Missing data are ubiquitous in many domains such as healthcare. When these data entries are not missing completely at random, the (conditional) independence relations in the observed data may be different from those in the complete data generated by the underlying causal process. Consequently, simply applying existing causal discovery methods to the observed data may lead to wrong conclusions. In this paper, we aim at developing a causal discovery method to recover the underlying causal structure from observed data that are missing under different mechanisms, including missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). With missingness mechanisms represented by missingness graphs (m-graphs), we analyze conditions under which additional correction is needed to derive conditional independence/dependence relations in the complete data. Based on our analysis, we propose Missing Value PC (MVPC), which extends the PC algorithm to incorporate additional corrections. Our proposed MVPC is shown in theory to give asymptotically correct results even on data that are MAR or MNAR. Experimental results on both synthetic data and real healthcare applications illustrate that the proposed algorithm is able to find correct causal relations even in the general case of MNAR.

Achilles Tendon Rupture (ATR) is one of the typical soft tissue injuries. Rehabilitation after such a musculoskeletal injury remains a prolonged process with a very variable outcome. Accurately predicting rehabilitation outcome is crucial for treatment decision support. However, it is challenging to train an automatic method for predicting the AT Rrehabilitation outcome from treatment data, due to a massive amount of missing entries in the data recorded from ATR patients, as well as complex nonlinear relations between measurements and outcomes. In this work, we design an end-to-end probabilistic framework to impute missing data entries and predict rehabilitation outcomes simultaneously. We evaluate our model on a real-life ATR clinical cohort, comparing with various baselines. The proposed method demonstrates its clear superiority over traditional methods which typically perform imputation and prediction in two separate stages.

The advent of media transition highlights the importance of user-generated content on social media. Amongst the methods of analysis of user-generated content, sentiment analysis is widely used. Nevertheless, few studies use sentiment analysis to investigate user-generated content on Instagram in the context of public libraries. Therefore, this study aims to fill this research gap by conducting sentiment analysis of two million captions on Instagram. Supervised machine learning algorithms were employed to create the classifier. Three opinion polarities and six emotions were ultimately identified via these captions. These polarities provide new insights for understanding readers, thus helping libraries to deliver better services.