What makes the recommendation problem unable to be solved by traditional machine learning algorithms directly?

Question

We have collaborative filtering and content based algorithms there for recommendation.

What stops traditional algorithms from directly being used to find missing values in the Utility matrix formulation of recommendation? Is it the sparsity of the matrix? If the matrix wasn’t sparse, what other algorithms also work? Do regressions work then?

Say given ratings for $n$ items for $m$ users, predicting the $n^{th}$ rating for a user with ratings of only $n-1$ items. Would collaborative filtering and content based algorithms still do better given less sparsity?

Is there some way in which SVMs, Neural Nets be used for recommendation directly? A naive Bayes approach to say whether a product will be bought or not? In my opinion wouldn't work because products are similar and can't be treated as independent variables.

Also, if these algorithms (collaborative filtering and content-based approaches) work nicely on sparse matrices with a lot of features, can it be used for prediction problems for sparse matrices and solve the high dimension less data problem?

I know these questions are a little spread and may be really naive, but I think an underlying difference between the two approaches of prediction would solve most of my questions. Is there a survey paper which compares machine learning algorithms with content-based and collaborative filtering-based approaches to prediction?

Answer 1

Regarding your question on using regression for predicting the nth item. Typically regression is preformed on a bunch of features that influence an observation. For eg., regression is a model that combines features of a house such as number of bedrooms, number of baths, school rating, area of the house to the values. Assume for every user $u$, for all the movies he has rated, if you have a matrix $V$ that has the features of the movies such as length of the movie, MPAA rating, genre etc and the rating of the movie, using this matrix $V$, you can build a regression model for the user $U$ that fits the rating of the movies. Collaborating filtering based recommender systems is exactly trying to build this statistically significant item/movie features automatically. Assume you have a rating matrix $R$, where rows are items and columns are users, the collaborative filtering based recommender system algorithm discovers two matrix $U$ and $V$ such that $R \approx VU$. The matrix $V$ is a feature-item matrix - for all the items, it discovers a hidden/latent feature matrix which you would have otherwise explicitly collected. Using this feature matrix $V$, for every user $u$, it also discovers the weights (similar to regression model). All the users weights $u$, is represented as the matrix $U$.