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By Joseph Rickert

Revolution’s resident economist, Saar Golde, is very fond of saying that “90% of what you might from a recommendation engine can be achieved with simple techniques”. To illustrate this point (without doing a lot of work), we downloaded the million row movie dataset from www.grouplens.org with the idea of just taking the first obvious exploratory step: finding the good movies. Three zipped up .dat files comprise this data set. The first file, ratings.dat, contains 1,000,209 records of UserID, MovieID, Rating, and Timestamp for 6,040 users rating 3,952 movies. Ratings are whole numbers on a 1 to 5 scale. The second file, users.dat, contains the UserID, Gender, Age, Occupation and Zip-code for each user. The third file, movies.dat, contains the MovieID, Title and Genre associated with each movie.

Although the movies dataset is not a large file, and can easily be read into my laptop’s memory (a Dell with 4, 1.86GHz cores and 8GB or RAM) it turns out that it doesn’t provide R with enough resources to run the simple regression model we had in mind. To get around this, we used the rxImport function to import the files into .XDF format used by the RevoScaleR package, transformed all of the variables except the times stamp into factors and merged them into one big file called “RUM”. The script “XDF import.R” shows how all of this was done. Everything in this script is straightforward except maybe the few lines of code beginning at line 101 where a little work needs to be done to make reconcile the levels of the MovieID factor variable between ratings and movies files. Working with factors can be a little in R, so it is nice to have the function rxFactors for setting factor levels in XDF files.

Once we got the RUM we could take the first naïve step of finding the best movie according to the user ratings. This can be done with the RevoScaleR function rxCube which produces a cross tabulation in long form. The following code which tabulates rating by titles produces the results in Table 1.

cube.3 <- as.data.frame(rxCube(Rating ~ fTitle,data="RUM"))

head(cube.3)

Table 1
	fTitle	Rating	Counts
1	Toy Story (1995)	4.147	2077
2	GoldenEye (1995)	3.541	888
3	City Hall (1996)	3.063	128
4	Curdled (1996)	3.050	20
5	Ed's Next Move (1996)	4.250	8
6	Extreme Measures (1996)	2.942	121

Rating contains the average rating and Counts gives the number of ratings that went into computing the average. After sorting cube.3 and including only movies with more than 50 ratings we come up with our top-six list in Table 2.

Table 2
	Title	Rating	Counts
1	Sanjuro (1962)	4.609	69
2	Seven Samurai (The Magnificent Seven) (Shichinin no samurai) (1954)	4.561	628
3	Shawshank Redemption, The (1994)	4.555	2227
4	Godfather, The (1972)	4.525	2223
5	Close Shave, A (1995)	4.521	657
6	Usual Suspects, The (1995)	4.517	1783

 (The code for this and the rest of our analysis is in the script “Best movie.R”.) This list certainly looked good to me: two films by Akira Kurosawa on top and the Godfather not far behind. These people know a good film when they see one. Well, maybe so, but maybe taking the ratings at face value from this particular movie buffs is not the best we can do. Better than just averaging ratings, with a simple regression we can look for the best movie while controlling for the users. The RevoScaleR functions to do this are:

form <- formula(Rating ~ UserID + fTitle)

mod.1 <- rxLinMod(form,data="RUM",cube=TRUE)

The regression looks inocuous enough. However, since UserID and fTitle are both factors we are computing a regression with 9,746 fixed effects! lm ran out of resource on my laptop trying to do this regression but rxLinMod completed the job in about 53 seconds. Sorting the model coefficients from high to low produces a new best movie list. Table 3 includes enough movies to show where the movies in our original list landed.

Table 3
	Title	Coef	Coef Std
1	Song of Freedom (1936)	3.298	0.9127
2	Mamma Roma (1962)	2.173	0.6445
3	Schlafes Bruder (Brother of Sleep) (1995)	1.717	0.9159
4	Hour of the Pig, The (1993)	1.637	0.6410
5	Smashing Time (1967)	1.636	0.6481
6	Ulysses (Ulisse) (1954)	1.583	0.9133
7	Gate of Heavenly Peace, The (1995)	1.577	0.5244
8	Apple, The (Sib) (1998)	1.554	0.3058
9	I Am Cuba (Soy Cuba/Ya Kuba) (1964)	1.532	0.4076
10	Lamerica (1994)	1.490	0.3243
11	One Little Indian (1973)	1.404	0.9066
12	Follow the Bitch (1998)	1.401	0.9178
13	Sanjuro (1962)	1.382	0.1213
14	Bells, The (1926)	1.323	0.6404
15	Lured (1947)	1.315	0.9090
16	Leather Jacket Love Story (1997)	1.311	0.6410
17	Chain of Fools (2000)	1.298	0.9127
18	Seven Samurai (The Magnificent Seven) (Shichinin no samurai) (1954)	1.281	0.0645
19	Shawshank Redemption, The (1994)	1.254	0.0568
20	Sunset Blvd. (a.k.a. Sunset Boulevard) (1950)	1.253	0.0678
21	For All Mankind (1989)	1.245	0.1822
22	Jar, The (Khomreh) (1992)	1.243	0.9045
23	Paths of Glory (1957)	1.232	0.0801
24	Close Shave, A (1995)	1.230	0.0641
25	Usual Suspects, The (1995)	1.229	0.0576
26	Godfather, The (1972)	1.229	0.0568

Pretty interesting, not only did the original top six move down, they also moved out of their original order. Moreover, having done the regression, we also have the standard deviations of the coefficients available. Now, we not only have a measure of how good a movie is, but we also have an estimate of the uncertainity of its quality, and we may want to use this to adjust our recommendations. For example, the 17^th movie on the list, Chain of Fools, has a coefficient of 1.298 with a standard deviation of 0.9127. This is a fairly large spread. Near the bottom of its range of uncertainty the coefficient of Chain of Fools would be smaller than the coefficients of the rest of the movies on the top 26 list. But, just below Chain of Fools in the 18^th slot, the coefficient of the The Seven Samurai, 1.281, has a much smaller standard deviation: 0.0645. It appears that this would be a better movie to recommend.

Although we have not shown it, our model also gives user fixed effects. So, we can see who the tougher raters are and, combined with other information about users, we might be able to figure out how to recognize a tough movie rater.

I think Saar made his point: good progress can be made with simple tools. Moreover, by thinking like a statistician (or an economist) and not merely letting the machine learning algorithms drive the process, it is possible to gain useful insight into how to make better recommendations.

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