Method predict_f

gpflow/models/cglb.py:173–253

The posterior mean for CGLB model is given by .. :math:: m(xs) = K_{sf}v + Q_{ff}Q⁻¹r where :math:`r = y - K v` is the residual from CG. Note that when :math:`v=0`, this agree with the SGPR mean, while if :math:`v = K⁻¹ y`, then :math:`r=0`, a

(
        self,
        Xnew: InputData,
        full_cov: bool = False,
        full_output_cov: bool = False,
        cg_tolerance: Optional[float] = 1e-3,
    )

    @inherit_check_shapes
    def predict_f(
        self,
        Xnew: InputData,
        full_cov: bool = False,
        full_output_cov: bool = False,
        cg_tolerance: Optional[float] = 1e-3,
    ) -> MeanAndVariance:
        """
        The posterior mean for CGLB model is given by

        .. :math::
            m(xs) = K_{sf}v + Q_{ff}Q⁻¹r

        where :math:`r = y - K v`  is the residual from CG.

        Note that when :math:`v=0`, this agree with the SGPR mean,
        while if :math:`v = K⁻¹ y`, then :math:`r=0`, and the exact
        GP mean is recovered.

        :param cg_tolerance: float or None: If None, the cached value of
            :math:`v` is used. If float, conjugate gradient is run until :math:`rᵀQ⁻¹r < ϵ`.
        """
        assert_params_false(self.predict_f, full_output_cov=full_output_cov)

        x, y = self.data
        err = y - self.mean_function(x)
        kxx = self.kernel(x, x)
        ksf = self.kernel(Xnew, x)
        sigma_sq = self.likelihood.variance
        sigma = tf.sqrt(sigma_sq)
        iv = self.inducing_variable
        kernel = self.kernel
        matmul = tf.linalg.matmul
        trisolve = tf.linalg.triangular_solve

        kmat = add_noise_cov(kxx, sigma_sq)

        common = self._common_calculation()
        A, LB, L = common.A, common.LB, common.L

        v = self.aux_vec
        if cg_tolerance is not None:
            preconditioner = NystromPreconditioner(A, LB, sigma_sq)
            err_t = tf.transpose(err)
            v = cglb_conjugate_gradient(
                kmat,
                err_t,
                v,
                preconditioner,
                cg_tolerance,
                self._max_cg_iters,
                self._restart_cg_iters,
            )

        cg_mean = matmul(ksf, v, transpose_b=True)
        res = err - matmul(kmat, v, transpose_b=True)

        Kus = Kuf(iv, kernel, Xnew)