Revision f66b45f991cbdca24732c38df1b2d5b6d15916ed authored by James Hensman on 13 April 2016, 22:07:31 UTC, committed by James Hensman on 13 April 2016, 22:07:31 UTC
sgpmc.py
import numpy as np
import tensorflow as tf
from .model import GPModel
from .param import Param
from .conditionals import conditional
from .priors import Gaussian
from .mean_functions import Zero
class SGPMC(GPModel):
def __init__(self, X, Y, kern, likelihood, Z, mean_function=Zero(), num_latent=None):
"""
X is a data matrix, size N x D
Y is a data matrix, size N x R
Z is a data matrix, of inducing inputs, size M x D
kern, likelihood, mean_function are appropriate GPflow objects
This is the Sparse Variational GP using MCMC (SGPMC). The key reference is
@inproceedings{hensman2015mcmc,
title={MCMC for Variatinoally Sparse Gaussian Processes},
author={Hensman, James and Matthews, Alexander G. de G. and Filippone, Maurizio and Ghahramani, Zoubin},
booktitle={Proceedings of NIPS},
year={2015}
}
The latent function values are represented by centered
(whitened) variables, so
v ~ N(0, I)
u = Lv
with
L L^T = K
"""
GPModel.__init__(self, X, Y, kern, likelihood, mean_function)
self.num_data = X.shape[0]
self.num_inducing = Z.shape[0]
self.num_latent = num_latent or Y.shape[1]
self.Z = Z # Z is not a parameter!
self.V = Param(np.zeros((self.num_inducing, self.num_latent)))
self.V.prior = Gaussian(0., 1.)
def build_likelihood(self):
"""
This function computes the (log) optimal distribution for v, q*(v).
"""
#get the (marginals of) q(f): exactly predicting!
fmean, fvar = conditional(self.X, self.Z, self.kern, self.V, num_columns=self.num_latent, full_cov=False, q_sqrt=None, whiten=True)
fmean += self.mean_function(self.X)
return tf.reduce_sum( self.likelihood.variational_expectations(fmean, fvar, self.Y) )
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* | (U=LV) )
where F* are points on the GP at Xnew, F=LV are points on the GP at Z,
"""
mu, var = conditional(Xnew, self.Z, self.kern, self.V, num_columns=self.num_latent, full_cov=full_cov, q_sqrt=None, whiten=True)
return mu + self.mean_function(Xnew), var
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