I have the exact same issue: I started noticing the problem when only my S4 is on wifi, the incoming data arrow for the wifi icon will flash, and of course, the phone battery drains faster than normal.
What I have found is the following, after I install the My Data Manager app (which, by the way, is a really cool app - it shows you exactly which app is using how much data, and when, broken down by wifi, mobile, and roaming):
1. the "OS Services" pulls data consistently between 1 - 4 mb per hour, and "Android System" pulls about 470KB per hour, doesn't matter the time of the day
2. I contacted Verizon for tech support (first call), Verizon told me to call Samsung
3. I called Samsung for support, Samsung tech suggested that I go down to Best Buy Samsung technician to do a hard reset
4. Went to Best Buy last night, waited for 45 minutes for the technician to come back from lunch (just my luck), did the hard reset.
5. Same problem came back.
6. Call Verizon back (second call), no solution other than replace the phone.
Samsung is willing to take a look at the phone, but since Samsung does not offer loaner phone, the tech girl at Best Buy actually told me that I could be without the phone for months before Samsung gets back with me.
And since I have a small crack on the corner of S4's front glass (that's the infamous S4 verses S3 quality issue), Verizon would charge me $300 for the replacement, and I dare not ask Samsung what they're willing to do.
It seems that this is one of those problems that no one has the answer.... Should have just stayed with my S3; I was perfectly happy with it :-$