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Consider the following statement from a textbook

the undirected models also offer a different and often simpler perspective on directed models, interms of both the independence structure and the inference task.

I am interpreting it as

the undirected models also offer a different and often simpler perspective about directed models, interms of both the independence structure and the inference task.

and it is equivocal to me as

the undirected models also offer a different and often simpler perspective compared to directed models, interms of both the independence structure and the inference task.

Which one is a correct interpretation?

is there any better way to present the fact? I am undergoing confusion because of the reason that the statement looks like praising one model over the other rather than its contribution to the other.

Context: I am providing the total paragraph in which the sentence is present

The second common class of probabilistic graphical models is called a Markov network or a Markov random field. The models are based on undirected graphical models. These models are useful in modeling a variety of phenomena where one cannot naturally ascribe a directionality to the interaction between variables. Furthermore, the undirected models also offer a different and often simpler perspective on directed models, both in terms of the independence structure and the inference task. Source

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  • This is a well formatted question. Keep it up! – Dhanishtha Ghosh Sep 26 '20 at 8:18
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    I would say the last one, compared to statement. – Dhanishtha Ghosh Sep 26 '20 at 8:29
  • It is possible that you might be able to ask this on another site in the network. It might be a bit too statistical for Mathematics but you might try CrossValidated. I think it might well mean that undirected models throw a new light on directed but these models are outside my area I am afraid. – mdewey Sep 26 '20 at 14:32
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This sentence is technical or academic writing on a subject that I do not know. Moreover, the sentence is given without any context and therefore may be opaque even to experts in the field. Finally, your question may partially relate to style, which is a matter of opinion. The sentence as presented, however, is far from clear.

a different perspective on

and

a different perspective about

are equivalent (not equivocal) in meaning though "on" is much more common (according to google ngram).

The fundamental problem with this sentence is that "different" does not imply ranking whereas "simpler" does. Simpler than what? The "also" in the sentence implies that at least the immediately preceding sentence was talking about "undirected models." Therefore, it is not clear what the undirected models are being compared to. In your proposed revision, you clarify that but lose any notion of what the different perspectives relate to. Can a model have a perspective on itself? Can a model have a perspective on a different model?

Here is what I suspect the author was trying to say.

Also, compared to a directed model, an undirected model is often simpler [to understand?] and provides a different perspective on the independence structure and the inference task.

I am not sure. You have provided no context. But, in the absence of context, that is at least a plausible interpretation of a poorly written sentence. But it appears to me that the author tried to cram several different thoughts into a single sentence. If that is correct, a better rewriting would probably break it into two or more sentences.

MAJOR EDIT: Thank you for providing additional context. I glanced at the paper you cited. I have not studied Markov chains in forty years and have not thought seriously about Bayesian inference in twenty years. Nor have I ever studied graph theory. Having looked at the paper, I am somewhat less sure about what the authors wanted to say. It really is a terribly written sentence.

I now think that part of what they are trying to say is that directed and undirected models represent different views on independence and consequently on what can be inferred. Moreover they may be trying to say that the undirected model sheds some sort of light on the directed model. That seems somewhat implausible to me given that the models apparently are based on contradictory assumptions, but I don't understand the math so my opinion is worth very little. And now I am even less sure about what is meant by "simpler." Simpler to understand? Simpler to implement? Simpler in its assumptions?

I suggest you write an e-mail to the authors asking THEM to clarify what they meant by this abortion of a sentence. It probably is one of those pieces of writing where the intended meaning was so clear to the author and editors that they could not see how obscure it would be to someone who is trying to divine that meaning.

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