def _compute_confidence_bounds_of_transform(self, transform, alpha, ci_labels):
        """
        This computes the confidence intervals of a transform of the parameters. Ex: take
        the fitted parameters, a function/transform and the variance matrix and give me
        back confidence intervals of the transform.

        Parameters
        -----------
        transform: function
            must a function of two parameters:
                ``params``, an iterable that stores the parameters
                ``times``, a numpy vector representing some timeline
            the function must use autograd imports (scipy and numpy)
        alpha: float
            confidence level
        ci_labels: tuple

        """
        alpha2 = 1 - alpha / 2.0
        z = inv_normal_cdf(alpha2)
        df = pd.DataFrame(index=self.timeline)

        # pylint: disable=no-value-for-parameter
        gradient_of_cum_hazard_at_mle = make_jvp_reversemode(transform)(
            self._fitted_parameters_, self.timeline.astype(float)
        )

        gradient_at_times = np.vstack(
            [gradient_of_cum_hazard_at_mle(basis) for basis in np.eye(len(self._fitted_parameters_), dtype=float)]
        )

        std_cumulative_hazard = np.sqrt(
            np.einsum("nj,jk,nk->n", gradient_at_times.T, self.variance_matrix_, gradient_at_times.T)
        )

        if ci_labels is None:
            ci_labels = ["%s_upper_%g" % (self._label, 1 - alpha), "%s_lower_%g" % (self._label, 1 - alpha)]
        assert len(ci_labels) == 2, "ci_labels should be a length 2 array."

        df[ci_labels[0]] = transform(self._fitted_parameters_, self.timeline) + z * std_cumulative_hazard
        df[ci_labels[1]] = transform(self._fitted_parameters_, self.timeline) - z * std_cumulative_hazard
        return df