Can I show my long-term research interests on SOP, which are very important topics but aren't constantly researched yet I hope you can share your insights with me. I'm struggling to figure out appropriate research questions in my SOP. I'm trying to get into a top CS graduate school in the USA.

I am a cs grad and have done bioinformatics research, which attracts me to tackle computational and statistical challenges of Personalized Medicine. My long-term research goals are heterogeneous data integration, and statistical methods to reduce false positives and negatives. Since those things are really cutting-edge topics and groundbreaking progress has been made infrequently over a decade, not many US researchers list those questions as their primary research interests on their websites, but there is a hope that more researchers would get into those questions in near future. 

So my concerns lead to two questions. First, would some of the top 20 CS graduate schools reject me because they don't have any researchers, who are currently researching those questions, but their research could help me work on those questions to some degree? Second, is it okay to state my long-term research goals I mentioned above on my SOP, rather than state which ongoing research at the school I'm interested in? I'm not sure what exact fields/topics would contribute to my long-term goals, but I think statistical machine learning and intelligent systems could offer some hopes.

Any opinions would be appreciated!
Only put something in your SOP as a research goal (short- or long-term) if you can make a credible case that (a) you understand broadly what it's about, and how it fits into your field as a whole, (b) you're capable of achieving it, and (c) the department you're applying to is a good place to do it, or start to do it. As an extreme example, saying you want to cure cancer is a bad idea because it's not realistic. But even saying you want to get into cancer research needs to be supported by evidence that you know something about it, and about the cancer group at the department you're applying to.

If you can't satisfy conditions (a), (b), and (c), it's not necessarily a bad thing, it just means you should be less specific about your goals. You could say, for example, that your end goal is to do research in applied CS, including bioinformatics. Then talk about what you've done already in that area, the skills you want to learn, and why department X is a good place to learn them. Make sure to keep it as focused on CS as possible. The last thing you want the committee to think is "why is this person applying to our department and not stats/applied math/biology?"