ML25M Data Description – LensKit Codex

Rating Statistics

This section describes the distribution of various item statistics from the data set.

What is the distribution of popularity?

Let’s also look at this as a Lorenz curve, for clarity:

What is the distribution of average ratings?

We now turn to the distribution of various user statistics.

How are user averages distributed?

And what is the distribution of user activity levels (# of ratings)?

The MovieLens ratings have timestamps, so we’ll also look at a temporal view of the data.

How did the data grow over time?

How many ratings are we getting each month through the life of the data set?

Monthly unique users is a good measure of user activity.

How long do users usually stick around?

Some downstream uses benefit from parametric distributions of user/item activity levels.

This section models the item popularity distribution with various parametric distributions.

Distribution	Params	Location	Scale	D(KL)	Δ(JS)
Log-normal	`s`=13.585	1	0.102	0.963	0.42
Pareto	`b`=0.382	0.372	0.626	0.135	0.163
Power law	`a`=0.236	0.732	999.645	inf	0.342
Geometric	`p`=0.002	0		2.672	0.583

Now the same, for user activity distributions.

Distribution	Params	Location	Scale	D(KL)	Δ(JS)
Log-normal	`s`=1.589	18.636	39.862	0.039	0.091
Pareto	`b`=0.721	0.063	19.729	0.095	0.16
Power law	`a`=0.334	19.509	999.780	inf	0.283
NegBinom	`n`=1.000, `p`=0.007	20		0.209	0.189
BetaNegBinom	`n`=327.000, `a`=2.711, `b`=0.694	20		0.017	0.064