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I am a M.Sc. student in computer science, working on information networks and recommender systems. This days when I went through the top-tier conferences papers in the field I have seen most of them use solely simple machine learning tools such as generalized linear model, Expectation Maximization, Maximum Likelihood, etc.

One may argue that this simple methods work better and We shouldn't take the blame for the sake of simplicity. That is true but I have not even seen an interest to try compare their results with some more advanced mathematical methods.

I am wondering why scientists don't try to explore more mathematics to involve in their research. Because there is not something better in exploding world of mathematics or because of its difficulty, etc?

Edit: I mean the areas that are more related to continuous mathematics than CS theory.

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    $\begingroup$ Perhaps it wasn't your intention but I, as an author of theoretical CS papers, find it rather offensive that you claim that I don't use advanced mathematics. My entire job is "exploring more mathematics." $\endgroup$ – David Richerby Jul 21 '15 at 21:35
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    $\begingroup$ Yeah, for machine learning, we're still just exploring the different uses of it, so there's still interesting research to be done with the simple models. There's also something to be said for simplicity: if an advanced statistical model has only a marginal improvement, but doesn't have pre-existing tools implementing it, or is much slower to run, then nobody is going to use it. Advanced doesn't always mean practical. $\endgroup$ – jmite Jul 21 '15 at 21:54
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    $\begingroup$ @jmite Also, "advanced" doesn't always mean "better". $\endgroup$ – mhum Jul 21 '15 at 22:43
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    $\begingroup$ @user35718 CS theory isn't "related to mathematics": it is mathematics! $\endgroup$ – David Richerby Jul 22 '15 at 5:54
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    $\begingroup$ talk about "loaded questions"... the question is obviously quite naive but maybe not intentionally disrespectful.... it could have been stated better. anyway check out Theoretical Computer Science for many advanced areas of math tied with CS. CS is very vast and youve apparently only sampled/ surveyed a tiny bit. CS specializes mainly in discrete math and there are some math "attitudes" about that. vast areas of math that are continuous are generally less applicable, but there are very highly advanced areas of math that are mostly discrete (and connect with CS), eg graph/ group theory etc.... $\endgroup$ – vzn Jul 23 '15 at 22:32
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There are many reasons that you may not see a lot of complex mathematics in the papers you are reading.

First, the tools used depend on the task at hand. If a task is simple, a simple tool might be adequate. Also, if the task runs on a simple system, a simple tool is often best.

Second, usually in Computer Science, the goal is usually to make things usable to a layprogrammer; therefore, it would be detrimental to make something depend on an advanced or abstract concept that few people understand. Often, the proofs sections of algorithms papers have much more advanced mathematics than the rest of the paper; the assumption is that anyone who wants to verify the correctness of the algorithm or its complexity can invest the time in understanding the proof, but that that is not essential to use the results.

Finally, some of this has to do with a lack of familiarity; people who spend their lives reading and writing computer science papers might never have the time to learn about new, highly complex mathematics. Actually, a great way to expand the field is to introduce a concept that many mathematicians understand in a way that it is accessible to and usable by computer scientists. (For instance, I have a friend whose PhD work applied known concepts of Control Theory to problems in Motion Planning. He did very little new work, but he did advance Motion Planning.)

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    $\begingroup$ "the goal is usually to make things usable to a layprogrammer" -- I can not confirm that. That may be the goal of the engineering faction later, but lots of people don't care about enabling programmers at all. $\endgroup$ – Raphael♦ Jul 24 '15 at 6:06

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