def model():
# Start with a zero kernels.
kernel_inputs = ZeroKernel() # Kernel over inputs.
kernel_outputs = ZeroKernel() # Kernel over outputs.
# Determine indices corresponding to the inputs and outputs.
m_inds, p_inds, p_num = _determine_indices(m, pi, markov)
# Add nonlinear kernel over the inputs.
variance = vs.bnd(name='{}/input/var'.format(pi), init=1.)
scales = vs.bnd(name='{}/input/scales'.format(0 if scale_tie else pi),
init=_vector_from_init(scale, m))
if rq:
k = RQ(
vs.bnd(name='{}/input/alpha', init=1e-2, lower=1e-3,
upper=1e3))
else:
k = EQ()
kernel_inputs += variance * k.stretch(scales)
# Add a locally periodic kernel over the inputs.
if per:
variance = vs.bnd(name='{}/input/per/var'.format(pi), init=1.)
scales = vs.bnd(name='{}/input/per/scales'.format(pi),
init=_vector_from_init(per_scale, 2 * m))
periods = vs.bnd(name='{}/input/per/pers'.format(pi),
init=_vector_from_init(per_period, m))
decays = vs.bnd(name='{}/input/per/decay'.format(pi),
init=_vector_from_init(per_decay, m))
kernel_inputs += variance * \
EQ().stretch(scales).periodic(periods) * \
EQ().stretch(decays)
# Add a linear kernel over the inputs.
if input_linear:
scales = vs.bnd(name='{}/input/lin/scales'.format(pi),
init=_vector_from_init(input_linear_scale, m))
const = vs.get(name='{}/input/lin/const'.format(pi), init=1.)
kernel_inputs += Linear().stretch(scales) + const
# Add linear kernel over the outputs.
if linear and pi > 0:
scales = vs.bnd(name='{}/output/lin/scales'.format(pi),
init=_vector_from_init(linear_scale, p_num))
kernel_outputs += Linear().stretch(scales)
# Add nonlinear kernel over the outputs.
if nonlinear and pi > 0:
variance = vs.bnd(name='{}/output/nonlin/var'.format(pi), init=1.)
scales = vs.bnd(name='{}/output/nonlin/scales'.format(pi),
init=_vector_from_init(nonlinear_scale, p_num))
if rq:
k = RQ(
vs.bnd(name='{}/output/nonlin/alpha'.format(pi),
init=1e-2,
lower=1e-3,
upper=1e3))
else:
k = EQ()
kernel_outputs += variance * k.stretch(scales)
# Construct noise kernel.
variance = vs.bnd(name='{}/noise'.format(pi),
init=_vector_from_init(noise, pi + 1)[pi],
lower=1e-8) # Allow noise to be small.
kernel_noise = variance * Delta()
# Construct model and return.
graph = Graph()
f = GP(kernel_inputs.select(m_inds) + kernel_outputs.select(p_inds),
graph=graph)
e = GP(kernel_noise, graph=graph)
return f, e
def model():
# Start with a zero kernels.
kernel_inputs = ZeroKernel() # Kernel over inputs.
kernel_outputs = ZeroKernel() # Kernel over outputs.
# Determine indices corresponding to the inputs and outputs.
m_inds, p_inds, p_num = _determine_indices(m, pi, markov)
# Add nonlinear kernel over the inputs.
variance = vs.bnd(name=f"{pi}/input/var", init=1.0)
scales = vs.bnd(
name=f"{0 if scale_tie else pi}/input/scales",
init=_vector_from_init(scale, m),
)
if rq:
k = RQ(
vs.bnd(name=f"{pi}/input/alpha",
init=1e-2,
lower=1e-3,
upper=1e3))
else:
k = EQ()
kernel_inputs += variance * k.stretch(scales)
# Add a locally periodic kernel over the inputs.
if per:
variance = vs.bnd(name=f"{pi}/input/per/var", init=1.0)
scales = vs.bnd(
name=f"{pi}/input/per/scales",
init=_vector_from_init(per_scale, 2 * m),
)
periods = vs.bnd(
name=f"{pi}/input/per/pers",
init=_vector_from_init(per_period, m),
)
decays = vs.bnd(
name=f"{pi}/input/per/decay",
init=_vector_from_init(per_decay, m),
)
kernel_inputs += (variance *
EQ().stretch(scales).periodic(periods) *
EQ().stretch(decays))
# Add a linear kernel over the inputs.
if input_linear:
scales = vs.bnd(
name=f"{pi}/input/lin/scales",
init=_vector_from_init(input_linear_scale, m),
)
const = vs.get(name=f"{pi}/input/lin/const", init=1.0)
kernel_inputs += Linear().stretch(scales) + const
# Add linear kernel over the outputs.
if linear and pi > 0:
scales = vs.bnd(
name=f"{pi}/output/lin/scales",
init=_vector_from_init(linear_scale, p_num),
)
kernel_outputs += Linear().stretch(scales)
# Add nonlinear kernel over the outputs.
if nonlinear and pi > 0:
variance = vs.bnd(name=f"{pi}/output/nonlin/var", init=1.0)
scales = vs.bnd(
name=f"{pi}/output/nonlin/scales",
init=_vector_from_init(nonlinear_scale, p_num),
)
if rq:
k = RQ(
vs.bnd(
name=f"{pi}/output/nonlin/alpha",
init=1e-2,
lower=1e-3,
upper=1e3,
))
else:
k = EQ()
kernel_outputs += variance * k.stretch(scales)
# Construct noise kernel.
variance = vs.bnd(
name=f"{pi}/noise",
init=_vector_from_init(noise, pi + 1)[pi],
lower=1e-8,
) # Allow noise to be small.
kernel_noise = variance * Delta()
# Construct model and return.
prior = Measure()
f = GP(kernel_inputs.select(m_inds) + kernel_outputs.select(p_inds),
measure=prior)
e = GP(kernel_noise, measure=prior)
return f, e
def model(vs):
"""Construct a model with learnable parameters."""
p = vs.struct # Varz handles positivity (and other) constraints.
kernel = p.variance.positive() * EQ().stretch(p.scale.positive())
return GP(kernel), p.noise.positive()
def model_alternative(vs, scale: Positive, variance: Positive,
noise: Positive):
"""Equivalent to :func:`model`, but with `@parametrised`."""
kernel = variance * EQ().stretch(scale)
return GP(kernel), noise
# Select only the first element of
y_context = y_context[0].data.squeeze()
x_context = x_context[0].data.squeeze()
x_target = x_target[0].data.squeeze()
y_target = y_target[0].data.squeeze()
name = f'epoch_{epoch}_sample_{i}'
# Fit the relevent GP to the data
if args.GP_type == 'RBF':
kernel = EQ().stretch(params[0].squeeze()) * (params[1].squeeze() ** 2)
elif args.GP_type == 'Matern':
kernel = Matern52().stretch(params[0].squeeze()) * (params[1].squeeze() ** 2)
f = GP(kernel)
e = GP(Delta()) * kernel_noise
gp = f + e | (x_context, y_context)
preds = gp(x_target)
gp_mean , gp_lower, gp_upper = preds.marginals()
gp_std = (gp_upper - gp_mean) / 2
if args.model in ['ANP', 'NP']:
plot_compare_processes_gp_latent(
x_target,
y_target,
x_context,
y_context,
y_target_mu.data.squeeze(),
y_target_sigma.data.squeeze(),
gp_mean,