  Implicit feedback data is extensively explored in recommendation as it is
easy to collect and generally applicable. However, predicting users' preference
on implicit feedback data is a challenging task since we can only observe
positive (voted) samples and unvoted samples. It is difficult to distinguish
between the negative samples and unlabeled positive samples from the unvoted
ones. Existing works, such as Bayesian Personalized Ranking (BPR), sample
unvoted items as negative samples uniformly, therefore suffer from a critical
noisy-label issue. To address this gap, we design an adaptive sampler based on
noisy-label robust learning for implicit feedback data.
  To formulate the issue, we first introduce Bayesian Point-wise Optimization
(BPO) to learn a model, e.g., Matrix Factorization (MF), by maximum likelihood
estimation. We predict users' preferences with the model and learn it by
maximizing likelihood of observed data labels, i.e., a user prefers her
positive samples and has no interests in her unvoted samples. However, in
reality, a user may have interests in some of her unvoted samples, which are
indeed positive samples mislabeled as negative ones. We then consider the risk
of these noisy labels, and propose a Noisy-label Robust BPO (NBPO). NBPO also
maximizes the observation likelihood while connects users' preference and
observed labels by the likelihood of label flipping based on the Bayes'
theorem. In NBPO, a user prefers her true positive samples and shows no
interests in her true negative samples, hence the optimization quality is
dramatically improved. Extensive experiments on two public real-world datasets
show the significant improvement of our proposed optimization methods.
