Modeling Set-structured Trajectory Data

This thesis advances machine learning approaches for modeling set-structured trajectory data. Specifically, this cumulative dissertation comprises five articles presenting deep learning solutions for capturing interactions both across sets of trajectories and within individual trajectories consisting of set-structured features. Empirically, the articles in this thesis investigate both types of interactions in the domains of multiagent trajectories in team sports and student interactions in educational contexts, respectively. Set-structured trajectory data – as defined in this thesis – is pervasive and increasingly important in a wide range of domains. Specifically, this thesis employs a generalized notion of trajectories, referring to spatio-temporal sequences encompassing both continuous and discrete state spaces. Set-structured trajectory data refers to both, instances consisting of sets of trajectories and instances of individual trajectories with sets of features per timestep. Regarding sets of trajectories, we investigate the use of latent variable models for multiagent trajectory modeling, demonstrating how two desirable properties of these models can be achieved with computationally simpler approaches. We propose a novel transformer-based approach for efficient autoregressive modeling of interactions within sets of trajectories, and we introduce a masked autoencoder for self-supervised pretraining of factorized transformer architectures for multiagent trajectory data. Regarding trajectories with set-structured features, we explore principled set-based representations of student interactions for transformer-based knowledge tracing, proposing a novel self-attention-based aggregation of set-structured features and improving upon transformer attention variants used in related work. We further leverage a transformer architecture that is based on a flat representation, relying on positional encoding rather than architectural design to capture dependencies in set-structured student interactions, and adapt a self-improvement training scheme from neural combinatorial optimization to computerized adaptive testing. Technical contributions presented in this thesis thus span probabilistic modeling, representation learning, self-supervised pretraining, structured prediction, and policy learning. In addition, this thesis reflects the broader trend toward homogenization in deep learning and can be read as an argument in favor of conceptually simpler models for set-structured trajectory data.