Note: I really want to stress that this theory was developed when there were only 933 chapters so there's very little data out there and any of the claims can be easily overturned by more information.
Lots of attention is focused on Rum or the sister from outside the domain, but not much is focused on Hyoue Kuroda. Here I make 3 possible claims about Hyoue Kuroda. Now I don't expect these to be all correct, but I do feel that they fit the general narrative structure developed by Gosho Aoyama in his previous arcs.
Claim 1: Hyoue Kuroda was put in a coma by Rum 10 years ago and left for dead.
If Hyoue Kuroda is a parallel, that must mean that he needs a personal relationship with Rum. We know nothing about Rum as a person so it can be too early to speculate what Hyoue and Rum have as a relationship. However, we know one important aspect about Hyoue: he got put into a coma for 10 years. The cause of that coma must be extremely important and it's very logical to believe that Rum caused the coma and Hyoue now wants revenge.
Claim 2: The Hyoue Kuroda we are introduced to is NOT actually Hyoue Kuroda, but someone else involved in the incident impersonating as him. This could be staged (faking his death) or legitimate (true loss of memories).
So why would the fake Hyoue impersonate him? There are three schools of thought I can think of. First, he could be Rum. As I explained, I think that possibility is low unless Gosho double bluffs. Second, this can be a honest mistake. Remember he has memory loss so perhaps he had amnesia and the nurses convinced him that he is Hyoue. The third and most plausible in my opinion is that he's faking his own death. After the incident 10 years ago, he was presumed dead and his body was wrongly identified as someone else, so he's taking advantage of that. He's pretending to be dead to protect himself and his family because he knows Rum will finish the job if word gets out there that he survived. With a fake disguise, it's much easier for him to investigate his own death and get revenge. Regardless of whether he legitimately lost his memories or is pretending, I feel by the time he transferred to Tokyo, he's already regained his memories since the only reason I think he's at Tokyo now is because of Rum.
Claim 3: Hyoue Kuroda is either the father to or someone with a close personal relationship with the Akai family, Bourbon or Scotch.
As for the relationship itself, there's one thing to clarify: Hyoue was put in a coma for 10 years. When he got out of this coma is still ambiguous, but assuming this happens recently, this means Hyoue was basically missing from his linked partner's life for 10 years. This makes me think the link has to be something that's strong enough to sustain time and that link is blood, more specifically father. One major obstacle at first appears to be names. After all, nobody else we know has last name Kuroda. This is why Claim 2 comes to the rescue, as it gives a perfectly logical explanation of why not only can he be some character's father but also why said character won't even be able to recognize him since his face looks completely different. Assuming Shuichi, Shukichi, Bourbon, Scotch are all in their late 20s, this makes it very possible for Hyoue to be their father, since Hyoue would first be a father in his early 20s. That's around the same age as Kogoro, Yusaku and Ginzo when they became fathers.
I've already established that Hyoue could be a father and who's daddy is currently missing? The Akais. In the series, it seems that good detective abilities is genetic. After all, let's look at the high school detectives. Shinichi, Heiji and Hakuba all have daddies that are detectives even better than themselves (Ok, I'm not sure about Hakuba but it's presumed). Both the father of Heiji and Hakuba are police superintendents in particular. Now, who else is a high school detective? Sera, as well as her older brothers previously. There's no doubt that their father must be some amazing detective and guess who randomly pops up as an extremely competent police superintendent? Hyoue. 2/3 of the high school detectives in the show have a superintendent daddy so the Akais having one as well is highly possible. A possible issue with this theory is in the Animal Crossing cards when Gosho writes "Akai's father is unfortunately already... it's a secret!" This is ambiguous but does seem to suggest that perhaps Papa Akai is dead. However, using similar logic, Hyoue could also be the father of either Bourbon or Scotch. Perhaps Bourbon or Scotch became police police and join the BO as undercover agents as revenge for what they did to daddy as a kid.
I'm still not entirely satisfied with this theory, since there's so little information, but I definitely think we've seen enough of Gosho's style to make sensible predictions about what he's going to do.
NOVEMBER 2017 UPDATE
Heh completely forgot I made this 2 years ago... I'm still standing by the claims I made back then, with the claims 2 and 3 being further narrowed and collapsed into one claim
Claim 2&3: The Hyoue Kuroda we are introduced to is NOT actually Hyoue Kuroda, but he's actually the father to the Akai family, Tsutomu Akai (who's faking his death).
Fully expecting an Akai family reunion at the climax of the Rum arc.