Modeling uncertain interventions
Kevin Murphy, University of British Columbia, Canada
Causality concerns reasoning about the effects of actions. This can be
modeled using conditional density models of the form p(x|a), where a
are the actions that you perform, and x are the observed
responses. Typically the action space will be factored; node aj is on
if action j is performed, and is off otherwise. Thus a causal model
can be represented by an influence or decision diagram with many
binary action nodes, acting as parents to all the components of x, but
without any utility nodes.
The main challenge is to predict the consequences of novel
(combinations of) actions. The traditional way to do this is to assume
that actions are "perfect interventions" on specific elements of
x. However, many real-world actions, such as "inject chemical j into
the cell", may have non-local, and unknown, effects. We propose two
ways to model this. The first way is to allow action nodes to target
many x nodes ("fat hand" interventions), and to learn this bipartite
graph using standard structure learning methods. The second, more
speculative, way is to
pass the action bit vector through a low dimensional bottleneck, call
it z, and then learn a model of p(x|z). This allows one to discover
different types of actions, and to use standard density estimation
techniques to predict the distribution of x for each action
type, thus illustrating that one can model causality without necessarily
talking about DAGs or graphs of any kind.