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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def LOO(self, kern, X, Y, likelihood, posterior, Y_metadata=None, K=None):
 """ Leave one out error as found in "Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models" Vehtari et al. 2014. """

        g = posterior.woodbury_vector
        c = posterior.woodbury_inv
        c_diag = np.diag(c)[:, None]
        neg_log_marginal_LOO = 0.5*np.log(2*np.pi) - 0.5*np.log(c_diag) + 0.5*(g**2)/c_diag
        #believe from Predictive Approaches for Choosing Hyperparameters in Gaussian Processes
        #this is the negative marginal LOO
        return -neg_log_marginal_LOO