Learning Neural Causal Models from Unknown Interventions
Authors: Nan Rosemary Ke, Olexa Bilaniuk, Anirudh Goyal, Stephan Bauer, Hugol Larochelle, Chris Pal, Yoshua Bengio
Keywords: deep learning, graphical models, meta learning
TL;DR: Using end-to-end deep learning to discover the structure of a graphical model which is robust to interventions and trained without knowing what the interventions are
Abstract: Meta-learning over a set of distributions can be interpreted as learning different types of parameters corresponding to short-term vs long-term aspects of the mechanisms underlying the generation of data. These are respectively captured by quickly-changing \textit{parameters} and slowly-changing \textit{meta-parameters}. We present a new framework for meta-learning causal models where the relationship between each variable and its parents is modeled by a neural network, modulated by structural meta-parameters which capture the overall topology of a directed graphical model. Our approach avoids a discrete search over models in favour of a continuous optimization procedure. We study a setting where interventional distributions are induced as a result of a random intervention on a single unknown variable of an unknown ground truth causal model, and the observations arising after such an intervention constitute one meta-example. To disentangle the slow-changing aspects of each conditional from the fast-changing adaptations to each intervention, we parametrize the neural network into fast parameters and slow meta-parameters. We introduce a meta-learning objective that favours solutions \textit{robust} to frequent but sparse interventional distribution change, and which generalize well to previously unseen interventions. Optimizing this objective is shown experimentally to recover the structure of the causal graph. Finally, we find that when the learner is unaware of the intervention variable, it is able to infer that information, improving results further and focusing the parameter and meta-parameter updates where needed.