self.assertEqual(X_alpha.plates, ())
self.assertEqual(X_alpha.dims, ((3, ), (3, 3), (), ()))
# mu is Gaussian-gamma
mu_tau = GaussianGammaISO(np.ones(3), np.identity(3), 5, 5)
X_alpha = GaussianGammaISO(mu_tau, np.identity(3), 5, 5)
self.assertEqual(X_alpha.plates, ())
self.assertEqual(X_alpha.dims, ((3, ), (3, 3), (), ()))
pass
def test_message_to_child(self):
"""
Test the message to child of GaussianGamma node.
"""
# Simple test
mu = np.array([1,2,3])
Lambda = np.identity(3)
a = 2
b = 10
X_alpha = GaussianGamma(mu, Lambda, a, b)
u = X_alpha._message_to_child()
self.assertEqual(len(u), 4)
tau = np.array(a/b)
self.assertAllClose(u[0],
tau[...,None] * mu)
self.assertAllClose(u[1],
(linalg.inv(Lambda)
+ tau[...,None,None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2],
tau)
self.assertAllClose(u[3],
-np.log(b) + special.psi(a))
# Test with unknown parents
mu = Gaussian(np.arange(3), 10*np.identity(3))
Lambda = Wishart(10, np.identity(3))
a = 2
b = Gamma(3, 15)
X_alpha = GaussianGamma(mu, Lambda, a, b)
u = X_alpha._message_to_child()
(mu, mumu) = mu._message_to_child()
Cov_mu = mumu - linalg.outer(mu, mu)
(Lambda, _) = Lambda._message_to_child()
(b, _) = b._message_to_child()
(tau, logtau) = Gamma(a, b + 0.5*np.sum(Lambda*Cov_mu))._message_to_child()
self.assertAllClose(u[0],
tau[...,None] * mu)
self.assertAllClose(u[1],
(linalg.inv(Lambda)
+ tau[...,None,None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2],
tau)
self.assertAllClose(u[3],
logtau)
# Test with plates
mu = Gaussian(np.reshape(np.arange(3*4), (4,3)),
10*np.identity(3),
plates=(4,))
Lambda = Wishart(10, np.identity(3))
a = 2
b = Gamma(3, 15)
X_alpha = GaussianGamma(mu, Lambda, a, b, plates=(4,))
u = X_alpha._message_to_child()
(mu, mumu) = mu._message_to_child()
Cov_mu = mumu - linalg.outer(mu, mu)
(Lambda, _) = Lambda._message_to_child()
(b, _) = b._message_to_child()
(tau, logtau) = Gamma(a,
b + 0.5*np.sum(Lambda*Cov_mu,
axis=(-1,-2)))._message_to_child()
self.assertAllClose(u[0] * np.ones((4,1)),
np.ones((4,1)) * tau[...,None] * mu)
self.assertAllClose(u[1] * np.ones((4,1,1)),
np.ones((4,1,1)) * (linalg.inv(Lambda)
+ tau[...,None,None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2] * np.ones(4),
np.ones(4) * tau)
self.assertAllClose(u[3] * np.ones(4),
np.ones(4) * logtau)
pass
def test_messages(self):
D = 2
M = 3
np.random.seed(42)
def check(mu, Lambda, alpha, beta, ndim):
X = GaussianGamma(
mu,
(
Lambda if isinstance(Lambda._moments, WishartMoments) else
Lambda.as_wishart(ndim=ndim)
),
alpha,
beta,
ndim=ndim
)
self.assert_moments(
X,
postprocess=lambda u: [
u[0],
u[1] + linalg.transpose(u[1], ndim=ndim),
u[2],
u[3]
],
rtol=1e-5,
atol=1e-6,
eps=1e-8
)
X.observe(
(
np.random.randn(*(X.plates + X.dims[0])),
np.random.rand(*X.plates)
)
)
self.assert_message_to_parent(X, mu)
self.assert_message_to_parent(
X,
Lambda,
postprocess=lambda m: [
m[0] + linalg.transpose(m[0], ndim=ndim),
m[1],
]
)
self.assert_message_to_parent(X, beta)
check(
Gaussian(np.random.randn(M, D), random.covariance(D), plates=(M,)),
Wishart(D + np.random.rand(M), random.covariance(D), plates=(M,)),
np.random.rand(M),
Gamma(np.random.rand(M), np.random.rand(M), plates=(M,)),
ndim=1
)
check(
GaussianARD(np.random.randn(M, D), np.random.rand(M, D), ndim=0),
Gamma(np.random.rand(M, D), np.random.rand(M, D)),
np.random.rand(M, D),
Gamma(np.random.rand(M, D), np.random.rand(M, D)),
ndim=0
)
pass
current_step = -1
# In[ ]:
# In[41]:
action_space = {-1, 0, 1}
# In[42]:
observations
# In[88]:
Lambda = Wishart(2, [[1, 0], [0, 1]])
np.zeros(D)
np.identity(D)
# In[135]:
#http://www.bayespy.org/user_api/generated/generated/bayespy.nodes.SwitchingGaussianMarkovChain.html#bayespy-nodes-switchinggaussianmarkovchain
obs_nodes = {}
action_nodes = {}
O_D = int(np.prod(env.observation_space.shape)
) # will only work with low dimensions. Need filter
if isinstance(env.action_space, gym.spaces.discrete.Discrete):
A_D = env.action_space.n
#mu = np.zeros(D)
#lambda_ = 1e-5*np.identity(D)