Academic

As we are entering the big data era with technological advances of data collection, high-dimensional and complex data is becoming prevalent and the development of effective analysis is gaining more attention to researchers in statistics and data science. Kernel-based methods are widely used in many applications as a nonparametric approach. A maximum mean discrepancy (MMD) is one of the most well-known kernel-based measures as it has the potential to capture any types of differences in the distribution. However, the MMD does not work well for a wide range of alternatives when the dimension of the data is moderate to high due to the curse of dimensionality. In this talk, we introduce novel kernel-based methods for high-dimensional data on two problems: (i) two-sample testing and (ii) change-point analysis. Specifically, we propose new test statistics that make use of patterns under high dimension and achieve substantial power improvement over existing kernel-based methods for general alternatives. We also propose alternative testing procedures that maintain high power with little computational cost, offering easy off-the-shelf tools for large datasets. We illustrate our new approaches on both synthetic and real-world data.