Can't pickle Poisson Emissions posterior object

[bantin]

If I create and fit an LDS with Poisson emissions, I can't pickle the resulting posterior object:

AttributeError: Can't pickle local object '_PoissonEmissionsMixin.__init__.<locals>.<lambda>'

This is bad-news-bears because we need a way of saving the output after fitting models. I think the cause is that you can't pickle lambda functions. Currently we use lambda functions in the init:

def __init__(self, N, K, D, M=0, single_subspace=True, link="softplus", bin_size=1.0, **kwargs):
        super(_PoissonEmissionsMixin, self).__init__(N, K, D, M, single_subspace=single_subspace, **kwargs)

        self.link_name = link
        self.bin_size = bin_size
        mean_functions = dict(
            log=lambda x: np.exp(x) * self.bin_size,
            softplus= lambda x: softplus(x) * self.bin_size
            )
        self.mean = mean_functions[link]

        link_functions = dict(
            log=lambda rate: np.log(rate) - np.log(self.bin_size),
            softplus=lambda rate: inv_softplus(rate / self.bin_size)
            )
        self.link = link_functions[link]

The solution here is probably to define the link/inverse links via def.