def _build_predict(self, Xnew, full_cov=False):
"""
Compute the mean and variance of the latent function at some new points
Xnew. For a derivation of the terms in here, see the associated SGPR
notebook.
"""
num_inducing = len(self.feature)
err = self.Y - self.mean_function(self.X)
Kuf = self.feature.Kuf(self.kern, self.X)
Kuu = self.feature.Kuu(self.kern, jitter=settings.numerics.jitter_level)
Kus = self.feature.Kuf(self.kern, Xnew)
sigma = tf.sqrt(self.likelihood.variance)
L = tf.cholesky(Kuu)
A = tf.matrix_triangular_solve(L, Kuf, lower=True) / sigma
B = tf.matmul(A, A, transpose_b=True) + tf.eye(num_inducing, dtype=settings.float_type)
LB = tf.cholesky(B)
Aerr = tf.matmul(A, err)
c = tf.matrix_triangular_solve(LB, Aerr, lower=True) / sigma
tmp1 = tf.matrix_triangular_solve(L, Kus, lower=True)
tmp2 = tf.matrix_triangular_solve(LB, tmp1, lower=True)
mean = tf.matmul(tmp2, c, transpose_a=True)
if full_cov:
var = self.kern.K(Xnew) + tf.matmul(tmp2, tmp2, transpose_a=True) \
- tf.matmul(tmp1, tmp1, transpose_a=True)
shape = tf.stack([1, 1, tf.shape(self.Y)[1]])
var = tf.tile(tf.expand_dims(var, 2), shape)
else:
var = self.kern.Kdiag(Xnew) + tf.reduce_sum(tf.square(tmp2), 0) \
- tf.reduce_sum(tf.square(tmp1), 0)
shape = tf.stack([1, tf.shape(self.Y)[1]])
var = tf.tile(tf.expand_dims(var, 1), shape)
return mean + self.mean_function(Xnew), var
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