This paper addresses the challenges of learning Matrix Factorization (MF) models from implicit feedback, which is common in many applications where explicit ratings are not available. The authors highlight two critical issues: the uniform weighting of missing data and the lack of efficiency in online learning. To tackle these issues, they propose a new method that weights missing data based on item popularity, which is more effective than uniform weighting. They also develop an efficient learning algorithm, eALS, which uses element-wise Alternating Least Squares to optimize the MF model with variably-weighted missing data. This algorithm is significantly faster than traditional ALS and can be used for real-time online learning. Extensive experiments on two public datasets show that their method outperforms state-of-the-art implicit MF methods in both offline and online settings. The implementation is available at https://github.com/hexiangnan/sigir16-eals.This paper addresses the challenges of learning Matrix Factorization (MF) models from implicit feedback, which is common in many applications where explicit ratings are not available. The authors highlight two critical issues: the uniform weighting of missing data and the lack of efficiency in online learning. To tackle these issues, they propose a new method that weights missing data based on item popularity, which is more effective than uniform weighting. They also develop an efficient learning algorithm, eALS, which uses element-wise Alternating Least Squares to optimize the MF model with variably-weighted missing data. This algorithm is significantly faster than traditional ALS and can be used for real-time online learning. Extensive experiments on two public datasets show that their method outperforms state-of-the-art implicit MF methods in both offline and online settings. The implementation is available at https://github.com/hexiangnan/sigir16-eals.