def predict_density(self, Fmus, Fvars, Y):
"""
Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y.
i.e. if :math:`p(f_* | y) = \\mathcal{N}(Fmu, Fvar)` and :math:`p(y_*|f_*)` is the likelihood, then this
method computes the log predictive density :math:`\\log \\int p(y_*|f)p(f_* | y) df`. Here, we implement a
Monte-Carlo routine.
Parameters
----------
Fmus : array/tensor, shape=(N, K)
Mean(s) of Gaussian density.
Fvars : array/tensor, shape=(N, K(, K))
Covariance(s) of Gaussian density.
Y : arrays/tensors, shape=(N(, K))
Deterministic arguments to be passed by name to funcs.
Returns
-------
log_density : array/tensor, shape=(N(, K))
Log predictive density.
"""
if isinstance(self.invlink, SoftArgMax):
return ndiag_mc(self.logp,
self.num_monte_carlo_points,
Fmus,
Fvars,
logspace=True,
epsilon=None,
Y=Y)
else:
raise NotImplementedError
def variational_expectations(self, Fmu, Fvar, Y, Y_var, freq):
r"""
Compute the expected log density of the data, given a Gaussian
distribution for the function values.
if
q(f) = N(Fmu, Fvar)
and this object represents
p(y|f)
then this method computes
\int (\log p(y|f)) q(f) df.
Here, we implement a default Gauss-Hermite quadrature routine, but some
likelihoods (Gaussian, Poisson) will implement specific cases.
"""
if self.use_mc:
return ndiagquad(self.logp,
self.num_gauss_hermite_points,
Fmu,
Fvar,
Y=Y,
Y_var=Y_var,
freq=freq)
return ndiag_mc(self.logp,
self.num_mc_samples,
Fmu,
Fvar,
Y=Y,
Y_var=Y_var,
freq=freq)
def _mc_quadrature(self,
funcs,
Fmu,
Fvar,
logspace: bool = False,
epsilon=None,
**Ys):
return ndiag_mc(funcs, self.num_monte_carlo_points, Fmu, Fvar,
logspace, epsilon, **Ys)
def single_predict_mean(args):
Fmu, Fvar = args
integrand2 = lambda *X: self.likelihood.conditional_variance(
*X) + tf.square(self.likelihood.conditional_mean(*X))
epsilon = None
E_y, E_y2 = ndiag_mc(
[self.likelihood.conditional_mean, integrand2],
S=self.likelihood.num_monte_carlo_points,
Fmu=Fmu,
Fvar=Fvar,
epsilon=epsilon)
return E_y
def variational_expectations(self,
Fmu,
Fvar,
Y,
Y_var,
freq,
mc=False,
mvn=False):
r"""
Compute the expected log density of the data, given a Gaussian
distribution for the function values.
if
q(f) = N(Fmu, Fvar)
and this object represents
p(y|f)
then this method computes
\int (\log p(y|f)) q(f) df.
Here, we implement a default Gauss-Hermite quadrature routine, but some
likelihoods (Gaussian, Poisson) will implement specific cases.
"""
if mvn:
assert len(Fvar.shape) == 3
if not mvn:
if not mc:
return ndiagquad(self.logp,
self.num_gauss_hermite_points,
Fmu,
Fvar,
Y=Y,
Y_var=Y_var,
freq=freq)
else:
return ndiag_mc(self.logp,
self.num_mc_samples,
Fmu,
Fvar,
Y=Y,
Y_var=Y_var,
freq=freq)
else:
if not mc:
raise ValueError("Too slow to do this")
else:
return mvn_mc(self.logp,
self.num_mc_samples,
Fmu,
Fvar,
Y=Y,
Y_var=Y_var,
freq=freq)