import tensorflow as tf
from .model import GPModel
from .densities import multivariate_normal
from .mean_functions import Zero
from . import likelihoods
from .tf_hacks import eye
class GPR(GPModel):
def __init__(self, X, Y, kern, mean_function=Zero()):
"""
X is a data matrix, size N x D
Y is a data matrix, size N x R
kern, mean_function are appropriate GPflow objects
This is a vanilla implementation of GP regression with a Gaussian
likelihood. Multiple columns of Y are treated independently.
"""
likelihood = likelihoods.Gaussian()
GPModel.__init__(self, X, Y, kern, likelihood, mean_function)
self.num_data = X.shape[0]
self.num_latent = Y.shape[1]
def build_likelihood(self):
"""
Construct a tensorflow function to compute the likelihood.
\log p(Y, V | theta).
"""
K = self.kern.K(self.X) + eye(self.num_data) * self.likelihood.variance
L = tf.cholesky(K)
m = self.mean_function(self.X)
return multivariate_normal(self.Y, m, L)
def build_predict(self, Xnew, full_cov=False):
"""
Xnew is a data matrix, point at which we want to predict
This method computes
p(F* | Y )
where F* are points on the GP at Xnew, Y are noisy observations at X.
"""
Kx = self.kern.K(self.X, Xnew)
K = self.kern.K(self.X) + eye(self.num_data) * self.likelihood.variance
L = tf.cholesky(K)
A = tf.matrix_triangular_solve(L, Kx, lower=True)
V = tf.matrix_triangular_solve(L, self.Y - self.mean_function(self.X))
fmean = tf.matmul(tf.transpose(A), V) + self.mean_function(Xnew)
if full_cov:
fvar = self.kern.K(Xnew) - tf.matmul(tf.transpose(A), A)
shape = tf.pack([1, 1, tf.shape(self.Y)[1]])
fvar = tf.tile(tf.expand_dims(fvar, 2), shape)
else:
fvar = self.kern.Kdiag(Xnew) - tf.reduce_sum(tf.square(A), 0)
fvar = tf.tile(tf.reshape(fvar, (-1, 1)), [1, self.Y.shape[1]])
return fmean, fvar