Ratings of a user to most items in recommender systems are usually missing not at random (MNAR), largely because users are free to choose which items to rate. To achieve unbiased learning of the prediction model under MNAR data, three typical solutions have been proposed, including error-imputation-based (EIB), inverse-propensity-scoring (IPS), and doubly robust (DR) methods. However, these methods ignore an alternative form of bias caused by the inconsistency between the observed ratings and the users' true preferences, also known as noisy feedback or outcome measurement errors (OME), e.g., due to public opinion or low-quality data collection process. In this work, we study intersectional threats to the unbiased learning of the prediction model from data MNAR and OME in the collected data. First, we design OME-EIB, OME-IPS, and OME-DR estimators, which largely extend the existing estimators to combat OME in real-world recommendation scenarios. Next, we theoretically prove the unbiasedness and generalization bound of the proposed estimators. We further propose an alternate denoising training approach to achieve unbiased learning of the prediction model under MNAR data with OME. Extensive experiments are conducted on three real-world datasets and one semi-synthetic dataset to show the effectiveness of our proposed approaches. The code is available at https://github.com/haoxuanli-pku/KDD24-OME-DR.

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