Deep neural networks are used for a wide range of regression problems. However, there exists a significant gap in accuracy between specialized approaches and generic direct regression in which a network is trained by minimizing the squared or absolute error of output labels. Prior work has shown that solving a regression problem with a set of binary classifiers can improve accuracy by utilizing well-studied binary classification algorithms. We introduce binary-encoded labels (BEL), which generalizes the application of binary classification to regression by providing a framework for considering arbitrary multi-bit values when encoding target values. We identify desirable properties of suitable encoding and decoding functions used for the conversion between real-valued and binary-encoded labels based on theoretical and empirical study. These properties highlight a tradeoff between classification error probability and error-correction capabilities of label encodings. BEL can be combined with off-the-shelf task-specific feature extractors and trained end-to-end. We propose a series of sample encoding, decoding, and training loss functions for BEL and demonstrate they result in lower error than direct regression and specialized approaches while being suitable for a diverse set of regression problems, network architectures, and evaluation metrics. BEL achieves state-of-the-art accuracies for several regression benchmarks. Code is available at https://github.com/ubc-aamodt-group/BEL_regression.

Massive deployment of Graph Neural Networks (GNNs) in high-stake applications generates a strong demand for explanations that are robust to noise and align well with human intuition. Most existing methods generate explanations by identifying a subgraph of an input graph that has a strong correlation with the prediction. These explanations are not robust to noise because independently optimizing the correlation for a single input can easily overfit noise. Moreover, they do not align well with human intuition because removing an identified subgraph from an input graph does not necessarily change the prediction result. In this paper, we propose a novel method to generate robust counterfactual explanations on GNNs by explicitly modelling the common decision logic of GNNs on similar input graphs. Our explanations are naturally robust to noise because they are produced from the common decision boundaries of a GNN that govern the predictions of many similar input graphs. The explanations also align well with human intuition because removing the set of edges identified by an explanation from the input graph changes the prediction significantly. Exhaustive experiments on many public datasets demonstrate the superior performance of our method.