Metrics for multi-label classification and recommendation problems

Recommender systems are one of the most popular applications of data analysis and machine learning, and there are quite a few competitions on Kaggle that have used the recommendation approach. For instance, the Quick, Draw! Doodle Recognition Challenge was a prediction evaluated as a recommender system. Some other competitions on Kaggle, however, truly strived to build effective recommender systems (such as Expedia Hotel Recommendations: https://www.kaggle.com/c/expedia-hotel-recommendations) and RecSYS, the conference on recommender systems (https://recsys.acm.org/), even hosted one of its yearly contests on Kaggle (RecSYS 2013: https://www.kaggle.com/c/yelp-recsys-2013).

Mean Average Precision at K (MAP@{K}) is typically the metric of choice for evaluating the performance of recommender systems, and it is the most common metric you will encounter on Kaggle in all the competitions that try to build or approach...