Calculate negative log-likelihood

GP_likelihood.py

    def Neglikelihood(self, theta):
        """Negative likelihood function
        
        Input
        -----
        theta: array, logarithm of the correlation legnths for different dimensions
        
        Output
        ------
        LnLike: likelihood value"""
        
        theta = 10**theta    # Correlation length
        n = self.X.shape[0]  # Number of training instances
        one = np.ones((n,1))      # Vector of ones
        
        # Construct correlation matrix
        K = self.Corr(self.X, self.X, theta) + np.eye(n)*1e-10
        inv_K = np.linalg.inv(K)   # Inverse of correlation matrix
        
        # Mean estimation
        mu = (one.T @ inv_K @ self.y)/ (one.T @ inv_K @ one)
        
        # Variance estimation
        SigmaSqr = (self.y-mu*one).T @ inv_K @ (self.y-mu*one) / n
        
        # Compute log-likelihood
        DetK = np.linalg.det(K)
        LnLike = -(n/2)*np.log(SigmaSqr) - 0.5*np.log(DetK)
        
        # Update attributes
        self.K, self.inv_K , self.mu, self.SigmaSqr = K, inv_K, mu, SigmaSqr
        
        return -LnLike.flatten()