Nathaniel Xu

Liang Zhang, Nathaniel Xu, Pengfei Yang et al.

Robust pedestrian trajectory forecasting is crucial to developing safe autonomous vehicles. Although previous works have studied adversarial robustness in the context of trajectory forecasting, some significant issues remain unaddressed. In this work, we try to tackle these crucial problems. Firstly, the previous definitions of robustness in trajectory prediction are ambiguous. We thus provide formal definitions for two kinds of robustness, namely label robustness and pure robustness. Secondly, as previous works fail to consider robustness about all points in a disturbance interval, we utilise a probably approximately correct (PAC) framework for robustness verification. Additionally, this framework can not only identify potential counterexamples, but also provides interpretable analyses of the original methods. Our approach is applied using a prototype tool named TrajPAC. With TrajPAC, we evaluate the robustness of four state-of-the-art trajectory prediction models -- Trajectron++, MemoNet, AgentFormer, and MID -- on trajectories from five scenes of the ETH/UCY dataset and scenes of the Stanford Drone Dataset. Using our framework, we also experimentally study various factors that could influence robustness performance.

Nathaniel Xu, Feng Liu, Danica J. Sutherland

Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any dependence with enough samples, standard tests may require an exorbitant amount of samples for detecting subtle dependencies between high-dimensional random variables with complex distributions. In this work, we study two related ways to learn powerful independence tests. First, we show how to construct powerful statistical tests with finite-sample validity by using variational estimators of mutual information, such as the InfoNCE or NWJ estimators. Second, we establish a close connection between these variational mutual information-based tests and tests based on the Hilbert-Schmidt Independence Criterion (HSIC); in particular, learning a variational bound (typically parameterized by a deep network) for mutual information is closely related to learning a kernel for HSIC. Finally, we show how to, rather than selecting a representation to maximize the statistic itself, select a representation which can maximize the power of a test, in either setting; we term the former case a Neural Dependency Statistic (NDS). While HSIC power optimization has been recently considered in the literature, we correct some important misconceptions and expand to considering deep kernels. In our experiments, while all approaches can yield powerful tests with exact level control, optimized HSIC tests generally outperform the other approaches on difficult problems of detecting structured dependence.

Nathaniel Xu

Training energy-based models (EBMs) with noise-contrastive estimation (NCE) is theoretically feasible but practically challenging. Effective learning requires the noise distribution to be approximately similar to the target distribution, especially in high-dimensional domains. Previous works have explored modelling the noise distribution as a separate generative model, and then concurrently training this noise model with the EBM. While this method allows for more effective noise-contrastive estimation, it comes at the cost of extra memory and training complexity. Instead, this thesis proposes a self-adapting NCE algorithm which uses static instances of the EBM along its training trajectory as the noise distribution. During training, these static instances progressively converge to the target distribution, thereby circumventing the need to simultaneously train an auxiliary noise model. Moreover, we express this self-adapting NCE algorithm in the framework of Bregman divergences and show that it is a generalization of maximum likelihood learning for EBMs. The performance of our algorithm is evaluated across a range of noise update intervals, and experimental results show that shorter update intervals are conducive to higher synthesis quality.