r"""
    Compute the expectation:
    expectation[n] = < prodK_{Z, x_n} prodK_{x_n, Z} >_p(x_n)
                   = < (\HadamardProd_i Ki_{Z[:, active_dims_i], x[n, active_dims_i]})  <-- Mx1
               1xM -->  (\HadamardProd_j Kj_{x[n, active_dims_j], Z[:, active_dims_j]}) >_p(x_n)  (MxM)

        - \HadamardProd_i Ki_{.,.}, \HadamardProd_j Kj_{.,.} :: Product kernels
        - p                        :: DiagonalGaussian distribution (p.cov NxD)

    :return: NxMxM

def _expectation(p, kern1, feat1, kern2, feat2, nghp=None):
    r"""
    Compute the expectation:
    expectation[n] = < prodK_{Z, x_n} prodK_{x_n, Z} >_p(x_n)
                   = < (\HadamardProd_i Ki_{Z[:, active_dims_i], x[n, active_dims_i]})  <-- Mx1
               1xM -->  (\HadamardProd_j Kj_{x[n, active_dims_j], Z[:, active_dims_j]}) >_p(x_n)  (MxM)

        - \HadamardProd_i Ki_{.,.}, \HadamardProd_j Kj_{.,.} :: Product kernels
        - p                        :: DiagonalGaussian distribution (p.cov NxD)

    :return: NxMxM
    """
    if feat1 != feat2:
        raise NotImplementedError("Different features are not supported.")
    if kern1 != kern2:
        raise NotImplementedError("Calculating the expectation over two "
                                  "different Product kernels is not supported.")

    kern = kern1
    feat = feat1

    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, feat), (k, feat), nghp=nghp) for k in kern.kernels])