利用先验知识的Gamma-Minimax估计器的对抗元学习
Adversarial Meta-Learning of Gamma-Minimax Estimators That Leverage Prior Knowledge
AI总结：
本文针对先验知识模糊时无法用单一先验表达的问题，提出为一般模型定义Gamma-minimax估计器，并设计对抗元学习算法在广义矩约束下计算，附收敛性保证，在熵估计和生物多样性预测中验证。
摘要：
众所周知，贝叶斯估计器提供了一种整合先验知识的手段，这些知识可以用单一先验分布来表达。然而，当这些知识过于模糊而无法用单一先验表达时，就需要一种替代方法。Gamma-minimax估计器提供了这样一种方法。这些估计器在由与可用知识兼容的先验分布集合 $\Gamma$ 上最小化最坏情况下的贝叶斯风险。传统上，Gamma-minimax性是为参数模型定义的。在这项工作中，我们为一般模型定义了Gamma-minimax估计器，并提出了对抗元学习算法来计算它们，当先验分布集合受广义矩约束时。同时提供了相应的收敛性保证。我们还引入了一个神经网络类，它提供了一个丰富但有限维的估计器类，从中可以选择Gamma-minimax估计器。我们在两种设置中说明了我们的方法，即熵估计和生物多样性研究中出现的预测问题。
英文摘要：
Bayes estimators are well known to provide a means to incorporate prior knowledge that can be expressed in terms of a single prior distribution. However, when this knowledge is too vague to express with a single prior, an alternative approach is needed. Gamma-minimax estimators provide such an approach. These estimators minimize the worst-case Bayes risk over a set $Γ$ of prior distributions that are compatible with the available knowledge. Traditionally, Gamma-minimaxity is defined for parametric models. In this work, we define Gamma-minimax estimators for general models and propose adversarial meta-learning algorithms to compute them when the set of prior distributions is constrained by generalized moments. Accompanying convergence guarantees are also provided. We also introduce a neural network class that provides a rich, but finite-dimensional, class of estimators from which a Gamma-minimax estimator can be selected. We illustrate our method in two settings, namely entropy estimation and a prediction problem that arises in biodiversity studies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
