Modern statistical and machine learning applications increasingly involve complex data structures--data that exhibit temporal dependence, high dimensionality, or that reside in general metric spaces (i.e., object-valued data). This talk presents our recent work on developing robust and reliable statistical inference procedures tailored to such complex settings.

In the first part, I will discuss a new change-point detection method for object-valued time series. The method combines sample splitting with self-normalization and is capable of detecting distributional changes under weak temporal dependence. The resulting statistic requires only pairwise distances, avoids bandwidth selection, and attains a pivotal limiting null distribution. Simulation studies and a real data application illustrate its practical performance.

In the second part, I will present a doubly robust framework for conditional independence testing that integrates kernel methods with generative neural networks. Our approach fully characterizes conditional independence and scales effectively to high-dimensional settings. It maintains strong performance even when the generative models are imperfectly estimated. Its advantages are demonstrated through simulation experiments and an application on feature extraction and image classification.