L. P. Semenov, V. A. Kalyagin, P. A. Koldanov, M. V. Batsyn, S. V. Golovanova, M. A. Voronina
Different network structures are compiared with respect to degree of robustnes of identification statistical procedures. It is shown that threshold (market) graph, cliques and independent sets in the threshold (market) graphs are preferable network structure from this point of view.
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Optimal Robustness Results for Some Bayesian Procedures and the Relationship to Prior-Data Conflict
基于统计证据的措施的贝叶斯推理程序的先验的鲁棒性被认为是。这些推论被证明具有最佳性能的鲁棒性。此外，鲁棒性和先验数据冲突之间的联系建立。特别是，推理被证明是有效的鲁棒性时，先验的选择不会导致先验数据冲突。然而，当存在先验数据冲突时，鲁棒性可能无法保持。
A statistical structure $(g, T)$ on a smooth manifold $M$ induced by $(\tilde M, \tilde g, \tilde T)$ is said to be {\em robust} if there exists an open neighborhood of $(g,T)$ in the fine $C^{\infty}$-topology consisting of statistical structures induced by $(\tilde M, \tilde g, \tilde T)$. Using Nash--Gromov implicit function theorem, we show robustness of the generic statistical structure induced on $M$ by the standard linear statistical structure on ${\R}^N$, for $N$ sufficiently large.
A statistical analysis of a deformation model with Wasserstein barycenters : estimation procedure and goodness of fit test
我们提出了一个一般变形函数的分布配准模型的研究。在这个框架中，我们提供了变形的估计以及模型的拟合优度检验。为此，我们考虑一个标准，研究的Fr{é}chet平均值（或重心）的翘曲分布的研究，使模型上的推断。特别是，我们得到的渐近分布和自举程序的Wasserstein变化。
Information Theory of Penalized Likelihoods and its Statistical Implications
我们扩展了数据压缩中的两阶段编码程序和统计估计中的惩罚似然程序之间的对应关系。传统上，这需要限制到可数参数空间。我们展示了如何扩展这种对应的不可数参数的情况下。利用惩罚似然程序的描述长度的解释，我们设计了新的技术，以获得自适应的风险界限，这样的程序。我们证明了参数空间的某些可数覆盖的存在性意味着自适应风险界，因此我们的理论是相当一般的。我们应用我们的技术来说明风险界$\ell_1$型惩罚程序在典型的高维统计问题，如线性回归和高斯图形模型。在线性回归问题中，我们还演示了如何传统的$l_0$惩罚时间$\frac{\log(n)}{2}$加上低阶项有两个阶段的描述长度的解释和目前的风险界限，这个惩罚似然程序。
Statistical distances, divergences, and similar quantities have a large history and play a fundamental role in statistics, machine learning and associated scientific disciplines. However, within the statistical literature, this extensive role has too often been played out behind the scenes, with other aspects of the statistical problems being viewed as more central, more interesting, or more important. The behind the scenes role of statistical distances shows up in estimation, where we often use estimators based on minimizing a distance, explicitly or implicitly, but rarely studying how the pr…
Hyperparameters tuning and model selection are important steps in machine learning. Unfortunately, classical hyperparameter calibration and model selection procedures are sensitive to outliers and heavy-tailed data. In this work, we construct a selection procedure which can be seen as a robust alternative to cross-validation and is based on a median-of-means principle. Using this procedure, we also build an ensemble method which, trained with algorithms and corrupted heavy-tailed data, selects an algorithm, trains it with a large uncorrupted subsample and automatically tune its hyperparameters…
Covariate-adaptive randomization (CAR) procedures are frequently used in comparative studies to increase the covariate balance across treatment groups. However, because randomization inevitably uses the covariate information when forming balanced treatment groups, the validity of classical statistical methods after such randomization is often unclear. In this article, we derive the theoretical properties of statistical methods based on general CAR under the linear model framework. More importantly, we explicitly unveil the relationship between covariate-adaptive and inference properties by der…
Recently a new algorithm for sampling posteriors of unnormalised probability densities, called ABC Shadow, was proposed in [8]. This talk introduces a global optimisation procedure based on the ABC Shadow simulation dynamics. First the general method is explained, and then results on simulated and real data are presented. The method is rather general, in the sense that it applies for probability densities that are continuously differentiable with respect to their parameters
rSRD: An R package for the Sum of Ranking Differences statistical procedure
rSRD包将排名差异和（SRD）统计程序的两个验证步骤简化为单次函数调用，并提供数据预处理与绘图工具，使该非参数方法更易被广泛用户使用。
On the Robustness of a Divergence based Test of Simple Statistical Hypotheses
最流行的假设检验程序，似然比检验，是众所周知的，在许多实际情况下是高度非鲁棒的。Basu等人（2013 a）提供了一种基于密度功率发散的假设检验的替代稳健程序;然而，尽管作者直观地论证了后一种检验的稳健性，并对其进行了广泛的经验证实，但在这项工作中没有提出理论稳健性。在本文中，我们将考虑一类更一般的检验，它们形成了Basu等人（2013 a）描述的程序的超族。该超家族来源于Basu等人最近提出的$S$ -分歧类（2013 a）。在这方面，我们从理论上证明了新的一类测试的鲁棒性结果，并说明他们在正常的模型。Basu等人（2013 a）提议的所有理论鲁棒性都是我们结果的特例。
An important property of statistical estimators is qualitative robustness, that is small changes in the distribution of the data only result in small chances of the distribution of the estimator. Moreover, in practice, the distribution of the data is commonly unknown, therefore bootstrap approximations can be used to approximate the distribution of the estimator. Hence qualitative robustness of the statistical estimator under the bootstrap approximation is a desirable property. Currently most theoretical investigations on qualitative robustness assume independent and identically distributed pa…
Sequential change-point detection: Computation versus statistical performance
本文从计算与统计能力权衡的新视角，综述经典及近期考虑内存效率与鲁棒性的非参数序贯变点检测方法，并总结可用于新程序分析的经典性能分析技术。
A statistical test can be seen as a procedure to produce a decision based on observed data, where some decisions consist of rejecting a hypothesis (yielding a significant result) and some do not, and where one controls the probability to make a wrong rejection at some pre-specified significance level. Whereas traditional hypothesis testing involves only two possible decisions (to reject or not a null hypothesis), Kaiser's directional two-sided test as well as the more recently introduced Jones and Tukey's testing procedure involve three possible decisions to infer on unidimensional parameter. …
Qualitative robustness of statistical functionals under strong mixing
引入了基于同分布可能相依观测值的插入式估计量的（渐近）定性稳健性的新概念，证明了一般度量$d$的Hampel定理仍然成立.由于Hampel定理假设UGC性质w.r.t. $d$，即经验概率测度的概率依概率收敛到真实边缘分布w.r. t。$d$在样本路径空间上的所有可容许律类中是一致的，对于一大类强混合律，对于三个不同的度量$d$，证明了这一性质.对于实值观测，建立了Kolomogorov $ϕ$ -度量和Lévy $ψ$ -度量的UGC性质;对于一般局部紧第二可数T2空间中的观测，建立了生成$ψ$ -弱拓扑的度量的UGC性质.关键是强混合随机变量的一个新的一致弱LLN。后者是独立的利益，并依赖于里约的极大不等式。
A definition of qualitative robustness for general point estimators, and examples
给出了一般统计模型中点估计量的定性稳健性定义。建立了稳健性的一些准则，并应用于参数、半参数和非参数模型的估计量。在特定的非参数模型中，所提出的定义归结为Hampel鲁棒性。它还解释了如何插件估计在某些非参数模型可以合理地分类w.r.t.他们的稳健程度。
Many standard estimators such as several maximum likelihood estimators or the empirical estimator for any law-invariant convex risk measure are not (qualitatively) robust in the classical sense. However, these estimators may nevertheless satisfy a weak (Krätschmer/Schied/Zähle 2012, 2014) or a local (Zähle 2016) robustness property on relevant sets of distributions. One aim of our paper is to identify sets of local robustness, and to explain the benefit of the knowledge of such sets. For instance, we will be able to demonstrate that many maximum likelihood estimators are robust on their natura…
Robustness of multiple testing procedures against dependence
多重假设检验的一个重要方面是控制显着性水平或I型错误的水平。当检验统计量不独立时，在不采取非常保守的程序的情况下处理这个问题可能特别具有挑战性。在本文中，我们表明，在当代的多重测试问题的背景下，测试的数量往往是非常大的，所造成的困难的依赖是不那么严重，比在经典的情况下。当检验统计量的零分布是相对轻尾的时，例如，当它们可以基于正态或学生$t$近似时，尤其如此。在那里，如果检验统计量可以被公平地看作是由线性过程产生的，那么当假设的数量发散时，基于不正确的独立性假设的分析是渐近正确的。特别地，表示统计上显著的检验结果出现的指数的零分布的点过程近似为泊松，就像独立的情况一样。泊松过程也具有与独立情况相同的均值，当然也没有出现错误发现的聚集。然而，如果零分布是特别重尾的，则该结果可能失败。即使原假设是正确的，也可能出现统计学显著性结果的集群。我们给出了一个直观的解释，这些不同的性质在轻尾和重尾的情况下，并提供了严格的理论支撑的直觉。
Continuity of the Solution of a Non-Parametric Bayesian Statistical Calibration Procedure
研究非参数贝叶斯校准方法中解算子对输入参数分布的连续性，证明其在总变差度量下一致连续且在广泛分布类中弱连续。
Asymptotic results and statistical procedures for time-changed Lévy processes sampled at hitting times
我们提供了渐近结果，并制定了高频统计程序的时变Lévy过程在随机时刻采样。采样时间由对称障碍物的首中时给出，对称障碍物相对于起始点的距离等于$\varepsilon$。这一设置可以被看作是建立一个允许大幅跳跃的逐时金融数据模型的第一步。对于一类Lévy过程，我们引入了一个依赖于$\varepsilon$的重整化，在此重整化下，当$\varepsilon$变为$0$时，Lévy过程依律收敛于$α$ -稳定过程.将收敛性推广到首中时和过冲时刻。特别是，这些结果使我们能够构建一致的估计的时变和Blumenthal-Getoor指数的基础Lévy过程。在附加的假设条件下，建立了收敛速度和中心极限定理.
High-dimensional datasets are well-approximated by low-dimensional structures. Over the past decade, this empirical observation motivated the investigation of detection, measurement, and modeling techniques to exploit these low-dimensional intrinsic structures, yielding numerous implications for high-dimensional statistics, machine learning, and signal processing. Manifold learning (where the low-dimensional structure is a manifold) and dictionary learning (where the low-dimensional structure is the set of sparse linear combinations of vectors from a finite dictionary) are two prominent theore…
On robustness of Spectral Rényi divergence
本文研究了时间序列谱密度的特定统计散度类——谱α-Rényi散度，揭示其与稳健统计中的γ-散度联系，并提出变分表示，证明其在频域中对异常值具有鲁棒性，提升了估计稳定性。
Spatial-temporal data mining procedure: LASR
本文关注的是我们的时空数据挖掘程序，LASR（发音为“激光”）的统计发展。LASR是大- $p$ -小- $n$数据自我配准纵向分析的缩写。它的动机是一项“神经肌肉电刺激”实验的研究，其中数据是嘈杂和异质的，可能不会从一个会话到另一个会话对齐，并且涉及大量的多重比较。LASR的三个主要组成部分是：（1）用于分离异质数据和区分异常值的数据分割，（2）用于空间和时间数据配准的自动方法，以及（3）用于基于错误发现率控制的$p$地图和电影识别"激活“区域的统计平滑映射。每一个组成部分本身都是令人感兴趣的。作为一种统计集合，LASR的思想适用于NMES实验之外的其他类型的时空数据集。
Bias robustness of depth estimators in multivariate settings
本文研究了多变量环境下深度估计器的偏置鲁棒性，分析了Tukey中位数、基于深度的散射矩阵和多元回归估计器的统计收敛性和鲁棒性。
Segmentation of the mean of heteroscedastic data via cross-validation
本文研究了在不知道噪声变化的情况下，通过模型选择检测异方差信号均值突变的问题。提出了一个新的家庭的变点检测程序，交叉验证方法可以成功的异方差框架，而大多数现有的程序是不稳健的异方差。一个广泛的模拟研究，以及最近的理论结果支持所提出的程序的异方差的鲁棒性。比较基因组杂交（CGH）数据的应用程序提供，表明异方差的鲁棒性确实可以要求他们的分析。
Some Robustness Properties of Label Cleaning
本文证明，依赖聚合标签（例如从噪声响应中提炼的标签信息）的学习过程具有数据清理无法实现的鲁棒性，体现在风险一致性、模型误设下的收敛性等方面。
Debiased Nonparametric Regression for Statistical Inference and Distributionally Robustness
本文提出一种无模型的非参数回归去偏方法，通过加入估计条件期望残差的校正项，使估计量在温和条件下具备风险收敛与渐近正态性，从而支持统计推断并提升协变量偏移下的鲁棒性。
Preserving the robustness of the procedure has, at the present time, become almost a default requirement for statistical data analysis. Since efficiency at the model and robustness under misspecification of the model are often in conflict, it is important to choose such inference procedures which provide the best compromise between these two concepts. Some minimum Bregman divergence estimators and related tests of hypothesis seem to be able to do well in this respect, with the procedures based on the density power divergence providing the existing standard. In this paper we propose a new famil…
This article describes the inferential procedures and Bayesian optimal life-testing issues under Type-II unified hybrid censoring scheme. First, the explicit expressions of expected number of failures, expected duration of testing and Fisher information matrix for the unknown parameters of the underlying lifetime model are derived. Then, using these quantities, the Bayesian optimal life-testing plans are computed in subsequent section. A cost constraint D-optimal optimization problem has been formulated and the corresponding solution algorithm is provided to obtain optimal plans. Computational…
Separating Statistical Inference from Experimental Runtime: An Architecture for Sequential Scientific Analysis
该研究提出一种将统计推断与数据处理、运行时等分离的序贯科学分析架构，定义了序贯程序抽象，推导7个一致性不变量并实现参考实现，适配多种序贯统计方法。
Statistical analysis of multimodal imaging data is a challenging task, since the data involves high-dimensionality, strong spatial correlations and complex data structures. In this paper, we propose rigorous statistical testing procedures for making inferences on the complex dependence of multimodal imaging data. Motivated by the analysis of multi-task fMRI data in the Human Connectome Project (HCP) study, we particularly address three hypothesis testing problems: (a) testing independence among imaging modalities over brain regions, (b) testing independence between brain regions within imaging…
On the Adversarial Robustness of Benjamini Hochberg
本文研究 BH 多重检验过程的对抗鲁棒性，提出简单的检验分数扰动算法，并通过组合重述与信息论分析给出 FDR 被破坏的非渐近保证。
A Progressive Statistical Method for Preconditioning Matrix-Free Solution of High-Order Discretization of Linear Time-Dependent Problems
由不定常偏微分方程的谱离散化得到的线性系的预处理往往会得到一个满矩阵，这是昂贵的计算和存储，特别是当问题规模增加时。无矩阵实现通常用于解决此问题。在这个框架中，预处理通常是具有挑战性的，因为矩阵的条目不是明确可用的。在这个简短的说明中，我们提出了一个统计方法，逐步创建一个预处理矩阵，通过收集信息，从矩阵向量积的Arnoldi循环的非预处理Krylov子空间算法。然后使用多个回归估计将收集的信息进行相关，其中假设误差呈正态分布。该过程产生带状对角矩阵，然后将其用作下一次迭代求解中的预条件子。这在迭代求解之间重复，直到在飞行中构造好的预处理器。这种统计迭代过程是渐进的，因为预处理矩阵的保真度通过在整个求解过程中添加从矩阵向量乘积获得的更多数据来提高。所提出的算法进行了验证的一个示例实现。
Achieving Optimal Misclassification Proportion in Stochastic Block Model
社区发现是网络数据分析中的一个基本统计问题。已经提出了许多算法来解决这个问题。这些算法中的大多数不能保证实现问题的统计最优性，而实现一般参数空间的信息理论极限的程序在计算上是不可处理的。本文针对弱正则条件下的随机块模型，提出了一种计算上可行的两阶段方法，该方法在误分类率方面具有最优的统计性能.我们的两个阶段的过程包括一个通用的细化步骤，可以采取广泛的弱一致的社区检测程序作为初始化，细化阶段适用于并输出一个社区分配实现最佳的误分类比例与高概率。数值结果表明了新算法的有效性。
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