apunkt/GPy
1
0
Fork 0
mirror of https://github.com/SheffieldML/GPy.git synced 2026-05-18 13:55:14 +02:00
Code Issues Projects Releases Packages Wiki Activity Actions

faster einsums in svgp

Browse source
This commit is contained in:
James Hensman 2015-04-30 10:10:48 +01:00
parent 3e4f272808
commit 5ad38ac640
1 changed files with 9 additions and 4 deletions
Download patch file Download diff file Expand all files Collapse all files

13
GPy/inference/latent_function_inference/svgp.py
View file

@ -4,6 +4,8 @@ from ...util import choleskies
import numpy as np
from .posterior import Posterior
def ij_ijk_to_ikl
class SVGP(LatentFunctionInference):
def inference(self, q_u_mean, q_u_chol, kern, X, Z, likelihood, Y, mean_function=None, Y_metadata=None, KL_scale=1.0, batch_scale=1.0):
@ -41,11 +43,12 @@ class SVGP(LatentFunctionInference):
#compute the marginal means and variances of q(f)
A = np.dot(Knm, Kmmi)
mu = prior_mean_f + np.dot(A, q_u_mean - prior_mean_u)
v = Knn_diag[:,None] - np.sum(A*Knm,1)[:,None] + np.sum(A[:,:,None] * np.einsum('ij,jkl->ikl', A, S),1)
#v = Knn_diag[:,None] - np.sum(A*Knm,1)[:,None] + np.sum(A[:,:,None] * np.einsum('ij,jkl->ikl', A, S),1)
v = Knn_diag[:,None] - np.sum(A*Knm,1)[:,None] + np.sum(A[:,:,None] *A.dot(S.reshape(S.shape[0],-1)).reshape(A.shape[0],S.shape[1],S.shape[2]),1)
#compute the KL term
Kmmim = np.dot(Kmmi, q_u_mean)
KLs = -0.5*logdetS -0.5*num_inducing + 0.5*logdetKmm + 0.5*np.einsum('ij,ijk->k', Kmmi, S) + 0.5*np.sum(q_u_mean*Kmmim,0)
KLs = -0.5*logdetS -0.5*num_inducing + 0.5*logdetKmm + 0.5*np.sum(Kmmi[:,:,None]*S,0).sum(0) + 0.5*np.sum(q_u_mean*Kmmim,0)
KL = KLs.sum()
#gradient of the KL term (assuming zero mean function)
dKL_dm = Kmmim.copy()
@ -78,11 +81,13 @@ class SVGP(LatentFunctionInference):
Adv = A.T[:,:,None]*dF_dv[None,:,:] # As if dF_Dv is diagonal
Admu = A.T.dot(dF_dmu)
AdvA = np.dstack([np.dot(A.T, Adv[:,:,i].T) for i in range(num_outputs)])
tmp = np.einsum('ijk,jlk->il', AdvA, S).dot(Kmmi)
#tmp = np.einsum('ijk,jlk->il', AdvA, S).dot(Kmmi)
tmp = np.sum([np.dot(AdvA[:,:,k], S[:,:,k]) for k in range(S.shape[-1])],0).dot(Kmmi)
dF_dKmm = -Admu.dot(Kmmim.T) + AdvA.sum(-1) - tmp - tmp.T
dF_dKmm = 0.5*(dF_dKmm + dF_dKmm.T) # necessary? GPy bug?
tmp = 2.*(np.einsum('ij,jlk->ilk', Kmmi,S) - np.eye(num_inducing)[:,:,None])
dF_dKmn = np.einsum('ijk,jlk->il', tmp, Adv) + Kmmim.dot(dF_dmu.T)
#dF_dKmn = np.einsum('ijk,jlk->il', tmp, Adv) + Kmmim.dot(dF_dmu.T)
dF_dKmn = np.sum([np.dot(tmp[:,:,k], Adv[:,:,k]) for k in range(Adv.shape[-1])],0) + Kmmim.dot(dF_dmu.T)
dF_dm = Admu
dF_dS = AdvA