def test_quadrature(white, mean):
with session_context() as session:
c = DataQuadrature
d = c.tensors(white, mean)
quad_args = d.Xmu, d.Xvar, c.H, c.D_in, (c.D_out, )
mean_quad = mvnquad(d.mean_fn, *quad_args)
var_quad = mvnquad(d.var_fn, *quad_args)
mean_sq_quad = mvnquad(d.mean_sq_fn, *quad_args)
mean_analytic, var_analytic = uncertain_conditional(
d.Xmu,
d.Xvar,
d.feat,
d.kern,
d.q_mu,
d.q_sqrt,
mean_function=d.mean_function,
full_cov_output=False,
white=white)
mean_quad, var_quad, mean_sq_quad = session.run(
[mean_quad, var_quad, mean_sq_quad], feed_dict=d.feed_dict)
var_quad = var_quad + (mean_sq_quad - mean_quad**2)
mean_analytic, var_analytic = session.run(
[mean_analytic, var_analytic], feed_dict=d.feed_dict)
assert_almost_equal(mean_quad, mean_analytic, decimal=6)
assert_almost_equal(var_quad, var_analytic, decimal=6)
def test_quadrature(white, mean):
kernel = gpflow.kernels.SquaredExponential()
inducing_variable = gpflow.inducing_variables.InducingPoints(DataQuad.Z)
mean_function = mean_function_factory(mean, DataQuad.D_in, DataQuad.D_out)
effective_mean = mean_function or (lambda X: 0.0)
def conditional_fn(X):
return conditional(
X,
inducing_variable,
kernel,
DataQuad.q_mu,
q_sqrt=DataQuad.q_sqrt,
white=white,
)
def mean_fn(X):
return conditional_fn(X)[0] + effective_mean(X)
def var_fn(X):
return conditional_fn(X)[1]
quad_args = (
DataQuad.Xmu,
DataQuad.Xvar,
DataQuad.H,
DataQuad.D_in,
(DataQuad.D_out, ),
)
mean_quad = mvnquad(mean_fn, *quad_args)
var_quad = mvnquad(var_fn, *quad_args)
def mean_sq_fn(X):
return mean_fn(X)**2
mean_sq_quad = mvnquad(mean_sq_fn, *quad_args)
var_quad = var_quad + (mean_sq_quad - mean_quad**2)
mean_analytic, var_analytic = uncertain_conditional(
DataQuad.Xmu,
DataQuad.Xvar,
inducing_variable,
kernel,
DataQuad.q_mu,
DataQuad.q_sqrt,
mean_function=mean_function,
full_output_cov=False,
white=white,
)
assert_allclose(mean_quad, mean_analytic, rtol=1e-6)
assert_allclose(var_quad, var_analytic, rtol=1e-6)
def test_quadrature(white, mean):
with session_context() as session:
c = DataQuadrature
d = c.tensors(white, mean)
quad_args = d.Xmu, d.Xvar, c.H, c.D_in, (c.D_out,)
mean_quad = mvnquad(d.mean_fn, *quad_args)
var_quad = mvnquad(d.var_fn, *quad_args)
mean_sq_quad = mvnquad(d.mean_sq_fn, *quad_args)
mean_analytic, var_analytic = uncertain_conditional(
d.Xmu, d.Xvar, d.feat, d.kern,
d.q_mu, d.q_sqrt,
mean_function=d.mean_function,
full_cov_output=False,
white=white)
mean_quad, var_quad, mean_sq_quad = session.run(
[mean_quad, var_quad, mean_sq_quad], feed_dict=d.feed_dict)
var_quad = var_quad + (mean_sq_quad - mean_quad**2)
mean_analytic, var_analytic = session.run(
[mean_analytic, var_analytic], feed_dict=d.feed_dict)
assert_almost_equal(mean_quad, mean_analytic, decimal=6)
assert_almost_equal(var_quad, var_analytic, decimal=6)