Existing long-tailed recognition methods, aiming to train class-balanced models from long-tailed data, generally assume the models would be evaluated on the uniform test class distribution. However, practical test class distributions often violate this assumption (e.g., being either long-tailed or even inversely long-tailed), which may lead existing methods to fail in real applications. In this paper, we study a more practical yet challenging task, called test-agnostic long-tailed recognition, where the training class distribution is long-tailed while the test class distribution is agnostic and not necessarily uniform. In addition to the issue of class imbalance, this task poses another challenge: the class distribution shift between the training and test data is unknown. To tackle this task, we propose a novel approach, called Self-supervised Aggregation of Diverse Experts, which consists of two strategies: (i) a new skill-diverse expert learning strategy that trains multiple experts from a single and stationary long-tailed dataset to separately handle different class distributions; (ii) a novel test-time expert aggregation strategy that leverages self-supervision to aggregate the learned multiple experts for handling unknown test class distributions. We theoretically show that our self-supervised strategy has a provable ability to simulate test-agnostic class distributions. Promising empirical results demonstrate the effectiveness of our method on both vanilla and test-agnostic long-tailed recognition.

We organize the supplementary materials as follows: Appendix A: the proofs for Theorem 1. Appendix B: the pseudo-code of the proposed method. Appendix E: more ablation studies on expert learning and the proposed inverse softmax loss. We first recall several key notations and define some new notations. As shown in Eq. (4), the optimization objective of our test-time self-supervised aggregation method Meanwhile, the mutual information between predictions ˆ Y and labels Y can be represented by: I ( ˆ Y; Y) = H ( ˆ Y) H( ˆ Y |Y). In this appendix, we provide more details on experimental settings.

Tabular data serve as a fundamental and ubiquitous representation of structured information in numerous real-world applications, e.g., finance and urban planning. In the realm of tabular imbalanced applications, data imbalance has been investigated in classification tasks with insufficient instances in certain labels, causing the model's ineffective generalizability. However, the imbalance issue of tabular regression tasks is underexplored, and yet is critical due to unclear boundaries for continuous labels and simplifying assumptions in existing imbalance regression work, which often rely on known and balanced test distributions. Such assumptions may not hold in practice and can lead to performance degradation. To address these issues, we propose MATI: Mixture Experts with Test-Time Self-Supervised Aggregation for Tabular Imbalance Regression, featuring two key innovations: (i) the Region-Aware Mixture Expert, which adopts a Gaussian Mixture Model to capture the underlying related regions. The statistical information of each Gaussian component is then used to synthesize and train region-specific experts to capture the unique characteristics of their respective regions. (ii) Test-Time Self-Supervised Expert Aggregation, which dynamically adjusts region expert weights based on test data features to reinforce expert adaptation across varying test distributions. We evaluated MATI on four real-world tabular imbalance regression datasets, including house pricing, bike sharing, and age prediction. To reflect realistic deployment scenarios, we adopted three types of test distributions: a balanced distribution with uniform target frequencies, a normal distribution that follows the training data, and an inverse distribution that emphasizes rare target regions. On average across these three test distributions, MATI achieved a 7.1% improvement in MAE compared to existing methods.

Existing long-tailed recognition methods, aiming to train class-balanced models from long-tailed data, generally assume the models would be evaluated on the uniform test class distribution. However, practical test class distributions often violate this assumption (e.g., being either long-tailed or even inversely long-tailed), which may lead existing methods to fail in real applications. In this paper, we study a more practical yet challenging task, called test-agnostic long-tailed recognition, where the training class distribution is long-tailed while the test class distribution is agnostic and not necessarily uniform. In addition to the issue of class imbalance, this task poses another challenge: the class distribution shift between the training and test data is unknown. To tackle this task, we propose a novel approach, called Self-supervised Aggregation of Diverse Experts, which consists of two strategies: (i) a new skill-diverse expert learning strategy that trains multiple experts from a single and stationary long-tailed dataset to separately handle different class distributions; (ii) a novel test-time expert aggregation strategy that leverages self-supervision to aggregate the learned multiple experts for handling unknown test class distributions.