Sensitivity estimation of conditional value at risk using randomized quasi-Monte Carlo

随机模型的基于方差的敏感性分析和正交逼近

Variance-based sensitivity analysis and orthogonal approximations for stochastic models

我们开发了新的无偏估计量的数量定义的功能的条件矩，如条件期望和方差，两个独立的随机变量的函数的第一个变量，包括某些输出的随机模型的模型参数。这些量包括基于方差的灵敏度指数、第一变量的函数的近似的均方误差、正交投影系数和新定义的非线性系数。我们定义了上述估计，并分析了它们的性能在蒙特卡罗程序使用广义概念的估计方案和它的无效常数。在化学反应网络的数值模拟中，使用Gillespie直接和随机时变方法，条件期望灵敏度指标的新方案在某些情况下优于以前提出的方案，并且某些估计量的方差显著依赖于所应用的模拟方法。

基于随机决策规则的生成对抗网络新范式

A New Paradigm for Generative Adversarial Networks based on Randomized Decision Rules

本文针对GAN的模式崩溃问题，提出基于随机决策规则的新公式，通过类似经验贝叶斯的方法和随机梯度MCMC算法训练，使生成器在纳什均衡处收敛到分布，并应用于图像生成、非参数聚类和条件独立性检验。

Ordering-Free Inference from Locally Dependent Data

This paper focuses on a data-rich environment where the data set has a very large cross-sectional dimension, is likely to exhibit local dependence, and yet is hard to determine the dependence ordering. Such a situation arises, for example, when the data set is collected from the Internet, through a method of web crawling. This paper proposes an approach of randomized subsampling inference, where one constructs a test statistic by aggregating many randomized test statistics using random draws of subsamples, and uses for inference the conditional distribution of the test statistic given data. Th…

Randomized Algorithms for Generalized Singular Value Decomposition with Application to Sensitivity Analysis

The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential sensitivity analysis (HDSA), we propose new randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization. Detailed error analysis is given which provides insight into the accuracy of the algorithms and the choice of the algorithmic parameters. We demonstrate the performance of our algorithms on test matr…

二元结果的CART选择性推断

Selective Inference for CART with Binary Outcomes

针对二元分类树的选择性推断问题，提出基于Gini CART的有限样本条件检验，通过均匀标签纤维和并行蒙特卡洛构造p值，在模拟中验证了其保守性和对较大风险差异的检测功效。

关于条件拟蒙特卡洛方法在不连续函数中的误差率

On the error rate of conditional quasi-Monte Carlo for discontinuous functions

本文研究了条件拟蒙特卡洛方法的收敛速率，针对定义在整个R^d空间上的不连续积分函数，证明其具有平滑效应并能显著降低积分误差，尤其在期权定价和希腊值估计中表现出O(n^{-1+ε})的误差率。