def logp(self, X):
v = self.v
p = self.p
S = self.S
Z = self.Z
result = -Z + log(det(X)) * -(v + p + 1.) / 2. - trace(S.dot(matrix_inverse(X))) / 2.
return ifelse(gt(v, p-1), result, self.invalid)
def logp(self, X):
v = self.v
p = self.p
Z = self.Z
inv_S = self.inv_S
result = -Z + log(det(X)) * (v - p - 1) / 2. - trace(inv_S.dot(X)) / 2.
return ifelse(gt(v, p-1), result, self.invalid)
def logp(X):
IVI = det(V)
return bound(
((n - p - 1) * log(IVI) - trace(solve(V, X)) -
n * p * log(
2) - n * log(IVI) - 2 * multigammaln(p, n / 2)) / 2,
n > p - 1)
def logp(X):
IVI = det(V)
return bound(
((n - p - 1) * log(IVI) - trace(matrix_inverse(V).dot(X)) -
n * p * log(
2) - n * log(IVI) - 2 * multigammaln(p, n / 2)) / 2,
all(n > p - 1))
def s_deg_of_freedom(self):
"""
Degrees of freedom aka "effective number of parameters"
of kernel smoother.
Defined pg. 25 of Rasmussen & Williams.
"""
K, y, var_y, N = self.kyn()
rK = psd(K + var_y * tensor.eye(N))
dof = trace(tensor.dot(K, matrix_inverse(rK)))
if dof.dtype != self.dtype:
raise TypeError('dof dtype', dof.dtype)
return dof
def s_deg_of_freedom(self):
"""
Degrees of freedom aka "effective number of parameters"
of kernel smoother.
Defined pg. 25 of Rasmussen & Williams.
"""
K, y, var_y, N = self.kyn()
rK = psd(K + var_y * tensor.eye(N))
dof = trace(tensor.dot(K, matrix_inverse(rK)))
if dof.dtype != self.dtype:
raise TypeError('dof dtype', dof.dtype)
return dof
def logp(self, X):
n = self.n
p = self.p
V = self.V
IVI = det(V)
return bound(
((n - p - 1) * log(IVI) - trace(matrix_inverse(V).dot(X)) -
n * p * log(
2) - n * log(IVI) - 2 * multigammaln(p, n / 2)) / 2,
n > (p - 1))
def trace(self):
from theano.sandbox.linalg import trace
return trace(self)
def trace(self):
from theano.sandbox.linalg import trace
return trace(self)
C2 = tt.dmatrix('C2')
v2 = tt.dscalar('v2')
logdet1 = tt.dscalar('logdet1')
logdet2 = tt.dscalar('logdet2')
# log-partition functions
A1 = log_partf(b1, s1, C1, v1)
A2 = log_partf(b2, s2, C2, v2)
A1s = log_partf(b1, s1, C1, v1, logdet1)
A2s = log_partf(b2, s2, C2, v2, logdet2)
# KL divergence
D_KL = A2s - A1s \
+ tt.dot((b1 - b2).T, tt.grad(A1, b1)) \
+ tl.trace(tt.dot(C1 - C2, tt.grad(A1, C1))) \
+ (s1 - s2) * tt.grad(A1, s1) \
+ (v1 - v2) * tt.grad(A1s, v1)
def KL_divergence(m1, s1, P1, v1, m2, s2, P2, v2):
# natural parameters
b1 = -2. * s1 * m1
b2 = -2. * s2 * m2
C1 = P1 + s1 * np.dot(m1, m1.T)
C2 = P2 + s2 * np.dot(m2, m2.T)
# precompute log-determinants
logdet1 = np.linalg.slogdet(P1)[1]
logdet2 = np.linalg.slogdet(P2)[1]
def logp(X):
IVI = det(V)
return bound(
((n - p - 1) * log(IVI) - trace(solve(V, X)) - n * p * log(2) -
n * log(IVI) - 2 * multigammaln(p, n / 2)) / 2, n > p - 1)
