Summary of Shusen Wang's tutorial: DPP to improve variety in Recommendation

 Determinantal Point Processes (DPP)

Let the vectors construct a volume. The larger the volume, the more variety. When the volume is low, then there are items similar to each other.

Given V to a d x k matrix, collecting k vectors of d dimensions. The volume is calculated as the determinant, which is V.transpose * V.

DPP math formula:

   argmax [ log det(V.transpose * V) ]

Hulu applied DPP in recommendation system:

   argmax [ a * total reward + (1- a) * log det(V.transpose * V) ]

  To solve this equation, Greedy search is applied to find 1 item at a time that has a good reward while not too close to the already picked items. Hulu provided a bit more efficient solution to find the similarity part, by using Cholesky Decomposition. 

Cholesky Decomposition is to make a matrix become a triangular matrix to multiply its own transpose. In Hulu's proposal, Cholesky Decomposition at each step is calculated based on Cholesky Decomposition of the previous step to avoid repeated calculation.

References:

https://www.youtube.com/watch?v=HjpJeUSekKs

https://www.youtube.com/watch?v=wi8xVHiZZr4

https://lsrs2017.files.wordpress.com/2017/08/lsrs_2017_lamingchen.pdf