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## Final 2019 Q25

Hello,

I couln't imagine a case how the number of observed entries can increase while all K, N, D are kept constant.

Aren't we using complete data in ALS which is stored in IDIXINI sized matrix? Where the newly observed entries will be placed? Or does the question want to ask about ALS with missing entries?

Thank you,

Question: For optimizing a matrix factorization problem in the recommender systems setting, as the number of observed entries increases but all K, N, D are kept constant, the computational cost of the matrix inversion in Alternating Least-Squares increases.## 1

This should help:

https://www.oknoname.com/EPFL/CS433/topic/2847/exam-2019-q24-25/#c2

I think K and N are the number of 'users' and 'movies', and 'observed entries' are available rating pairs.

Me too, I don't get the difference between N and the number of observed entries.

This should help:

https://www.oknoname.com/EPFL/CS433/topic/2847/exam-2019-q24-25/#c2

I think K and N are the number of 'users' and 'movies', and 'observed entries' are available rating pairs.

But in ALS, we make an assumption that the matrix has no missing entries thus all rating pairs are present, no? Because if this is the case we cant have new observed entries unless we increase the size of K or N.

You can still use ALS with missing entries. You can take https://github.com/epfml/ML_course/blob/master/labs/ex13/solution/ex13.ipynb as an example.

If you fix the representations for either 'users' or 'movies', perfectly minimizing for the others (even over the sparse objective with missing entries) is a quadratic problem.

Oh, I see. I got stuck over how there can be new observations in a full entry matrix because the question says ALS, so I assumed no missing entries. Thank you for the clarification!

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