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
svgp.py
import tensorflow as tf
import numpy as np
from param import Param
from .model import GPModel
import transforms
import conditionals
from .mean_functions import Zero
from tf_hacks import eye
import kullback_leiblers
class SVGP(GPModel):
"""
This is the Sparse Variational GP (SVGP). The key reference is
@inproceedings{hensman2014scalable,
title={Scalable Variational Gaussian Process Classification},
author={Hensman, James and Matthews, Alexander G. de G. and Ghahramani, Zoubin},
booktitle={Proceedings of AISTATS},
year={2015}
}
"""
def __init__(self, X, Y, kern, likelihood, Z, mean_function=Zero(), num_latent=None, q_diag=False, whiten=True, minibatch=None):
"""
X is a data matrix, size N x D
Y is a data matrix, size N x R
kern, likelihood, mean_function are appropriate GPflow objects
Z is a matrix of pseudo inputs, size M x D
num_latent is the number of latent process to use, default to Y.shape[1]
q_diag is a boolean. If True, the covariance is approximated by a diagonal matrix.
whiten is a boolean. It True, we use the whitened represenation of the inducing points.
"""
GPModel.__init__(self, X, Y, kern, likelihood, mean_function)
self.q_diag, self.whiten = q_diag, whiten
self.Z = Param(Z)
self.num_latent = num_latent or Y.shape[1]
self.num_inducing = Z.shape[0]
#these variables used for minibatching
self._tfX = tf.Variable(self.X, name="tfX")
self._tfY = tf.Variable(self.Y, name="tfY")
self.minibatch = minibatch
self.q_mu = Param(np.zeros((self.num_inducing, self.num_latent)))
if self.q_diag:
self.q_sqrt = Param(np.ones((self.num_inducing, self.num_latent)), transforms.positive)
else:
self.q_sqrt = Param(np.array([np.eye(self.num_inducing) for _ in range(self.num_latent)]).swapaxes(0,2))
@property
def minibatch(self):
if self._minibatch is None:
return len(self.X)
else:
return self._minibatch
@minibatch.setter
def minibatch(self, val):
self._minibatch = val
def build_prior_KL(self):
if self.whiten:
if self.q_diag:
KL = kullback_leiblers.gauss_kl_white_diag(self.q_mu, self.q_sqrt, self.num_latent)
else:
KL = kullback_leiblers.gauss_kl_white(self.q_mu, self.q_sqrt, self.num_latent)
else:
K = self.kern.K(self.Z) + eye(self.num_inducing) * 1e-6
if self.q_diag:
KL = kullback_leiblers.gauss_kl_diag(self.q_mu, self.q_sqrt, K, self.num_latent)
else:
KL = kullback_leiblers.gauss_kl(self.q_mu, self.q_sqrt, K, self.num_latent)
return KL
def _compile(self, optimizer=None):
"""
compile the tensorflow function "self._objective"
"""
opt_step = GPModel._compile(self, optimizer)
def obj(x):
if self.minibatch / float(len(self.X)) > 0.5:
ss = np.random.permutation(len(self.X))[:self.minibatch]
else:
# This is much faster than above, and for N >> minibatch, it doesn't make much difference. This actually
# becomes the limit when N is around 10**6, which isn't uncommon when using SVI.
ss = np.random.randint(len(self.X), size=self.minibatch)
return self._session.run([self._minusF, self._minusG], feed_dict={self._free_vars: x,
self._tfX: self.X[ss, :],
self._tfY: self.Y[ss, :]})
self._objective = obj
return opt_step
def optimize(self, method='L-BFGS-B', tol=None, callback=None, max_iters=1000, **kw):
def calc_feed_dict():
ss = np.random.randint(len(self.dX), size=self.minibatch)
return {self.X: self.dX[ss, :], self.Y: self.dY[ss, :]}
return GPModel.optimize(self, method, tol, callback, max_iters, calc_feed_dict, **kw)
def build_likelihood(self):
"""
This gives a variational bound on the model likelihood.
"""
#Get prior KL.
KL = self.build_prior_KL()
#Get conditionals
if self.whiten:
fmean, fvar = conditionals.gaussian_gp_predict_whitened(self._tfX, self.Z, self.kern, self.q_mu, self.q_sqrt, self.num_latent)
else:
fmean, fvar = conditionals.gaussian_gp_predict(self._tfX, self.Z, self.kern, self.q_mu, self.q_sqrt, self.num_latent)
#add in mean function to conditionals.
fmean += self.mean_function(self._tfX)
#Get variational expectations.
variational_expectations = self.likelihood.variational_expectations(fmean, fvar, self._tfY)
minibatch_scale = len(self.X) / tf.cast(tf.shape(self._tfX)[0], tf.float64)
return tf.reduce_sum(variational_expectations) * minibatch_scale - KL
def build_predict(self, Xnew, full_cov=False):
if self.whiten:
mu, var = conditionals.gaussian_gp_predict_whitened(Xnew, self.Z, self.kern, self.q_mu, self.q_sqrt, self.num_latent, full_cov)
else:
mu, var = conditionals.gaussian_gp_predict(Xnew, self.Z, self.kern, self.q_mu, self.q_sqrt, self.num_latent, full_cov)
return mu + self.mean_function(Xnew), var
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