通过广义拉普拉斯近似解决贝叶斯深度学习中的不一致性问题
Addressing the Inconsistency in Bayesian Deep Learning via Generalized Laplace Approximation
AI总结：
本文提出广义拉普拉斯近似方法，通过简单修改海森矩阵计算实现可扩展的高质量后验推断，并将后验温度调节解释为对模型误设和先验不确定性的修正，在真实数据上验证了其提升预测性能的效果。
摘要：
近年来，贝叶斯深度学习中的不一致性问题引起了广泛关注。温度调节或广义后验分布常被用作直接而有效的解决方案。然而，广义后验的底层机制和有效性仍是活跃的研究课题。在本工作中，我们将后验温度调节解释为通过调整联合概率对模型误设进行修正，并通过降低任意不确定性（aleatoric uncertainty）对先验进行重新校准。我们还引入了广义拉普拉斯近似（generalized Laplace approximation），该方法只需对正则化损失的海森矩阵（Hessian）计算进行简单修改，即可为高质量后验推断提供灵活且可扩展的框架。我们在最先进的神经网络和真实世界数据集上评估了所提出的方法，结果表明广义拉普拉斯近似能够提升预测性能。
英文摘要：
In recent years, inconsistency in Bayesian deep learning has attracted significant attention. Tempered or generalized posterior distributions are frequently employed as direct and effective solutions. Nonetheless, the underlying mechanisms and the effectiveness of generalized posteriors remain active research topics. In this work, we interpret posterior tempering as a correction for model misspecification via adjustments to the joint probability, and as a recalibration of priors by reducing aleatoric uncertainty. We also introduce the generalized Laplace approximation, which requires only a simple modification to the Hessian calculation of the regularized loss and provides a flexible and scalable framework for high-quality posterior inference. We evaluate the proposed method on state-of-the-art neural networks and real-world datasets, demonstrating that the generalized Laplace approximation enhances predictive performance.
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