Xiaotong Liu

Dipak Wani, Samuel Ackerman, Eitan Farchi et al.

Logs enable the monitoring of infrastructure status and the performance of associated applications. Logs are also invaluable for diagnosing the root causes of any problems that may arise. Log Anomaly Detection (LAD) pipelines automate the detection of anomalies in logs, providing assistance to site reliability engineers (SREs) in system diagnosis. Log patterns change over time, necessitating updates to the LAD model defining the `normal' log activity profile. In this paper, we introduce a Bayes Factor-based drift detection method that identifies when intervention, retraining, and updating of the LAD model are required with human involvement. We illustrate our method using sequences of log activity, both from unaltered data, and simulated activity with controlled levels of anomaly contamination, based on real collected log data.

Xiaotong Liu, Jinxin Wang, Di Wang et al.

Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect approximation performance. However, in dealing with noisy data, kernel interpolation frequently behaves not so well due to the large condition number of the kernel matrix and instability of the interpolation process. In this paper, we introduce a weighted spectral filter approach to reduce the condition number of the kernel matrix and then stabilize kernel interpolation. The main building blocks of the proposed method are the well developed spherical positive quadrature rules and high-pass spectral filters. Using a recently developed integral operator approach for spherical data analysis, we theoretically demonstrate that the proposed weighted spectral filter approach succeeds in breaking through the bottleneck of kernel interpolation, especially in fitting noisy data. We provide optimal approximation rates of the new method to show that our approach does not compromise the predicting accuracy. Furthermore, we conduct both toy simulations and two real-world data experiments with synthetically added noise in geophysical image reconstruction and climate image processing to verify our theoretical assertions and show the feasibility of the weighted spectral filter approach.

Xiaotong Liu, Hong Xuan, Zeyu Zhang et al.

Deep metric learning is often used to learn an embedding function that captures the semantic differences within a dataset. A key factor in many problem domains is how this embedding generalizes to new classes of data. In observing many triplet selection strategies for Metric Learning, we find that the best performance consistently arises from approaches that focus on a few, well selected triplets.We introduce visualization tools to illustrate how an embedding generalizes beyond measuring accuracy on validation data, and we illustrate the behavior of a range of triplet selection strategies.