本文整理汇总了Python中bayespy.nodes.GaussianARD.lower_bound_contribution方法的典型用法代码示例。如果您正苦于以下问题：Python GaussianARD.lower_bound_contribution方法的具体用法？Python GaussianARD.lower_bound_contribution怎么用？Python GaussianARD.lower_bound_contribution使用的例子？那么恭喜您, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类bayespy.nodes.GaussianARD的用法示例。
在下文中一共展示了GaussianARD.lower_bound_contribution方法的3个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: check_lower_bound
# 需要导入模块: from bayespy.nodes import GaussianARD [as 别名]
# 或者: from bayespy.nodes.GaussianARD import lower_bound_contribution [as 别名]
def check_lower_bound(shape_mu, shape_alpha, plates_mu=(), **kwargs):
M = GaussianARD(np.ones(plates_mu + shape_mu),
np.ones(plates_mu + shape_mu),
shape=shape_mu,
plates=plates_mu)
if not ('ndim' in kwargs or 'shape' in kwargs):
kwargs['ndim'] = len(shape_mu)
X = GaussianARD(M,
2*np.ones(shape_alpha),
**kwargs)
Y = GaussianARD(X,
3*np.ones(X.get_shape(0)),
**kwargs)
Y.observe(4*np.ones(Y.get_shape(0)))
X.update()
Cov = 1/(2+3)
mu = Cov * (2*1 + 3*4)
x2 = mu**2 + Cov
logH_X = (+ 0.5*(1+np.log(2*np.pi))
+ 0.5*np.log(Cov))
logp_X = (- 0.5*np.log(2*np.pi)
+ 0.5*np.log(2)
- 0.5*2*(x2 - 2*mu*1 + 1**2+1))
r = np.prod(X.get_shape(0))
self.assertAllClose(r * (logp_X + logH_X),
X.lower_bound_contribution())示例2: test_lower_bound_contribution
# 需要导入模块: from bayespy.nodes import GaussianARD [as 别名]
# 或者: from bayespy.nodes.GaussianARD import lower_bound_contribution [as 别名]
def test_lower_bound_contribution(self):
a = 15
b = 21
y = 4
x = Gamma(a, b)
x.observe(y)
testing.assert_allclose(
x.lower_bound_contribution(),
(
a * np.log(b) +
(a - 1) * np.log(y) -
b * y -
special.gammaln(a)
)
)
# Just one latent node so we'll get exact marginal likelihood
#
# p(Y) = p(Y,X)/p(X|Y) = p(Y|X) * p(X) / p(X|Y)
a = 2.3
b = 4.1
x = 1.9
y = 4.8
tau = Gamma(a, b)
Y = GaussianARD(x, tau)
Y.observe(y)
mu = x
nu = 2 * a
s2 = b / a
a_post = a + 0.5
b_post = b + 0.5*(y - x)**2
tau.update()
testing.assert_allclose(
[-b_post, a_post],
tau.phi
)
testing.assert_allclose(
Y.lower_bound_contribution() + tau.lower_bound_contribution(), # + tau.g,
(
special.gammaln((nu+1)/2)
- special.gammaln(nu/2)
- 0.5 * np.log(nu)
- 0.5 * np.log(np.pi)
- 0.5 * np.log(s2)
- 0.5 * (nu + 1) * np.log(
1 + (y - mu)**2 / (nu * s2)
)
)
)
return示例3: test_lowerbound
# 需要导入模块: from bayespy.nodes import GaussianARD [as 别名]
# 或者: from bayespy.nodes.GaussianARD import lower_bound_contribution [as 别名]
def test_lowerbound(self):
"""
Test the variational Bayesian lower bound term for GaussianARD.
"""
# Test vector formula with full noise covariance
m = np.random.randn(2)
alpha = np.random.rand(2)
y = np.random.randn(2)
X = GaussianARD(m, alpha, ndim=1)
V = np.array([[3,1],[1,3]])
Y = Gaussian(X, V)
Y.observe(y)
X.update()
Cov = np.linalg.inv(np.diag(alpha) + V)
mu = np.dot(Cov, np.dot(V, y) + alpha*m)
x2 = np.outer(mu, mu) + Cov
logH_X = (+ 2*0.5*(1+np.log(2*np.pi))
+ 0.5*np.log(np.linalg.det(Cov)))
logp_X = (- 2*0.5*np.log(2*np.pi)
+ 0.5*np.log(np.linalg.det(np.diag(alpha)))
- 0.5*np.sum(np.diag(alpha)
* (x2
- np.outer(mu,m)
- np.outer(m,mu)
+ np.outer(m,m))))
self.assertAllClose(logp_X + logH_X,
X.lower_bound_contribution())
def check_lower_bound(shape_mu, shape_alpha, plates_mu=(), **kwargs):
M = GaussianARD(np.ones(plates_mu + shape_mu),
np.ones(plates_mu + shape_mu),
shape=shape_mu,
plates=plates_mu)
if not ('ndim' in kwargs or 'shape' in kwargs):
kwargs['ndim'] = len(shape_mu)
X = GaussianARD(M,
2*np.ones(shape_alpha),
**kwargs)
Y = GaussianARD(X,
3*np.ones(X.get_shape(0)),
**kwargs)
Y.observe(4*np.ones(Y.get_shape(0)))
X.update()
Cov = 1/(2+3)
mu = Cov * (2*1 + 3*4)
x2 = mu**2 + Cov
logH_X = (+ 0.5*(1+np.log(2*np.pi))
+ 0.5*np.log(Cov))
logp_X = (- 0.5*np.log(2*np.pi)
+ 0.5*np.log(2)
- 0.5*2*(x2 - 2*mu*1 + 1**2+1))
r = np.prod(X.get_shape(0))
self.assertAllClose(r * (logp_X + logH_X),
X.lower_bound_contribution())
# Test scalar formula
check_lower_bound((), ())
# Test array formula
check_lower_bound((2,3), (2,3))
# Test dim-broadcasting of mu
check_lower_bound((3,1), (2,3,4))
# Test dim-broadcasting of alpha
check_lower_bound((2,3,4), (3,1))
# Test dim-broadcasting of mu and alpha
check_lower_bound((3,1), (3,1),
shape=(2,3,4))
# Test dim-broadcasting of mu with plates
check_lower_bound((), (),
plates_mu=(),
shape=(),
plates=(5,))
# BUG: Scalar parents for array variable caused einsum error
check_lower_bound((), (),
shape=(3,))
# BUG: Log-det was summed over plates
check_lower_bound((), (),
shape=(3,),
plates=(4,))
pass