Support time-weighted popularity

[ZiyaoWei]

Creating a new ticket for time-weighted popularity; see #359 for prior discussions.

[ZiyaoWei]

Continuing the discussion from #359 - @mdekstrand any pointers on which algorithms exist in the literature?

[mdekstrand]

The first things that come to mind are the Hacker News & Reddit ranking algorithms — they time-weight up and down votes for the home page or subreddit topic lists. I'd have to do some further looking to dig up academic cites; feel free to search & share any if you find some! Unfortunately the link I had for Hacker News now 404s.

A simple half-life decay model would be a reasonable starting point, though.

There will be a couple of other things needed technically: in particular, we need a way to feed the time into the system. There are a couple of designs we can think about technically:

• We decay based on query time. This will require the ability to provide a query timestamp, which we eventually need to do anyway, but likely requires additional evaluation work, and only makes a difference when we're incorporating new ratings live. It also requires a decay model that progressively increases weights as time goes forward instead of retroactiely decaying waits of historical ratings (or it's very time-consuming to compute).
• We decay based on training time. This fits well with the current paradigm and is the easiest to implement.

To implement the second option, though, we do need a concept of the time when training happened. This should probably be an attribute of the dataset; if the user doesn't specify, we can use the last item timestamp.