Note: Updating with additional information from the series, since the time of this post.
As we learn, in "No Good Deed" (1x22), it was Nathan Ingram, who used his administrative access to install a new function named "Contingency" just before the Machine was handed over to the government.
In "One Percent" (2x14), we learn that the Machine is sending the numbers on the "Irrelevant" list to Nathan, and he has been trying to save their lives. It seems like a easy assumption to make that this is the result of the "Contingency" function / backdoor inserted into the Machine by Nathan.
We now know that:
Giving out the 'Irrelevant' Numbers to someone, was a function included into the Machine by Nathan Ingram.
The Machine is a self-learning and sentient intelligence, which can, had and does make decisions for itself.
Looking at the real-world facts, it seems unbelievable that there is only a single act of premeditated fatal violence in the entirety of New York City, at any given time (and that there are actually 'breaks' when no such planned violence is imminent)
As such it seems likely that even if Nathan did not include such filtering as a part of "Contingency" from the start, then at some time after the introduction of the 'Contingency' function to the Machine, and the initial failures of save people, the Machine learnt and started filtering the list of all 'Irrelevant' pre-meditated violence. And only gives out those numbers to Finch which it thinks Finch would have the resources and ability to try and stop (or, as Season 3 progresses, which are increasingly 'relevant' to its own, and its people's (Finch, Reese, Shaw, Root's) survival.
Given that Finch is based in New York City, those numbers would largely be based in that location as well.