修复了Kumaraswamy分布的数值不稳定性，使其更适合大规模生成模型。
Stabilizing the Kumaraswamy Distribution
- 通过改进逆CDF和对数概率计算，解决原分布的数值问题。
- 在上下文多臂赌博机中提升探索与利用的平衡，在图神经网络中增强不确定性量化。
- 适合需要有界潜变量的可扩展变分模型研究者使用。
大规模潜在变量模型需要表达能力强且支持高效采样和低方差梯度的连续分布，可通过重参数化技巧实现。Kumaraswamy（KS）分布既具表达力，又可通过简单闭式逆CDF实现重参数化。然而其应用仍受限。本文识别并解决了逆CDF与对数概率中的数值不稳定性，揭示了PyTorch和TensorFlow等库中的问题。随后提出简单且可扩展的基于KS的潜在变量模型，在上下文多臂赌博机中改善探索-利用权衡，并提升图神经网络在链接预测中的不确定性量化能力。结果表明，经过稳定的KS分布可成为有界潜变量可扩展变分模型的核心组件。
原文摘要 · Abstract (English)
Large-scale latent variable models require expressive continuous distributions that support efficient sampling and low-variance differentiation, achievable through the reparameterization trick. The Kumaraswamy (KS) distribution is both expressive and supports the reparameterization trick with a simple closed-form inverse CDF. Yet, its adoption remains limited. We identify and resolve numerical instabilities in the inverse CDF and log-pdf, exposing issues in libraries like PyTorch and TensorFlow. We then introduce simple and scalable latent variable models based on the KS, improving exploration-exploitation trade-offs in contextual multi-armed bandits and enhancing uncertainty quantification for link prediction with graph neural networks. Our results support the stabilized KS distribution as a core component in scalable variational models for bounded latent variables.
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