def logp(value, n, p):
return check_parameters(
factln(n) - factln(value).sum() + (value * at.log(p)).sum(),
at.all(value >= 0),
at.all(0 <= p),
at.all(p <= 1),
at.isclose(p.sum(), 1),
)
def logp(value, n, p):
return bound(
factln(n) - factln(value).sum() + (value * at.log(p)).sum(),
at.all(value >= 0),
at.all(0 <= p),
at.all(p <= 1),
at.isclose(p.sum(), 1),
broadcast_conditions=False,
)
def logp(self, value):
n = self.n
p = self.p
return bound(
factln(n) - factln(value).sum() + (value * aet.log(p)).sum(),
aet.all(value >= 0),
aet.all(0 <= p),
aet.all(p <= 1),
aet.isclose(p.sum(), 1),
broadcast_conditions=False,
)
def dlogp(inputs, gradients):
(g_logp, ) = gradients
cov, delta = inputs
g_logp.tag.test_value = floatX(1.0)
n, k = delta.shape
chol_cov = cholesky(cov)
diag = aet.nlinalg.diag(chol_cov)
ok = aet.all(diag > 0)
chol_cov = aet.switch(ok, chol_cov, aet.fill(chol_cov, 1))
delta_trans = solve_lower(chol_cov, delta.T).T
inner = n * aet.eye(k) - aet.dot(delta_trans.T, delta_trans)
g_cov = solve_upper(chol_cov.T, inner)
g_cov = solve_upper(chol_cov.T, g_cov.T)
tau_delta = solve_upper(chol_cov.T, delta_trans.T)
g_delta = tau_delta.T
g_cov = aet.switch(ok, g_cov, -np.nan)
g_delta = aet.switch(ok, g_delta, -np.nan)
return [-0.5 * g_cov * g_logp, -g_delta * g_logp]
def check_parameters(logp: Variable, *conditions: Iterable[Variable], msg: str = ""):
"""
Wrap a log probability graph in a CheckParameterValue that asserts several
conditions are True. When conditions are not met a ParameterValueError assertion is
raised, with an optional custom message defined by `msg`
Note that check_parameter should not be used to enforce the logic of the logp
expression under the normal parameter support as it can be disabled by the user via
check_bounds = False in pm.Model()
"""
# at.all does not accept True/False, but accepts np.array(True)/np.array(False)
conditions = [
cond if (cond is not True and cond is not False) else np.array(cond) for cond in conditions
]
all_true_scalar = at.all([at.all(cond) for cond in conditions])
return CheckParameterValue(msg)(logp, all_true_scalar)
def local_check_parameter_to_ninf_switch(fgraph, node):
if isinstance(node.op, CheckParameterValue):
logp_expr, *logp_conds = node.inputs
if len(logp_conds) > 1:
logp_cond = at.all(logp_conds)
else:
(logp_cond,) = logp_conds
out = at.switch(logp_cond, logp_expr, -np.inf)
out.name = node.op.msg
if out.dtype != node.outputs[0].dtype:
out = at.cast(out, node.outputs[0].dtype)
return [out]
def alltrue_scalar(vals):
return aet.all([aet.all(1 * val) for val in vals])
def MvNormalLogp():
"""Compute the log pdf of a multivariate normal distribution.
This should be used in MvNormal.logp once Theano#5908 is released.
Parameters
----------
cov: aet.matrix
The covariance matrix.
delta: aet.matrix
Array of deviations from the mean.
"""
cov = aet.matrix("cov")
cov.tag.test_value = floatX(np.eye(3))
delta = aet.matrix("delta")
delta.tag.test_value = floatX(np.zeros((2, 3)))
solve_lower = Solve(A_structure="lower_triangular")
solve_upper = Solve(A_structure="upper_triangular")
cholesky = Cholesky(lower=True, on_error="nan")
n, k = delta.shape
n, k = f(n), f(k)
chol_cov = cholesky(cov)
diag = aet.nlinalg.diag(chol_cov)
ok = aet.all(diag > 0)
chol_cov = aet.switch(ok, chol_cov, aet.fill(chol_cov, 1))
delta_trans = solve_lower(chol_cov, delta.T).T
result = n * k * aet.log(f(2) * np.pi)
result += f(2) * n * aet.sum(aet.log(diag))
result += (delta_trans**f(2)).sum()
result = f(-0.5) * result
logp = aet.switch(ok, result, -np.inf)
def dlogp(inputs, gradients):
(g_logp, ) = gradients
cov, delta = inputs
g_logp.tag.test_value = floatX(1.0)
n, k = delta.shape
chol_cov = cholesky(cov)
diag = aet.nlinalg.diag(chol_cov)
ok = aet.all(diag > 0)
chol_cov = aet.switch(ok, chol_cov, aet.fill(chol_cov, 1))
delta_trans = solve_lower(chol_cov, delta.T).T
inner = n * aet.eye(k) - aet.dot(delta_trans.T, delta_trans)
g_cov = solve_upper(chol_cov.T, inner)
g_cov = solve_upper(chol_cov.T, g_cov.T)
tau_delta = solve_upper(chol_cov.T, delta_trans.T)
g_delta = tau_delta.T
g_cov = aet.switch(ok, g_cov, -np.nan)
g_delta = aet.switch(ok, g_delta, -np.nan)
return [-0.5 * g_cov * g_logp, -g_delta * g_logp]
return OpFromGraph([cov, delta], [logp], grad_overrides=dlogp, inline=True)
