def inference(self, kern, X, likelihood, Y, Y_metadata=None):
N = X.shape[<NUM_LIT:0>] <EOL>D = X.shape[<NUM_LIT:1>] <EOL>Kds = np.zeros(D, dtype=object) <EOL>Qs = np.zeros(D, dtype=object) <EOL>QTs = np.zeros(D, dtype=object) <EOL>V_kron = <NUM_LIT:1> <EOL>oneDkernel = kern.get_one_dimensional_kernel(D)<EOL>for d in range(D):<EOL><INDENT>xg = list(set(X[:,d])) <EOL>xg = np.reshape(xg, (len(xg), <NUM_LIT:1>))<EOL>oneDkernel.lengthscale = kern.lengthscale[d]<EOL>Kds[d] = oneDkernel.K(xg)<EOL>[V, Q] = np.linalg.eig(Kds[d])<EOL>V_kron = np.kron(V_kron, V)<EOL>Qs[d] = Q<EOL>QTs[d] = Q.T<EOL><DEDENT>noise = likelihood.variance + <NUM_LIT><EOL>alpha_kron = self.kron_mvprod(QTs, Y)<EOL>V_kron = V_kron.reshape(-<NUM_LIT:1>, <NUM_LIT:1>)<EOL>alpha_kron = alpha_kron / (V_kron + noise)<EOL>alpha_kron = self.kron_mvprod(Qs, alpha_kron)<EOL>log_likelihood = -<NUM_LIT:0.5> * (np.dot(Y.T, alpha_kron) + np.sum((np.log(V_kron + noise))) + N*log_2_pi)<EOL>derivs = np.zeros(D+<NUM_LIT:2>, dtype='<STR_LIT:object>')<EOL>for t in range(len(derivs)):<EOL><INDENT>dKd_dTheta = np.zeros(D, dtype='<STR_LIT:object>')<EOL>gamma = np.zeros(D, dtype='<STR_LIT:object>')<EOL>gam = <NUM_LIT:1><EOL>for d in range(D):<EOL><INDENT>xg = list(set(X[:,d]))<EOL>xg = np.reshape(xg, (len(xg), <NUM_LIT:1>))<EOL>oneDkernel.lengthscale = kern.lengthscale[d]<EOL>if t < D:<EOL><INDENT>dKd_dTheta[d] = oneDkernel.dKd_dLen(xg, (t==d), lengthscale=kern.lengthscale[t]) <EOL><DEDENT>elif (t == D):<EOL><INDENT>dKd_dTheta[d] = oneDkernel.dKd_dVar(xg) <EOL><DEDENT>else:<EOL><INDENT>dKd_dTheta[d] = np.identity(len(xg)) <EOL><DEDENT>gamma[d] = np.diag(np.dot(np.dot(QTs[d], dKd_dTheta[d].T), Qs[d]))<EOL>gam = np.kron(gam, gamma[d])<EOL><DEDENT>gam = gam.reshape(-<NUM_LIT:1>,<NUM_LIT:1>)<EOL>kappa = self.kron_mvprod(dKd_dTheta, alpha_kron)<EOL>derivs[t] = <NUM_LIT:0.5>*np.dot(alpha_kron.T,kappa) - <NUM_LIT:0.5>*np.sum(gam / (V_kron + noise))<EOL><DEDENT>dL_dLen = derivs[:D]<EOL>dL_dVar = derivs[D]<EOL>dL_dThetaL = derivs[D+<NUM_LIT:1>]<EOL>return GridPosterior(alpha_kron=alpha_kron, QTs=QTs, Qs=Qs, V_kron=V_kron),log_likelihood, {'<STR_LIT>':dL_dLen, '<STR_LIT>':dL_dVar, '<STR_LIT>':dL_dThetaL}<EOL>
Returns a GridPosterior class containing essential quantities of the posterior