# Author: Yin Cheng Ng
# The code in this file is mainly derived from GPflow https://github.com/markvdw/GPflow-inter-domain/tree/master/GPflow
# with minor modifications to speed-up computation for GGP.
from __future__ import absolute_import
from GPflow.svgp import SVGP
from GPflow._settings import settings
import tensorflow as tf
float_type = settings.dtypes.float_type
class GraphSVGP(SVGP):
# Does not support Minibatch
def build_likelihood(self):
"""
This gives a variational bound on the model likelihood.
"""
# Get prior KL.
KL = self.build_prior_KL()
# Get conditionals
fmean, fvar = self._elbo_helper()
# Get variational expectations.
var_exp = self.likelihood.variational_expectations(fmean, fvar, self.Y)
# re-scale for minibatch size
scale = tf.cast(self.num_data, float_type)/tf.cast(tf.shape(self.X)[0], float_type)
return tf.reduce_sum(var_exp) * scale - KL
def _elbo_helper(self):
# compute kernel stuff
kern = self.kern; f = self.q_mu;
num_data = tf.shape(self.Z)[0] # M
num_func = tf.shape(f)[1] # K
Kmn = kern.Kzx(self.Z, self.X)
Kmm = kern.Kzz(self.Z) + tf.eye(num_data, dtype=float_type) * settings.numerics.jitter_level
Lm = tf.cholesky(Kmm)
# Compute the projection matrix A
A = tf.matrix_triangular_solve(Lm, Kmn, lower=True)
# compute the covariance due to the conditioning
fvar = kern.Kdiag_tr() - tf.reduce_sum(tf.square(A), 0)
shape = tf.stack([num_func, 1])
fvar = tf.tile(tf.expand_dims(fvar, 0), shape) # K x N x N or K x N
# another backsubstitution in the unwhitened case
if not self.whiten:
A = tf.matrix_triangular_solve(tf.transpose(Lm), A, lower=False)
# construct the conditional mean
fmean = tf.matmul(A, f, transpose_a=True)
if self.q_sqrt is not None:
if self.q_sqrt.get_shape().ndims == 2:
LTA = A * tf.expand_dims(tf.transpose(self.q_sqrt), 2) # K x M x N
elif self.q_sqrt.get_shape().ndims == 3:
L = tf.matrix_band_part(tf.transpose(self.q_sqrt, (2, 0, 1)), -1, 0) # K x M x M
A_tiled = tf.tile(tf.expand_dims(A, 0), tf.stack([num_func, 1, 1]))
LTA = tf.matmul(L, A_tiled, transpose_a=True) # K x M x N
else: # pragma: no cover
raise ValueError("Bad dimension for q_sqrt: %s" %
str(self.q_sqrt.get_shape().ndims))
fvar = fvar + tf.reduce_sum(tf.square(LTA), 1) # K x N
fvar = tf.transpose(fvar) # N x K or N x N x K
return fmean + self.mean_function(self.X), fvar
