Learn English – What are the differences between “assume”, “presume” and “suppose”

Here's my opinion of your alternatives.

1. "because" is your best choice for clear, correct, unambiguous communication, especially if you want to be understood easily by other non-native speakers.

2. "since" is acceptable, although it makes your statement ambiguous; the second meaning would be that statement A became true at the time that statement B became true. Example: "I study more often since I enrolled in class" conveys that when you enrolled in class, then you began studying more often. Rule of thumb: prefer "since" when your intent is to convey "from the time that".

3. "as" is somewhat acceptable, but in your particular statement structure "as" has more useful meanings of "abstractly analogous" or "synchronously". Example: "I like apples as you like oranges" conveys that my liking is similar to your liking, i.e. equivalently strong/weak/notable/etc. Example: "I make dinner as you set the table" conveys that we do these tasks at the same time in the same place. Rule of thumb: prefer "as" when your intent is to convey "sameness".

4. "for" can be acceptable, although I would never expect to hear it in normal conversation. It would come across as overly-academic, or possibly epic or religious. Example: "We eat well tonight, for tomorrow we go to war." Rule of thumb: prefer "for" when you want to be poetic and inspirational.

The meanings of jargon terms often have essentially nothing to do with the meanings of the English words they're made from. Nowhere is this more the case than in mathematics.

I would use whichever term seems better established—regardless of whether it sounds artificial to native English speakers who aren't mathematicians—so as to give the reader the best possible chance to figure out what I'm talking about.

Updated: I should just answer your question. To my ear, there is a verb filter, and a count noun filter. There is also a non-count noun filtration. (You can count coffee filters, but the filtration of water through coffee grounds isn't something you can count.) So already the mathematical use of filtration as a count noun ("a filtration") differs from the everyday use.

I am pretty sure I never heard the verb filtrate used in everyday English until I started searching for such uses just now. A Google search for filtrated hits mainly dictionary sites. At the moment, the first non-dictionary hit is a link to this question! I can confirm that to my ear, it's hardly a word, and it sounds weird and artificial. Filtered sounds much nicer to me. It is an actual common, everyday word (and, correspondingly, gets hundreds of times as many Google hits).