SLACE: A Monotone and Balance-Sensitive Loss Function for Ordinal Regression

Ordinal regression classifies an object to a class out of a given set of possible classes, where labels possess a natural order. It is relevant to a wide array of domains including risk assessment, sentiment analysis, image ranking, and recommender systems. Like common classification, the primary goal of ordinal regression is accuracy. Yet, in this context, the severity of prediction errors varies, e.g., in risk assessment, Critical Risk is more urgent than High risk and significantly more urgent than No risk. This leads to a modified objective of ensuring that the model's output is as close as possible to the correct class, considering the order of labels. Therefore, ordinal regression models should use ordinality-aware loss for training. In this work, we focus on two properties of ordinality-aware losses, namely monotonicity and balance sensitivity. We show that existing ordinal loss functions lack these properties and introduce SLACE (Soft Labels Accumulating Cross Entropy), a novel loss function that provably satisfies said properties. We demonstrate empirically that SLACE outperforms the state-of-the-art ordinal loss functions on most tabular ordinal regression benchmarks.