<s> import numpy as np <EOL> from ... util . linalg import pdinv <EOL> from . posterior import Posterior <EOL> from . import LatentFunctionInference <EOL> log_2_pi = np . log ( <NUM_LIT:2> * np . pi ) <EOL> class VarGauss ( LatentFunctionInference ) : <EOL> """<STR_LIT>""" <EOL> def __init__ ( self , alpha , beta ) : <EOL> """<STR_LIT>""" <EOL> self . alpha , self . beta = alpha , beta <EOL> def inference ( self , kern , X , likelihood , Y , mean_function = None , Y_metadata = None , Z = None ) : <EOL> if mean_function is not None : <EOL> raise NotImplementedError <EOL> num_data , output_dim = Y . shape <EOL> assert output_dim == <NUM_LIT:1> , "<STR_LIT>" <EOL> K = kern . K ( X ) <EOL> m = K . dot ( self . alpha ) <EOL> KB = K * self . beta [ : , None ] <EOL> BKB = KB * self . beta [ None , : ] <EOL> A = np . eye ( num_data ) + BKB <EOL> Ai , LA , _ , Alogdet = pdinv ( A ) <EOL> Sigma = np . diag ( self . beta ** - <NUM_LIT:2> ) - Ai / self . beta [ : , None ] / self . beta [ None , : ] <EOL> var = np . diag ( Sigma ) . reshape ( - <NUM_LIT:1> , <NUM_LIT:1> ) <EOL> F , dF_dm , dF_dv , dF_dthetaL = likelihood . variational_expectations ( Y , m , var , Y_metadata = Y_metadata ) <EOL> if dF_dthetaL is not None : <EOL> dL_dthetaL = dF_dthetaL . sum ( <NUM_LIT:1> ) . sum ( <NUM_LIT:1> ) <EOL> else : <EOL> dL_dthetaL = np . array ( [ ] ) <EOL> dF_da = np . dot ( K , dF_dm ) <EOL> SigmaB = Sigma * self . beta <EOL> dF_db = - <NUM_LIT:2> * np . sum ( Sigma ** <NUM_LIT:2> * ( dF_dv * self . beta ) , <NUM_LIT:0> ) <EOL> KL = <NUM_LIT:0.5> * ( Alogdet + np . trace ( Ai ) - num_data + np . sum ( m * self . alpha ) ) <EOL> dKL_da = m <EOL> A_A2 = Ai - Ai . dot ( Ai ) <EOL> dKL_db = np . diag ( np . dot ( KB . T , A_A2 ) ) <EOL> log_marginal = F . sum ( ) - KL <EOL> self . alpha . gradient = dF_da - dKL_da <EOL> self . beta . gradient = dF_db - dKL_db <EOL> dKL_dK = <NUM_LIT:0.5> * ( self . alpha * self . alpha . T + self . beta [ : , None ] * self . beta [ None , : ] * A_A2 ) <EOL> tmp = Ai * self . beta [ : , None ] / self . beta [ None , : ] <EOL> dF_dK = self . alpha * dF_dm . T + np . dot ( tmp * dF_dv , tmp . T ) <EOL> return Posterior ( mean = m , cov = Sigma , K = K ) , log_marginal , { '<STR_LIT>' : dF_dK - dKL_dK , '<STR_LIT>' : dL_dthetaL } </s>
