gplvm.py 文件源码

def _build_likelihood(self):
        """
        Construct a tensorflow function to compute the bound on the marginal
        likelihood.
        """
        num_inducing = tf.shape(self.Z)[0]
        psi0 = tf.reduce_sum(self.kern.eKdiag(self.X_mean, self.X_var), 0)
        psi1 = self.kern.eKxz(self.Z, self.X_mean, self.X_var)
        psi2 = tf.reduce_sum(self.kern.eKzxKxz(self.Z, self.X_mean, self.X_var), 0)
        Kuu = self.kern.K(self.Z) + tf.eye(num_inducing, dtype=settings.float_type) * settings.numerics.jitter_level
        L = tf.cholesky(Kuu)
        sigma2 = self.likelihood.variance
        sigma = tf.sqrt(sigma2)

        # Compute intermediate matrices
        A = tf.matrix_triangular_solve(L, tf.transpose(psi1), lower=True) / sigma
        tmp = tf.matrix_triangular_solve(L, psi2, lower=True)
        AAT = tf.matrix_triangular_solve(L, tf.transpose(tmp), lower=True) / sigma2
        B = AAT + tf.eye(num_inducing, dtype=settings.float_type)
        LB = tf.cholesky(B)
        log_det_B = 2. * tf.reduce_sum(tf.log(tf.matrix_diag_part(LB)))
        c = tf.matrix_triangular_solve(LB, tf.matmul(A, self.Y), lower=True) / sigma

        # KL[q(x) || p(x)]
        dX_var = self.X_var if len(self.X_var.get_shape()) == 2 else tf.matrix_diag_part(self.X_var)
        NQ = tf.cast(tf.size(self.X_mean), settings.float_type)
        D = tf.cast(tf.shape(self.Y)[1], settings.float_type)
        KL = -0.5 * tf.reduce_sum(tf.log(dX_var)) \
             + 0.5 * tf.reduce_sum(tf.log(self.X_prior_var)) \
             - 0.5 * NQ \
             + 0.5 * tf.reduce_sum((tf.square(self.X_mean - self.X_prior_mean) + dX_var) / self.X_prior_var)

        # compute log marginal bound
        ND = tf.cast(tf.size(self.Y), settings.float_type)
        bound = -0.5 * ND * tf.log(2 * np.pi * sigma2)
        bound += -0.5 * D * log_det_B
        bound += -0.5 * tf.reduce_sum(tf.square(self.Y)) / sigma2
        bound += 0.5 * tf.reduce_sum(tf.square(c))
        bound += -0.5 * D * (tf.reduce_sum(psi0) / sigma2 -
                             tf.reduce_sum(tf.matrix_diag_part(AAT)))
        bound -= KL
        return bound