Method compute_qu

gpflow/models/sgpr.py:346–377

Computes the mean and variance of q(u) = N(mu, cov), the variational distribution on inducing outputs. SVGP with this q(u) should predict identically to SGPR. :return: mu, cov

(self)

        "return[1]: [M, M]",
    )
    def compute_qu(self) -> Tuple[tf.Tensor, tf.Tensor]:
        """
        Computes the mean and variance of q(u) = N(mu, cov), the variational distribution on
        inducing outputs.

        SVGP with this q(u) should predict identically to SGPR.

        :return: mu, cov
        """
        X_data, Y_data = self.data

        kuf = Kuf(self.inducing_variable, self.kernel, X_data)
        kuu = Kuu(self.inducing_variable, self.kernel, jitter=default_jitter())

        var = tf.squeeze(self.likelihood.variance_at(X_data), axis=-1)
        std = tf.sqrt(var)
        scaled_kuf = kuf / std
        sig = kuu + tf.matmul(scaled_kuf, scaled_kuf, transpose_b=True)
        sig_sqrt = tf.linalg.cholesky(sig)

        sig_sqrt_kuu = tf.linalg.triangular_solve(sig_sqrt, kuu)

        cov = tf.linalg.matmul(sig_sqrt_kuu, sig_sqrt_kuu, transpose_a=True)
        err = Y_data - self.mean_function(X_data)
        scaled_err = err / std[..., None]
        mu = tf.linalg.matmul(
            sig_sqrt_kuu,
            tf.linalg.triangular_solve(sig_sqrt, tf.linalg.matmul(scaled_kuf, scaled_err)),
            transpose_a=True,
        )

        return mu, cov


class GPRFITC(SGPRBase_deprecated):