Learning from implicit feedback is one of the most common cases in the application of recommender systems. Generally speaking, interacted examples are considered as positive while negative examples are sampled from uninteracted ones. However, noisy examples are prevalent in real-world implicit feedback. A noisy positive example could be interacted but it actually leads to negative user preference. A noisy negative example which is uninteracted because of unawareness of the user could also denote potential positive user preference. Conventional training methods overlook these noisy examples, leading to sub-optimal recommendation. In this work, we propose probabilistic and variational recommendation denoising for implicit feedback. Through an empirical study, we find that different models make relatively similar predictions on clean examples which denote the real user preference, while the predictions on noisy examples vary much more across different models. Motivated by this observation, we propose denoising with probabilistic inference (DPI) which aims to minimize the KL-divergence between the real user preference distributions parameterized by two recommendation models while maximize the likelihood of data observation. We then show that DPI recovers the evidence lower bound of an variational auto-encoder when the real user preference is considered as the latent variables. This leads to our second learning framework denoising with variational autoencoder (DVAE). We employ the proposed DPI and DVAE on four state-of-the-art recommendation models and conduct experiments on three datasets. Experimental results demonstrate that DPI and DVAE significantly improve recommendation performance compared with normal training and other denoising methods. Codes will be open-sourced.
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