Summary on Shusen Wang's video of: Ways to combine click rate, like rate, favorite rate, etc. into 1 score

 In multi-target prediction, click probability, like rate, favorite rate, etc are generated together for an item recommended to a user. They need to be combined into 1 score to make ordering easy. Here are a few ways to combine the predictions.

Simple weighted sum:

   click_rate + w1 * like_rate + w2 * favorite_rate + ...

Weighted sum with click_rate as precondition: (as like action has to happen after click happens)

  click_rate * (1 + w1 * like_rate + w2 * favorite_rate + ... )

Weighted product instead of weighted sum:

   [(1 + w1 * click_rate) ** a1] * [1 + w2 * like_rate)] ** a2 ] * ...

Weighted sum based on ranks from the list sorting by 1 dimension. For example, the

   w1 / (click_rank ** a1 + b1) + w2 / (like_rank ** a2 + b2) + ...

For online purchase, it has to go through all steps for a transaction to happen. Thus the probability needs to be multiplied to make 1 score:

   ( click_rate ** a1 ) *    ( cart_rate ** a2 ) *  ( pay_rate ** a3 ) * ( price ** a4 )

Reference: https://www.youtube.com/watch?v=D2iqM2puJ2I