Predicting Survival Outcomes in the Presence of Unlabeled Data

Many clinical studies require the follow-up of patients over time. This is challenging: apart from frequently observed drop-out, there are often also organizational and financial challenges, which can lead to reduced data collection and, in turn, can complicate subsequent analyses. In contrast, there is often plenty of baseline data available of patients with similar characteristics and background information, e.g., from patients that fall outside the study time window. In this article, we investigate whether we can benefit from the inclusion of such unlabeled data instances to predict accurate survival times. In other words, we introduce a third level of supervision in the context of survival analysis, apart from fully observed and censored instances, we also include unlabeled instances. We propose three approaches to deal with this novel setting and provide an empirical comparison over fifteen real-life clinical and gene expression survival datasets. Our results demonstrate that all approaches are able to increase the predictive performance over independent test data. We also show that integrating the partial supervision provided by censored data in a semi-supervised wrapper approach generally provides the best results, often achieving high improvements, compared to not using unlabeled data.

Supervised Fuzzy Partitioning

Centroid-based methods including k-means and fuzzy c-means are known as effective and easy-to-implement approaches to clustering purposes in many applications. However, these algorithms cannot be directly applied to supervised tasks. This paper thus presents a generative model extending the centroid-based clustering approach to be applicable to classification and regression tasks. Given an arbitrary loss function, the proposed approach, termed Supervised Fuzzy Partitioning (SFP), incorporates labels information into its objective function through a surrogate term penalizing the empirical risk. Entropy-based regularization is also employed to fuzzify the partition and to weight features, enabling the method to capture more complex patterns, identify significant features, and yield better performance facing high-dimensional data. An iterative algorithm based on block coordinate descent scheme is formulated to efficiently find a local optimum. Extensive classification experiments on synthetic, real-world, and high-dimensional datasets demonstrate that the predictive performance of SFP is competitive with state-of-the-art algorithms such as random forest and SVM. The SFP has a major advantage over such methods, in that it not only leads to a flexible, nonlinear model but also can exploit any convex loss function in the training phase without compromising computational efficiency.