# Copyright (c) 2014, James Hensman, Alex Matthews
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
from ..util import choleskies
from .sparse_gp import SparseGP
from .parameterization.param import Param
from ..inference.latent_function_inference.svgp import SVGP as svgp_inf
[docs]class SVGP(SparseGP):
def __init__(self, X, Y, Z, kernel, likelihood, mean_function=None, name='SVGP', Y_metadata=None, batchsize=None, num_latent_functions=None):
"""
Stochastic Variational GP.
For Gaussian Likelihoods, this implements
Gaussian Processes for Big data, Hensman, Fusi and Lawrence, UAI 2013,
But without natural gradients. We'll use the lower-triangluar
representation of the covariance matrix to ensure
positive-definiteness.
For Non Gaussian Likelihoods, this implements
Hensman, Matthews and Ghahramani, Scalable Variational GP Classification, ArXiv 1411.2005
"""
self.batchsize = batchsize
self.X_all, self.Y_all = X, Y
if batchsize is None:
X_batch, Y_batch = X, Y
else:
import climin.util
#Make a climin slicer to make drawing minibatches much quicker
self.slicer = climin.util.draw_mini_slices(self.X_all.shape[0], self.batchsize)
X_batch, Y_batch = self.new_batch()
#create the SVI inference method
inf_method = svgp_inf()
super(SVGP, self).__init__(X_batch, Y_batch, Z, kernel, likelihood, mean_function=mean_function, inference_method=inf_method,
name=name, Y_metadata=Y_metadata, normalizer=False)
#assume the number of latent functions is one per col of Y unless specified
if num_latent_functions is None:
num_latent_functions = Y.shape[1]
self.m = Param('q_u_mean', np.zeros((self.num_inducing, num_latent_functions)))
chol = choleskies.triang_to_flat(np.tile(np.eye(self.num_inducing)[None,:,:], (num_latent_functions, 1,1)))
self.chol = Param('q_u_chol', chol)
self.link_parameter(self.chol)
self.link_parameter(self.m)
[docs] def parameters_changed(self):
self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.q_u_mean, self.q_u_chol, self.kern, self.X, self.Z, self.likelihood, self.Y, self.mean_function, self.Y_metadata, KL_scale=1.0, batch_scale=float(self.X_all.shape[0])/float(self.X.shape[0]))
#update the kernel gradients
self.kern.update_gradients_full(self.grad_dict['dL_dKmm'], self.Z)
grad = self.kern.gradient.copy()
self.kern.update_gradients_full(self.grad_dict['dL_dKmn'], self.Z, self.X)
grad += self.kern.gradient.copy()
self.kern.update_gradients_diag(self.grad_dict['dL_dKdiag'], self.X)
self.kern.gradient += grad
if not self.Z.is_fixed:# only compute these expensive gradients if we need them
self.Z.gradient = self.kern.gradients_X(self.grad_dict['dL_dKmm'], self.Z) + self.kern.gradients_X(self.grad_dict['dL_dKmn'], self.Z, self.X)
self.likelihood.update_gradients(self.grad_dict['dL_dthetaL'])
#update the variational parameter gradients:
self.m.gradient = self.grad_dict['dL_dm']
self.chol.gradient = self.grad_dict['dL_dchol']
if self.mean_function is not None:
self.mean_function.update_gradients(self.grad_dict['dL_dmfX'], self.X)
g = self.mean_function.gradient[:].copy()
self.mean_function.update_gradients(self.grad_dict['dL_dmfZ'], self.Z)
self.mean_function.gradient[:] += g
self.Z.gradient[:] += self.mean_function.gradients_X(self.grad_dict['dL_dmfZ'], self.Z)
[docs] def set_data(self, X, Y):
"""
Set the data without calling parameters_changed to avoid wasted computation
If this is called by the stochastic_grad function this will immediately update the gradients
"""
assert X.shape[1]==self.Z.shape[1]
self.X, self.Y = X, Y
[docs] def new_batch(self):
"""
Return a new batch of X and Y by taking a chunk of data from the complete X and Y
"""
i = next(self.slicer)
return self.X_all[i], self.Y_all[i]
[docs] def stochastic_grad(self, parameters):
self.set_data(*self.new_batch())
return self._grads(parameters)
[docs] def optimizeWithFreezingZ(self):
self.Z.fix()
self.kern.fix()
self.optimize('bfgs')
self.Z.unfix()
self.kern.constrain_positive()
self.optimize('bfgs')