Ke Ren

Hoda Bidkhori, John P Dickerson, Duncan C McElfresh et al.

Motivated by kidney exchange, we study a stochastic cycle and chain packing problem, where we aim to identify structures in a directed graph to maximize the expectation of matched edge weights. All edges are subject to failure, and the failures can have nonidentical probabilities. To the best of our knowledge, the state-of-the-art approaches are only tractable when failure probabilities are identical. We formulate a relevant non-convex optimization problem and propose a tractable mixed-integer linear programming reformulation to solve it. In addition, we propose a model that integrates both risks and the expected utilities of the matching by incorporating conditional value at risk (CVaR) into the objective function, providing a robust formulation for this problem. Subsequently, we propose a sample-average-approximation (SAA) based approach to solve this problem. We test our approaches on data from the United Network for Organ Sharing (UNOS) and compare against state-of-the-art approaches. Our model provides better performance with the same running time as a leading deterministic approach (PICEF). Our CVaR extensions with an SAA-based method improves the $α\times 100\%$ ($0<α\leqslant 1$) worst-case performance substantially compared to existing models.

Ke Ren, Haichuan Yang, Yu Zhao et al.

The positive-unlabeled (PU) classification is a common scenario in real-world applications such as healthcare, text classification, and bioinformatics, in which we only observe a few samples labeled as "positive" together with a large volume of "unlabeled" samples that may contain both positive and negative samples. Building robust classifier for the PU problem is very challenging, especially for complex data where the negative samples overwhelm and mislabeled samples or corrupted features exist. To address these three issues, we propose a robust learning framework that unifies AUC maximization (a robust metric for biased labels), outlier detection (for excluding wrong labels), and feature selection (for excluding corrupted features). The generalization error bounds are provided for the proposed model that give valuable insight into the theoretical performance of the method and lead to useful practical guidance, e.g., to train a model, we find that the included unlabeled samples are sufficient as long as the sample size is comparable to the number of positive samples in the training process. Empirical comparisons and two real-world applications on surgical site infection (SSI) and EEG seizure detection are also conducted to show the effectiveness of the proposed model.