A.1 Implementation of the GPs We use the GPyTorch4 package for the computations of GPs and their kernels. The NN linear kernel is implemented in all experiments as a 1-layer MLP with ReLU activations and hidden dimension 16. For the Spectral Mixture Kernel, we use 4 mixtures. A.2 Sines Dataset For the first experiments on sines functions, we use the dataset from [9]. For each task, the input points x are sampled from the range [ 5,5], and the target values y are obtained by applying y = Asin(x ')+, where the amplitude A and phase ' are drawn uniformly at random from ranges [0.1,5] and [0, ], respectively.

Improving the generalization of deep networks is an important open challenge, particularly in domains without plentiful data. The mixup algorithm improves generalization by linearly interpolating a pair of examples and their corresponding labels. These interpolated examples augment the original training set. Mixup has shown promising results in various classification tasks, but systematic analysis of mixup in regression remains underexplored. Using mixup directly on regression labels can result in arbitrarily incorrect labels.

State-of-the-art (SOTA) semi-supervised learning techniques, such as FixMatch and it's variants, have demonstrated impressive performance in classification tasks. However, these methods are not directly applicable to regression tasks. In this paper, we present RankUp, a simple yet effective approach that adapts existing semi-supervised classification techniques to enhance the performance of regression tasks. RankUp achieves this by converting the original regression task into a ranking problem and training it concurrently with the original regression objective.

Graph regression is a fundamental task that has gained significant attention invarious graph learning tasks. However, the inference process is often not easilyinterpretable. Current explanation techniques are limited to understanding GraphNeural Network (GNN) behaviors in classification tasks, leaving an explanation gapfor graph regression models. In this work, we propose a novel explanation methodto interpret the graph regression models (XAIG-R). Our method addresses thedistribution shifting problem and continuously ordered decision boundary issuesthat hinder existing methods away from being applied in regression tasks. Weintroduce a novel objective based on the graph information bottleneck theory (GIB)and a new mix-up framework, which can support various GNNs and explainersin a model-agnostic manner. Additionally, we present a self-supervised learningstrategy to tackle the continuously ordered labels in regression tasks. We evaluateour proposed method on three benchmark datasets and a real-life dataset introducedby us, and extensive experiments demonstrate its effectiveness in interpreting GNNmodels in regression tasks.

Conformal Prediction (CP) is a popular uncertainty quantification method that provides distribution-free, statistically valid prediction sets, assuming that training and test data are exchangeable. In such a case, CP's prediction sets are guaranteed to cover the (unknown) true test output with a user-specified probability. Nevertheless, this guarantee is violated when the data is subjected to adversarial attacks, which often result in a significant loss of coverage. Recently, several approaches have been put forward to recover CP guarantees in this setting. These approaches leverage variations of randomised smoothing to produce conservative sets which account for the effect of the adversarial perturbations.

The proposed layers lead toamore data efficient representation and areduction in computation by exploiting symmetry. We evaluate chirality nets on the task ofhuman poseregression, which naturally exploits theleft/right mirroring ofthe human body.