论文标题
整体概率指标pac-bayes边界
Integral Probability Metrics PAC-Bayes Bounds
论文作者
论文摘要
我们提出了Pac-Bayes风格的概括结合，该结合可以用各种积分概率指标（IPM）替换KL-Divergence。我们提供了这种结合的实例，IPM是总变异度量和Wasserstein距离。所获得边界的一个显着特征是，它们在最坏的情况下（当前和后距离彼此远距离时）在经典均匀收敛边界之间自然插值，并且在有利的情况下（后验和先验都接近），它的边界得到了改善。这说明了使用算法和数据依赖性组件加强经典概括界限的可能性，从而使它们更适合分析使用大型假设空间的算法。
We present a PAC-Bayes-style generalization bound which enables the replacement of the KL-divergence with a variety of Integral Probability Metrics (IPM). We provide instances of this bound with the IPM being the total variation metric and the Wasserstein distance. A notable feature of the obtained bounds is that they naturally interpolate between classical uniform convergence bounds in the worst case (when the prior and posterior are far away from each other), and improved bounds in favorable cases (when the posterior and prior are close). This illustrates the possibility of reinforcing classical generalization bounds with algorithm- and data-dependent components, thus making them more suitable to analyze algorithms that use a large hypothesis space.
