Alarms can go off for odd reasons, such as a temporary and brief power outtages, which does happen a lot around here in the middle of the night, as we have found that our alarm needs resetting sometimes. Our fax machine used to produce revealing print outs of supply disruption.
We have also been woken up in the middle of the night with the cd player blaring out loud music downstairs. Apparently outtages can bring these to life unexpectedly too! Scary as you think someones broken in and having a party without you in your own home.
These people may have something on a timer , even a central heating timer or cooker timer either coming on or off at 3 am which can overload the electrical system and blow a fuse. If the alarm is on the same circuit as the appliance then it may go off also and need resetting. Thats all I can think of. Good luck with your detective work!