Method _common_calculation

gpflow/models/sgpr.py:181–209

Matrices used in log-det calculation :return: * :math:`σ²`, * :math:`σ`, * :math:`A = L⁻¹K_{uf}/σ`, where :math:`LLᵀ = Kᵤᵤ`, * :math:`B = AAT+I`, * :math:`LB` where :math`LBLBᵀ = B`, * :math:`AAT = AAᵀ`,

(self)

        "return.AAT: [M, M]",
    )
    def _common_calculation(self) -> "SGPR.CommonTensors":
        """
        Matrices used in log-det calculation

        :return:
            * :math:`σ²`,
            * :math:`σ`,
            * :math:`A = L⁻¹K_{uf}/σ`, where :math:`LLᵀ = Kᵤᵤ`,
            * :math:`B = AAT+I`,
            * :math:`LB` where :math`LBLBᵀ = B`,
            * :math:`AAT = AAᵀ`,
        """
        x, _ = self.data  # [N]
        iv = self.inducing_variable  # [M]

        sigma_sq = tf.squeeze(self.likelihood.variance_at(x), axis=-1)  # [N]
        sigma = tf.sqrt(sigma_sq)  # [N]

        kuf = Kuf(iv, self.kernel, x)  # [M, N]
        kuu = Kuu(iv, self.kernel, jitter=default_jitter())  # [M, M]
        L = tf.linalg.cholesky(kuu)  # [M, M]

        # Compute intermediate matrices
        A = tf.linalg.triangular_solve(L, kuf / sigma, lower=True)
        AAT = tf.linalg.matmul(A, A, transpose_b=True)
        B = add_noise_cov(AAT, tf.cast(1.0, AAT.dtype))
        LB = tf.linalg.cholesky(B)

        return self.CommonTensors(sigma_sq, sigma, A, B, LB, AAT, L)

    @check_shapes(
        "return: []",