论文标题
加权M估计的生成多功能采样器
Generative Multiple-purpose Sampler for Weighted M-estimation
论文作者
论文摘要
为了克服各种数据扰动过程（例如自举和交叉验证）的计算瓶颈，我们提出了生成的多用途采样器（GMS），该采样器（GMS）构建了一个生成器功能，以产生一组给定权重和调音参数的加权M测验器的解决方案。 GMS通过单个优化实现，而无需重复评估加权损失的最小化，因此能够显着减少计算时间。我们证明，GMS框架可以实施各种统计程序，这些程序在常规框架中将是不可行的，例如迭代的引导，自动启动的跨验验，以进行惩罚，以无效的经验贝叶斯，具有非参数的最大可能性等，以构建一个计算能力的生成器，我们还构建了一个新的形式，我们还可以构建一个新的形式，我们还构建了一个新的形式。乘法多层感知}以实现快速收敛。我们的数值结果表明，与常规速度相比，新的神经网络结构具有几个幅度速度优势。提供了称为GMS的R软件包，该软件包在Pytorch下运行以实现所提出的方法，并允许用户提供自定义的损失功能以量身定制其自己感兴趣的模型。
To overcome the computational bottleneck of various data perturbation procedures such as the bootstrap and cross validations, we propose the Generative Multiple-purpose Sampler (GMS), which constructs a generator function to produce solutions of weighted M-estimators from a set of given weights and tuning parameters. The GMS is implemented by a single optimization without having to repeatedly evaluate the minimizers of weighted losses, and is thus capable of significantly reducing the computational time. We demonstrate that the GMS framework enables the implementation of various statistical procedures that would be unfeasible in a conventional framework, such as the iterated bootstrap, bootstrapped cross-validation for penalized likelihood, bootstrapped empirical Bayes with nonparametric maximum likelihood, etc. To construct a computationally efficient generator function, we also propose a novel form of neural network called the \emph{weight multiplicative multilayer perceptron} to achieve fast convergence. Our numerical results demonstrate that the new neural network structure enjoys a few orders of magnitude speed advantage in comparison to the conventional one. An R package called GMS is provided, which runs under Pytorch to implement the proposed methods and allows the user to provide a customized loss function to tailor to their own models of interest.
