[tabacof]

Causality is a bit harder to integrate with current machine learning models as it's hard even with standard probabilistic graphical models. On the other hand, there has been a lot of work integrating deep neural networks with probabilistic models.

For example, the variational auto-encoders are a graphical model with Gaussian latent variables whose mean and variance are determined by (deep) neural networks [1]. There has been work exploring the neural network weights as latent variables themselves [2]. Finally, some new developments such as dropout can be interpreted as some form of deep Gaussian processes [3].

I believe there will be a lot further developments on this area in the near-future.

[1] http://arxiv.org/abs/1312.6114

[2] http://arxiv.org/abs/1505.05424

[3] http://arxiv.org/abs/1506.02142