Sometimes Math is not the answer

I would love to stand corrected in this case, though. Let me explain first the reason behind this claim—It will take a minute, so bear with me:

Say there is a new movie released, and you would like to know how good it is, or whether you and your partner will enjoy watching it together. There are plenty of online resources out there that will give you enough information to make an educated opinion but, let’s face it, you will not have the complete picture unless you actually go see the movie (sorry for the pun).

For example, I fell for “The Blair Witch Project:” their amazing advertising campaign promised me thrill and originality. On top of that, the averaged evaluation of many movie critics that had access to previews claimed that this was a flick not to be missed… Heck, I even bought the DVD for my sister before even watching it!—She and I have a similar taste with respect to movies. The disappointment was, obviously, epic. Before that, and many a time afterwards, I have tripped over the same stone. If nothing else, I learned not to trust commercials and sneak previews any more (“Release the Kraken!,” anyone?)

The only remaining resource should then be the advice of the knowledgeable movie critics—provided you trust on their integrity, that is. Then it hit me: My taste in movies, so similar to my sister’s, could be completely different to that of the “average critic”. Being that the case, why would I trust what a bunch of experts have to say? The mathematician in me took over, and started planning a potential algorithm:

• step 1: go ahead and score a bunch of movies.
• step 2: A first function would compare my artistic taste with that of another given critic, and decide how much should I trust this person. I assign to each of these individuals a numerical value between 0 and 1: the closer to zero, the least likely I would trust their opinion—in Approximation theory we call this a weight.
• step 3: Once I have a reliable set of weights, and given a precise movie, I could gather the scores of a bunch of critics and, instead of performing a standard average of their evaluations, do a weighted one.

So far, Math seems to be the answer.

Let’s say that I would like to make this application available to the public (this is where the problem gets interesting). Once new users acquire this product, the first step is, obviously, to let them train the program by allowing to give their opinion about a large number of movies (ala Netflix). The more films they watch, and the more they evaluate them, the better, right? Not necessarily!

Say I am a compulsive and avid SciFi geek, that watches nothing but Star(Wars|Trek|Man), “Galactica Serenity of Thrones,” “Captain Terminator of the Rings,” “Conan, the Batman Alien Avatar,” or whatever. How good will the response of my basic code to, say, “Citizen Kane,” or “West Side Story?”

A decent app should encourage users to watch and provide an opinion on a set of carefully chosen movies (famous or not, good or terrible, fuzzy-feeling or Ôdishon-uncomfortable) If this selection is good enough, we are on business.

I would like to pose this question to all (no matter whether mathematician, statistician or none of the above): What should be the minimum number of movies so that this application works reliably? The question is tricky and subtle: the answer probably depends heavily on the user. And related to this question there is another, more crucial: What would be a good set of movies to choose from?

I am sure that you would include in this list…

• A few classics (Casablanca?),
• some Westerns (is Guy Pierce’s “The Proposition” a Western, technically?),
• a bunch of Hitchcocks, Kubrics, Spielbergs, Fellinis, Almodovars, Kurosawas,
• musicals (even if you hate them),
• horror movies (“A Nightmare on Elm Street,” according to my wife, but you probably might want to ask Scotty‘s opinion here),
• scifi from different decades (“The Day the Earth Stood Still,” “Solaris,” “E.T.: The Extra-Terrestrial.”),
• a handful of terribly acted/directed movies (“Spider-Man 3,” Ed Wood’s “Glen or Glenda.”),
• shocking scripts (“Memento,” the original “Sleuth” with Laurence Olivier and Michael Caine, “Sixth Sense.”),
• war movies (“The Bridge on the River Kwai,” or “The Guns of Navarone.”),
• animation (Akira, some Disneys, Shrek),
• comedies (SNL-based, comedy of errors, slapstick),
• exposure to different actors and actresses, movies with amazing photography, crappy music scores, infantile plots (Robin William’s “Popeye.”), barely-decent adaptations of literary masterpieces, sublime technological achievements (Transformers, Avatar, “The Matrix.”), etc.

This is where I am not sure there is still a good mathematical model to make that choice of movies. Maybe data mining could do the trick. Why don’t you give me a hand, and start posting a selection of about ten-to-twenty films that should be included (and why!)? Remember: they don’t necessarily have to be all masterpieces: as a matter of fact, I believe that you need to have some terrible movies in the list, especially if you don’t believe they are all that bad.

Data Mining: Practical Machine Learning Tools and Techniques, Third Edition (The Morgan Kaufmann Series in Data Management Systems)