  Predicting the effect of unseen interventions is a fundamental research
question across the data sciences. It is well established that in general such
questions cannot be answered definitively from observational data. This
realization has fuelled a growing literature introducing various identifying
assumptions, for example in the form of a causal diagram among relevant
variables. In practice, this paradigm is still too rigid for many practical
applications as it is generally not possible to confidently delineate the true
causal diagram. In this paper, we consider the derivation of bounds on causal
effects given only observational data. We propose to take as input a less
informative structure known as a Partial Ancestral Graph, which represents a
Markov equivalence class of causal diagrams and is learnable from data. In this
more ``data-driven'' setting, we provide a systematic algorithm to derive
bounds on causal effects that exploit the invariant properties of the
equivalence class, and that can be computed analytically. We demonstrate our
method with synthetic and real data examples.
