1
$\begingroup$

On Bayesian Networks, Ghahramani (2001) says:

A node is independent of its non-descendants given its parents.

This point is fundamental enough that Ghahramani calls it the “semantics” of a Bayesian network. It is certainly useful, and it is simple enough to prove using d-separation. But his characterization suggests that the property should be even more primitive than something provable by d-separation.

Overall, I feel that I am missing something. Is there a more primitive way to verify the statement than to use d-separation? Why does Gharamani equate that fact specifically to the semantics of a Bayesian network, rather than equating the semantics to the overall conditional independencies in the network (given by d-separation)? And if the statement is a consequence of d-separation, why focus on this fact specifically rather than the (arguably equally useful) fact about Markov blankets?

Reference: Ghahramani, Z. (2001). An introduction to hidden Markov models and Bayesian networks. In Hidden Markov models: applications in computer vision (pp. 9-41).

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ Maybe stats.stackexchange.com would be a better place for this question? $\endgroup$
    – Erwan
    Nov 10, 2020 at 14:51
  • $\begingroup$ Yes, perhaps. I think it's generally unclear where to ask machine learning questions. $\endgroup$
    – ashman
    Nov 10, 2020 at 14:54
  • $\begingroup$ Is it kosher to re-post the exact same question there, while leaving it up here? Or should I follow some other process? $\endgroup$
    – ashman
    Nov 11, 2020 at 17:39
  • 1
    $\begingroup$ I think it's fine, otherwise you can flag your own question and ask a moderator to migrate it properly (it might take longer, I don't know). Your question fits on both sites, I recommended CrossValidatedSE mostly because there are more contributors there, so you'd have a better chance to get a good answer. $\endgroup$
    – Erwan
    Nov 11, 2020 at 18:33

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.