def _expectation(p, kern, none1, none2, none3, nghp=None):
    r"""
    Compute the expectation:
    <\HadamardProd_i diag(Ki_{X[:, active_dims_i], X[:, active_dims_i]})>_p(X)
        - \HadamardProd_i Ki_{.,.} :: Product kernel
        - p                        :: DiagonalGaussian distribution (p.cov NxD)

    :return: N
    """
    if not kern.on_separate_dimensions:
        raise NotImplementedError(
            "Product currently needs to be defined on separate dimensions.")  # pragma: no cover

    return functools.reduce(tf.multiply, [
        expectation(p, k, nghp=nghp) for k in kern.kernels])