which show you don’t even need conditional independences to orient edges. For example if the true dag is this:
1 → 2 → 3 → 4, 1 ← u1 → 3, 1 ← u2 → 4,
and we observe p(1, 2, 3, 4) (no conditional independences in this marginal), I can recover the graph exactly with enough data. (The graph would be causal if we assume the underlying true graph is, otherwise it’s just a statistical model).
People’s intuitions about what’s possible in causal discovery aren’t very good.
It would be good if statisticians and machine learning / comp. sci. people came together to hash out their differences regarding causal inference.
You can do it with enough causal assumptions (e.g. not “from nothing”). There is a series of magical papers, e.g. this:
http://www.cs.helsinki.fi/u/phoyer/papers/pdf/hoyer2008nips.pdf
which show you can use additive noise assumptions to orient edges.
I have a series of papers:
http://www.auai.org/uai2012/papers/248.pdf
http://arxiv.org/abs/1207.5058
which show you don’t even need conditional independences to orient edges. For example if the true dag is this:
1 → 2 → 3 → 4, 1 ← u1 → 3, 1 ← u2 → 4,
and we observe p(1, 2, 3, 4) (no conditional independences in this marginal), I can recover the graph exactly with enough data. (The graph would be causal if we assume the underlying true graph is, otherwise it’s just a statistical model).
People’s intuitions about what’s possible in causal discovery aren’t very good.
It would be good if statisticians and machine learning / comp. sci. people came together to hash out their differences regarding causal inference.