Conditional-$t^3$VAE: Equitable Latent Space Allocation for Fair Generation

2025-09-02

AI Summary

To address unfair latent space allocation and poor generation quality for tail classes in class-imbalanced data, this paper proposes Conditional-t³VAE. First, it introduces a class-conditional Student’s t joint prior—marking the first such use in VAEs—to explicitly model heavy-tailed structure and balance class-wise latent distributions. Second, it derives a closed-form, differentiable objective based on γ-divergence, jointly optimizing for generation fairness and robustness against outliers. Third, it employs an equal-weight latent variable mixing strategy to ensure balanced sampling across classes. Evaluated on long-tailed benchmarks—including SVHN-LT, CIFAR-100-LT, and CelebA—Conditional-t³VAE achieves significantly lower FID scores and higher F1 scores compared to both t³VAE and Gaussian VAE baselines. Notably, it delivers substantial gains in generation fairness under severe class imbalance, demonstrating superior calibration of tail-class representation and synthesis.

Technology Category

• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Machine Learning: Calibration & Uncertainty Quantification
• Natural Language Processing: Generation

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Variational Autoencoders (VAEs) with global priors mirror the training set's class frequency in latent space, underrepresenting tail classes and reducing generative fairness on imbalanced datasets. While $t^3$VAE improves robustness via heavy-tailed Student's t-distribution priors, it still allocates latent volume proportionally to the class frequency.In this work, we address this issue by explicitly enforcing equitable latent space allocation across classes. To this end, we propose Conditional-$t^3$VAE, which defines a per-class mbox{Student's t} joint prior over latent and output variables, preventing dominance by majority classes. Our model is optimized using a closed-form objective derived from the $γ$-power divergence. Moreover, for class-balanced generation, we derive an equal-weight latent mixture of Student's t-distributions. On SVHN-LT, CIFAR100-LT, and CelebA, Conditional-$t^3$VAE consistently achieves lower FID scores than both $t^3$VAE and Gaussian-based VAE baselines, particularly under severe class imbalance. In per-class F1 evaluations, Conditional-$t^3$VAE also outperforms the conditional Gaussian VAE across all highly imbalanced settings. While Gaussian-based models remain competitive under mild imbalance ratio ($ρlesssim 3$), our approach substantially improves generative fairness and diversity in more extreme regimes.

Problem

• Addresses inequitable latent space allocation in VAEs
• Improves generative fairness for minority classes
• Enhances diversity under severe class imbalance

Innovation

• Per-class Student's t joint prior allocation
• Closed-form optimization using γ-power divergence
• Equal-weight latent mixture for balanced generation