human
Complete the below
def black_box_variational_inference(logprob, D, num_samples):

    ''''Implements http://arxiv.org/abs/1401.0118, and uses the
    local reparameterization trick from http://arxiv.org/abs/1506.02557'
    '''
 Write me a the Python program you requested?
assistant
#Here is the Python program you requested.
    def unpack_params(params):
        (mean, log_std) = (params[:D], params[D:])
        return (mean, log_std)
    def gaussian_entropy(log_std):
        return (((0.5 * D) * (1.0 + np.log((2 * np.pi)))) + np.sum(log_std))
    rs = npr.RandomState(0)
    def variational_objective(params, t):
        'Provides    a    stochastic    estimate    of    the    variational    lower    bound.'
        (mean, log_std) = unpack_params(params)
        samples = ((rs.randn(num_samples, D) * np.exp(log_std)) + mean)
        lower_bound = (gaussian_entropy(log_std) + np.mean(logprob(samples, t)))
        return (- lower_bound)
    gradient = grad(variational_objective)
    return (variational_objective, gradient, unpack_params)