The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem. Network-based tests have the computational advantage that the algorithm scales to large samples. This paper proposes a two-sample statistic which is the difference of the logit function, provided by a trained classification neural network, evaluated on the testing set split of the two datasets. Theoretically, we prove the testing power to differentiate two sub-exponential densities given that the network is sufficiently parametrized. When the two densities lie on or near to low-dimensional manifolds embedded in possibly high-dimensional space, the needed network complexity is reduced to only scale with the intrinsic dimensionality. Both the approximation and estimation error analysis are based on a new result of near-manifold integral approximation. In experiments, the proposed method demonstrates better performance than previous network-based tests using classification accuracy as the two-sample statistic, and compares favorably to certain kernel maximum mean discrepancy tests on synthetic datasets and hand-written digit datasets.
Combinatorial Inference on the Optimal Assortment in Multinomial Logit Models
Harvard T.H. Chan School of Public Health（哈佛陈曾熙公共卫生学院）；Leonard N. Stern School of Business, New York University（纽约大学伦纳德·N·斯特恩商学院）；Duke University（杜克大学）
Reject Illegal Inputs with Generative Classifier Derived from Any Discriminative Classifier
The University of Hong Kong（香港大学）
生成式分类器已被证明有希望检测非法输入，包括对抗性样本和分布外样本。Supervised Deep Infomax~（SDIM）是一个可扩展的端到端框架，用于学习生成分类器。在本文中，我们提出了一个修改的SDIM称为SDIM- \emph{logit}。SDIM- \emph{logit}不是从头开始训练生成分类器，而是首先将任何给定的判别分类器产生的logit作为输入，并生成logit表示;然后通过对logit表示施加统计约束来导出生成分类器。SDIM- \emph{logit}能够继承判别分类器的性能而不损失。SDIM- \emph{logit}引起的额外参数的数量可以忽略不计，并且可以有效地训练与基本分类器固定。我们执行\emph{classification with rejection}，其中类条件小于预先选择的阈值的测试样本将被拒绝而不进行预测。在非法输入（包括对抗样本、常见错误样本和分布外样本）上的实验表明，SDIM- \emph{logit}允许拒绝一部分测试样本，显著提高了在左测试集上的性能.
Exponential convergence of testing error for stochastic gradient methods
INRIA（法国国家信息与自动化研究所）；Département d’Informatique de l’ENS（巴黎高等师范学院计算机系）；Ecole Normale Supérieure（巴黎高等师范学院）；CNRS（法国国家科学研究中心）；PSL Research University（巴黎文理研究大学）
Optimal Provable Robustness of Quantum Classification via Quantum Hypothesis Testing
ETH Zürich（苏黎世联邦理工学院）；Shanghai Jiao Tong University（上海交通大学）；University of Michigan-Shanghai Jiao Tong University Joint Institute（上海交通大学密歇根学院）；University of Illinois（伊利诺伊大学）
