This is a quick visualization of data from the netflix prize. A vertical bar is drawn for every customer rating a movie. Ratings go from 1 to 5 stars (represented top to bottom.) Note how “Alien” (on the left) received many ratings of 4 and 5 stars, but “Predator” (on the right) mostly received ratings of 4 stars. This depicts approximately 50,000 customer ratings.

The problem:

I know how I rated a whole bunch of movies. I know how everyone else has rated a whole bunch of movies. For any given movie that I have not yet rated (but others have), predict how I would rate it based on my and everyone else’s rating history. Netflix uses the root mean squared error (RMSE) to evaluate results. In other words, let’s guess that I would give the movie Purple Rain a rating of 5, when in reality, I would only rate it a 4. And let’s also guess that I would rate Singin’ in the Rain a 3.5 when my true rating is a 5. Here’s how we would calculate the RMSE:

Purple Rain Prediction Error:  5 - 4 = 1
Singin' in the Rain Prediction Error: 3.5 - 5 = -1.5
 
Squaring each error:  1*1 = 1, -1.5*-1.5 = 2.25
Add the squares of all errors together = 3.25
 
MSE = Sum of Squares divided by Total Guesses = 3.25 / 2 = 1.625
 
RMSE = square root of MSE = sqrt(1.625) = 1.275

Let’s take a simple algorithm to solve the problem: for any user rating any movie, predict a future rating as the global average rating for that movie. This algorithm produces an RMSE of 1.05, not too shabby. The RSME for Netflix’s Cinematch system (which presumably employs collaborative filtering techniques) is around 0.95, a mere 10% improvement. The problem is indeed a difficult one. Netflix will award a one million dollar prize to anyone who can improve the system by an additional 10%.

I submitted my first prediction file today, mostly as a test, nowhere near the leaderboard, with the following algorithm:

A customer C will rating a movie M based on the following function:

rating(C,M) = 0.5 * (the global netflix average rating for movie M) + 0.5 * (the customer’s average rating)

My RMSE?

Your prediction file submitted 2006-10-10 21:31:56 has been decompressed and processed.
The computed RMSE for the quiz subset was 1.0147.

More to come. . .