Missingness-Pattern-Adaptive Learning With Incomplete Data

Many real-world problems deal with collections of data with missing values, e.g., RNA sequential analytics, image completion, video processing, etc. Usually, such missing data is a serious impediment to a good learning achievement. Existing methods tend to use a universal model for all incomplete data, resulting in a suboptimal model for each missingness pattern. In this paper, we present a general model for learning with incomplete data. The proposed model can be appropriately adjusted with different missingness patterns, alleviating competitions between data. Our model is based on observable features only, so it does not incur errors from data imputation. We further introduce a low-rank constraint to promote the generalization ability of our model. Analysis of the generalization error justifies our idea theoretically. In additional, a subgradient method is proposed to optimize our model with a proven convergence rate. Experiments on different types of data show that our method compares favorably with typical imputation strategies and other state-of-the-art models for incomplete data. More importantly, our method can be seamlessly incorporated into the neural networks with the best results achieved. The source code is released at https://github.com/YS-GONG/missingness-patterns.