[jacobobryant]

For the interleaving, yes we want to prefer the item that's been skipped fewer times. I got the wording backwards in the article; I'll fix that.

For shuffling, I was trying to come up with an approach that would recommend the top k items roughly the same amount regardless of how many total items are in the list. E.g. say you have 10 subscriptions that you really like--I want to have those be a reasonable portion of your recommendations whether you've subscribed to 100 other subs or 1000 other subs.

Contrast that to a weighted random shuffle where each subscription's weight is its affinity score and we sample them based on weight without regard to their order in the original list. That approach is much more influenced by the size of the total list, and my experience is the handful of subscriptions that I really liked were always drowned out by all the other "speculative" subscriptions I had accumulated in my account.

The computational complexity ends up being OK because we generally don't actually need to shuffle the whole list. I recommend items in batches of 30, so we just need to get that many items and then we can abort the shuffle. There probably is some more efficient way to implement this though.

During implementation I was mostly thinking of this as "sampling" rather than "shuffling" actually, and just ended up describing it as the latter when I wrote the post.

[jacobobryant]

Also--I think the pseudo code you have isn't /quite/ correct. If x is greater than p, we don't immediately take a random element from the list; rather we go to the next element and generate a new x and repeat. I.e. with p=0.1, there's a 10% we immediately take the first item, and if we don't do that, then there's a 10% chance we immediately take the second item, etc. we only pick a completely random item as a fallback if we get to the end of the list without picking anything.

[vitus]

Ah, I overlooked the `some`. Interesting, that's even more skewed than I initially thought.

[vitus]

Thanks for providing more insight into the development process that went into designing this algorithm! :)

> Contrast that to a weighted random shuffle where each subscription's weight is its affinity score and we sample them based on weight without regard to their order in the original list. That approach is much more influenced by the size of the total list, and my experience is the handful of subscriptions that I really liked were always drowned out by all the other "speculative" subscriptions I had accumulated in my account.

I personally see that as an argument for having the original position affect the weight.

I experimented with modifying Fisher-Yates to generate a slightly less left-skewed distribution, and decided upon inverse transform sampling as a fairly cheap solution -- basically, with some function f(X): [0,1) -> [0,1), you can transform a uniformly-distributed random variable X ~ Unif[0,1), which then allows you to bias the shuffle without affecting its asymptotic performance.

> There probably is some more efficient way to implement this though.

One potential optimization is to use rejection sampling: keep track of the elements you've seen, then reject any duplicates when pulling out a sample (instead of manually constructing a new list every time). Now, this interacts poorly with your biasing -- in the extreme case where p=1, you'd keep trying to select the first element, then rejecting it. I might then suggest tracking the first element you haven't selected yet, but at some point this ends up being a lot of complexity for asymptotic behavior when what you have is more than good enough for the scale that you're considering.

This also only addresses the "copy the list every iteration of the sampling" aspect of your algorithm's performance, not the fact that with p=0 (or arbitrarily low) you may end up walking the entire list.

(Rejection sampling is more generally using some criterion to reject samples, e.g. if you were trying to select points within a circle by checking x^2 + y^2 < r^2.)

[jacobobryant]

It is pretty subjective--I design the algorithm with myself in mind first, but I can definitely see a heavier bias toward exploration/variety being better for some others. Something to experiment with.

Thanks for the sampling ideas! Interesting stuff.