With tracking systems becoming more widespread in sports research and regular training and competitions, more data are available for sports analytics and performance prediction. We analyzed 2523 ski jumps from 205 athletes on five venues. For every jump, the dataset includes the 3D trajectory, 3D velocity, skis’ orientation, and metadata such as wind, starting gate, and ski jumping hill data. Using this dataset, we aimed to predict the expected jump length (xLength) inspired by the expected goals metric in soccer (xG). We evaluate the performance of a fully connected neural network, a convolutional neural network (CNN), a long short-term memory (LSTM), and a ResNet architecture to estimate the xLength. For the prediction of the jump length one second after take-off, we achieve a mean absolute error (MAE) of 5.3 m for the generalization to new athletes and an MAE of 5.9 m for the generalization to new ski jumping hills using ResNet architectures. Additionally, we investigated the influence of the input time after the take-off on the predictions’ accuracy. As expected, the MAE becomes smaller with longer inputs. Due to the real-time transmission of the sensor’s data, xLength can be updated during the flight phase and used in live TV broadcasting. xLength could also be used as an analysis tool for experts to quantify the quality of the take-off and flight phases.
The reliability of neural networks is essential for their use in safety-critical applications. Existing approaches generally aim at improving the robustness of neural networks to either real-world distribution shifts (e.g., common corruptions and perturbations, spatial transformations, and natural adversarial examples) or worst-case distribution shifts (e.g., optimized adversarial examples). In this work, we propose the Decision Region Quantification (DRQ) algorithm to improve the robustness of any differentiable pre-trained model against both real-world and worst-case distribution shifts in the data. DRQ analyzes the robustness of local decision regions in the vicinity of a given data point to make more reliable predictions. We theoretically motivate the DRQ algorithm by showing that it effectively smooths spurious local extrema in the decision surface. Furthermore, we propose an implementation using targeted and untargeted adversarial attacks. An extensive empirical evaluation shows that DRQ increases the robustness of adversarially and nonadversarially trained models against real-world and worst-case distribution shifts on several computer vision benchmark datasets.
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