seems like it is missing something in terms of making predictions about any world
I mean, you’re right, but that’s not what I was going for with that sentence. Suppose we were talking about a tiny philosophical “world” of opaque variables, rather than the real physical universe in all its richness and complexity. If you’re just drawing samples from the original joint distribution, both networks will tell you exactly what you should predict to see. But if we suppose that there are “further facts” about some underlying mechanisms that generate that distribution, the two networks are expressing different beliefs about those further facts (e.g., whether changing X1 will change X4, which you can’t tell if you don’t change it).
claiming implicitly that the original post (or its author) are missing [...] some of the points above
Not the author, but some readers (not necessarily you). This post is trying to fill in a gap, of something that people who Actually Read The Serious Textbook and Done Exercises already know, but people who have only read one or two intro blog posts maybe don’t know. (It’s no one’s fault; any one blog post can only say so much.)
I mean, you’re right, but that’s not what I was going for with that sentence. Suppose we were talking about a tiny philosophical “world” of opaque variables, rather than the real physical universe in all its richness and complexity. If you’re just drawing samples from the original joint distribution, both networks will tell you exactly what you should predict to see. But if we suppose that there are “further facts” about some underlying mechanisms that generate that distribution, the two networks are expressing different beliefs about those further facts (e.g., whether changing X1 will change X4, which you can’t tell if you don’t change it).
Not the author, but some readers (not necessarily you). This post is trying to fill in a gap, of something that people who Actually Read The Serious Textbook and Done Exercises already know, but people who have only read one or two intro blog posts maybe don’t know. (It’s no one’s fault; any one blog post can only say so much.)