Pang Du

Xin Xing, Zuofeng Shang, Pang Du et al.

We consider the problem of comparing probability densities between two groups. A new probabilistic tensor product smoothing spline framework is developed to model the joint density of two variables. Under such a framework, the probability density comparison is equivalent to testing the presence/absence of interactions. We propose a penalized likelihood ratio test for such interaction testing and show that the test statistic is asymptotically chi-square distributed under the null hypothesis. Furthermore, we derive a sharp minimax testing rate based on the Bernstein width for nonparametric two-sample tests and show that our proposed test statistics is minimax optimal. In addition, a data-adaptive tuning criterion is developed to choose the penalty parameter. Simulations and real applications demonstrate that the proposed test outperforms the conventional approaches under various scenarios.

Pang Du, Zheyuan Sun, Huashan Chen et al.

The accurate measurement of security metrics is a critical research problem because an improper or inaccurate measurement process can ruin the usefulness of the metrics, no matter how well they are defined. This is a highly challenging problem particularly when the ground truth is unknown or noisy. In contrast to the well perceived importance of defining security metrics, the measurement of security metrics has been little understood in the literature. In this paper, we measure five malware detection metrics in the {\em absence} of ground truth, which is a realistic setting that imposes many technical challenges. The ultimate goal is to develop principled, automated methods for measuring these metrics at the maximum accuracy possible. The problem naturally calls for investigations into statistical estimators by casting the measurement problem as a {\em statistical estimation} problem. We propose statistical estimators for these five malware detection metrics. By investigating the statistical properties of these estimators, we are able to characterize when the estimators are accurate, and what adjustments can be made to improve them under what circumstances. We use synthetic data with known ground truth to validate these statistical estimators. Then, we employ these estimators to measure five metrics with respect to a large dataset collected from VirusTotal. We believe our study touches upon a vital problem that has not been paid due attention and will inspire many future investigations.