标题： 贝叶斯双降度 显示英文标题

标题： Bayesian Double Descent

摘要： 双下降是过参数化统计模型的一种现象。 我们的目标是从贝叶斯的角度来看待双下降。 过参数化模型，如深度神经网络，在其风险特征中具有有趣的再下降特性。 这是机器学习中的一个近期现象，并已成为许多研究的主题。 随着模型复杂性的增加，存在一个对应于传统偏差-方差权衡的U形区域，但随后当参数数量等于观测数量且模型变为插值模型时，风险可能变为无限大，然后在过参数化区域中再次下降——这就是双下降效应。 我们表明，这有一个自然的贝叶斯解释。 此外，我们表明它并不与贝叶斯模型所具有的传统奥卡姆剃刀原理相冲突，因为在可能的情况下，贝叶斯模型倾向于选择更简单的模型。 我们通过神经网络中的贝叶斯模型选择示例来说明该方法。 最后，我们对未来的研究方向进行总结。 显示英文摘要

摘要： Double descent is a phenomenon of over-parameterized statistical models. Our goal is to view double descent from a Bayesian perspective. Over-parameterized models such as deep neural networks have an interesting re-descending property in their risk characteristics. This is a recent phenomenon in machine learning and has been the subject of many studies. As the complexity of the model increases, there is a U-shaped region corresponding to the traditional bias-variance trade-off, but then as the number of parameters equals the number of observations and the model becomes one of interpolation, the risk can become infinite and then, in the over-parameterized region, it re-descends -- the double descent effect. We show that this has a natural Bayesian interpretation. Moreover, we show that it is not in conflict with the traditional Occam's razor that Bayesian models possess, in that they tend to prefer simpler models when possible. We illustrate the approach with an example of Bayesian model selection in neural networks. Finally, we conclude with directions for future research.