With rising application demands and inherent complexity, graph OOD problems call for specialized solutions. While data-centric methods exhibit performance enhancements on many generic machine learning tasks, there is a notable absence of data augmentation methods tailored for graph OOD generalization. In this work, we propose to achieve graph OOD generalization with the novel design of non-Euclidean-space linear extrapolation. The proposed augmentation strategy extrapolates both structure and feature spaces to generate OOD graph data.

The quantile function is a mathematical function that takes a quantile (a percentage of a distribution, from 0 to 1) as input and outputs the value of a variable. It can answer questions like, "If I want to guarantee that 95% of my customers receive their orders within 24 hours, how much inventory do I need to keep on hand?" As such, the quantile function is commonly used in the context of forecasting questions. In practical cases, however, we rarely have a tidy formula for computing the quantile function. Instead, statisticians usually use regression analysis to approximate it for a single quantile level at a time.

'The quantile function is a mathematical function that takes a quantile (a percentage of a distribution ranging from 0 to 1) as an input and returns the value of a variable as an output.' It can answer queries such as, "How much inventory do I need to maintain on hand if I want to guarantee that 95 percent of my customers receive their orders within 24 hours?" As a result, the quantile function is frequently utilized in forecasting questions. However, in practice, there is rarely a neat method for computing the quantile function. That means that if you want to compute it for a different quantile, you'll need to create a new regression model, which nowadays usually entails retraining a neural network.

Sophisticated trajectory prediction models that effectively mimic team dynamics have many potential uses for sports coaches, broadcasters and spectators. However, through experiments on soccer data we found that it can be surprisingly challenging to train a deep learning model for player trajectory prediction which outperforms linear extrapolation on average distance between predicted and true future trajectories. We propose and test a novel method for improving training by predicting a sparse trajectory and interpolating using constant acceleration, which improves performance for several models. This interpolation can also be used on models that aren't trained with sparse outputs, and we find that this consistently improves performance for all tested models. Additionally, we find that the accuracy of predicted trajectories for a subset of players can be improved by conditioning on the full trajectories of the other players, and that this is further improved when combined with sparse predictions. We also propose a novel architecture using graph networks and multi-head attention (GraN-MA) which achieves better performance than other tested state-of-the-art models on our dataset and is trivially adapted for both sparse trajectories and full-trajectory conditioned trajectory prediction.