def laplace_approximation(self, *args, **kwargs):
"""
Returns a :class:`AutoMultivariateNormal` instance whose posterior's `loc` and
`scale_tril` are given by Laplace approximation.
"""
guide_trace = poutine.trace(self).get_trace(*args, **kwargs)
model_trace = poutine.trace(
poutine.replay(self.model, trace=guide_trace)).get_trace(*args, **kwargs)
loss = guide_trace.log_prob_sum() - model_trace.log_prob_sum()
loc = pyro.param("{}_loc".format(self.prefix))
H = hessian(loss, loc.unconstrained())
cov = H.inverse()
scale_tril = cov.cholesky()
# calculate scale_tril from self.guide()
scale_tril_name = "{}_scale_tril".format(self.prefix)
pyro.param(scale_tril_name, scale_tril,
constraint=constraints.lower_cholesky)
# force an update to scale_tril even if it already exists
pyro.get_param_store()[scale_tril_name] = scale_tril
gaussian_guide = AutoMultivariateNormal(self.model, prefix=self.prefix)
gaussian_guide._setup_prototype(*args, **kwargs)
return gaussian_guide
def laplace_approximation(self, *args, **kwargs):
"""
Returns a :class:`AutoMultivariateNormal` instance whose posterior's `loc` and
`scale_tril` are given by Laplace approximation.
"""
guide_trace = poutine.trace(self).get_trace(*args, **kwargs)
model_trace = poutine.trace(
poutine.replay(self.model,
trace=guide_trace)).get_trace(*args, **kwargs)
loss = guide_trace.log_prob_sum() - model_trace.log_prob_sum()
H = hessian(loss, self.loc)
with torch.no_grad():
loc = self.loc.detach()
cov = H.inverse()
scale = cov.diagonal().sqrt()
cov /= scale[:, None]
cov /= scale[None, :]
scale_tril = torch.linalg.cholesky(cov)
gaussian_guide = AutoMultivariateNormal(self.model)
gaussian_guide._setup_prototype(*args, **kwargs)
# Set detached loc, scale, scale_tril parameters as computed above.
del gaussian_guide.loc
del gaussian_guide.scale
del gaussian_guide.scale_tril
gaussian_guide.register_buffer("loc", loc)
gaussian_guide.register_buffer("scale", scale)
gaussian_guide.register_buffer("scale_tril", scale_tril)
return gaussian_guide
def test_hessian_mvn():
tmp = torch.randn(3, 10)
cov = torch.matmul(tmp, tmp.t())
mvn = dist.MultivariateNormal(cov.new_zeros(3), cov)
x = torch.randn(3, requires_grad=True)
y = mvn.log_prob(x)
assert_equal(hessian(y, x), -mvn.precision_matrix)
def test_hessian_multi_variables():
x = torch.randn(3, requires_grad=True)
z = torch.randn(3, requires_grad=True)
y = (x ** 2 * z + z ** 3).sum()
H = hessian(y, (x, z))
Hxx = (2 * z).diag()
Hxz = (2 * x).diag()
Hzz = (6 * z).diag()
target_H = torch.cat([torch.cat([Hxx, Hxz]), torch.cat([Hxz, Hzz])], dim=1)
assert_equal(H, target_H)
def laplace_approximation(self, *args, **kwargs):
"""
Returns a :class:`AutoMultivariateNormal` instance whose posterior's `loc` and
`scale_tril` are given by Laplace approximation.
"""
guide_trace = poutine.trace(self).get_trace(*args, **kwargs)
model_trace = poutine.trace(
poutine.replay(self.model, trace=guide_trace)).get_trace(*args, **kwargs)
loss = guide_trace.log_prob_sum() - model_trace.log_prob_sum()
H = hessian(loss, self.loc)
cov = H.inverse()
loc = self.loc
scale_tril = cov.cholesky()
gaussian_guide = AutoMultivariateNormal(self.model)
gaussian_guide._setup_prototype(*args, **kwargs)
# Set loc, scale_tril parameters as computed above.
gaussian_guide.loc = loc
gaussian_guide.scale_tril = scale_tril
return gaussian_guide