统计学学术速递[6.23]

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stat统计学，共计48篇

【1】 Rank-one matrix estimation with groupwise heteroskedasticity 标题：具有GroupWise异方差的秩一矩阵估计

作者：Joshua K. Behne,Galen Reeves 备注：22 pages, 3 figures 链接：https://arxiv.org/abs/2106.11950 摘要：研究了在不同噪声水平下，由高斯观测值估计秩一矩阵的问题。这个问题是由聚类和社区检测中的应用程序引起的，其中潜在变量可以被划分为固定数量的已知组（例如，用户和项目），并且矩阵的块对应于不同类型的成对交互（例如，用户-用户、用户-项目或项目-项目交互）。在块数固定而变量数趋于无穷大的情况下，我们证明了矩阵和潜变量估计的最小均方误差的渐近精确公式。这些公式描述了问题的弱恢复阈值，并揭示了噪声方差在一定尺度下的不变性。我们还推导了一个近似的消息传递算法和一个梯度下降算法，并通过实验证明了这些算法在一定的区域内达到了信息论的极限。 摘要：We study the problem of estimating a rank-one matrix from Gaussian observations where different blocks of the matrix are observed under different noise levels. This problem is motivated by applications in clustering and community detection where latent variables can be partitioned into a fixed number of known groups (e.g., users and items) and the blocks of the matrix correspond to different types of pairwise interactions (e.g., user-user, user-item, or item-item interactions). In the setting where the number of blocks is fixed while the number of variables tends to infinity, we prove asymptotically exact formulas for the minimum mean-squared error in estimating both the matrix and the latent variables. These formulas describe the weak recovery thresholds for the problem and reveal invariance properties with respect to certain scalings of the noise variance. We also derive an approximate message passing algorithm and a gradient descent algorithm and show empirically that these algorithms achieve the information-theoretic limits in certain regimes.

【2】 Doubly Robust Feature Selection with Mean and Variance Outlier Detection and Oracle Properties 标题：基于均值和方差离群点检测和Oracle属性的双稳健特征选择

作者：Luca Insolia,Francesca Chiaromonte,Runze Li,Marco Riani 备注：35 pages, 9 figures (including supplementary material) 链接：https://arxiv.org/abs/2106.11941 摘要：我们提出了一种处理数据污染的通用方法，这种数据污染可能会破坏高维线性模型的特征选择和估计过程的性能。具体地说，我们考虑均值漂移和方差膨胀异常值的同时出现，这两个异常值可以分别建模为附加的固定和随机分量，并且可以独立地进行评估。我们的方案在进行特征选择的同时检测和降低方差膨胀异常值的权重，检测和排除均值漂移异常值，并保留完全权重的非离群情况。特征选择和均值漂移异常检测是通过一类鲁棒的非惩罚方法来实现的。方差膨胀离群点检测是基于受限后验模式的惩罚。由此产生的方法在存在数据污染的情况下满足用于特征选择的健壮oracle属性—这允许特征的数量随着样本大小呈指数增长—并以渐近概率1检测每种类型的真正孤立的情况。这提供了高故障点和效率之间的最佳权衡。计算效率高的启发式程序也被提出。我们通过广泛的模拟研究和实际应用来说明我们的方案的有限样本性能。 摘要：We propose a general approach to handle data contaminations that might disrupt the performance of feature selection and estimation procedures for high-dimensional linear models. Specifically, we consider the co-occurrence of mean-shift and variance-inflation outliers, which can be modeled as additional fixed and random components, respectively, and evaluated independently. Our proposal performs feature selection while detecting and down-weighting variance-inflation outliers, detecting and excluding mean-shift outliers, and retaining non-outlying cases with full weights. Feature selection and mean-shift outlier detection are performed through a robust class of nonconcave penalization methods. Variance-inflation outlier detection is based on the penalization of the restricted posterior mode. The resulting approach satisfies a robust oracle property for feature selection in the presence of data contamination -- which allows the number of features to exponentially increase with the sample size -- and detects truly outlying cases of each type with asymptotic probability one. This provides an optimal trade-off between a high breakdown point and efficiency. Computationally efficient heuristic procedures are also presented. We illustrate the finite-sample performance of our proposal through an extensive simulation study and a real-world application.

【3】 Sparsistent Model Discovery 标题：稀疏模型发现

作者：Georges Tod,Gert-Jan Both,Remy Kusters 机构：Université de Paris, INSERM U, Center for Research and Interdisciplinarity (CRI), F-, Paris, France 链接：https://arxiv.org/abs/2106.11936 摘要：从非常有限的观测数据中发现时空数据集下的偏微分方程在许多科学领域都是非常重要的。然而，基于稀疏回归的模型发现算法何时能够真正恢复底层物理过程仍然是一个悬而未决的问题。我们将基于Lasso的模型发现算法性能不佳的原因追溯到其潜在的变量选择不一致性：这意味着即使库中存在真实的模型，也可能无法选择。通过首先重新审视套索的不可再现性条件（IRC），我们获得了一些关于何时可能发生这种情况的见解。然后，我们证明了自适应套索比套索有更多的机会验证IRC，并建议将其集成到具有稳定性选择和错误控制的深度学习模型发现框架中。实验结果表明，在高噪声水平下，我们可以用一组超参数从有限的样本中恢复出多个非线性混沌正则偏微分方程。 摘要：Discovering the partial differential equations underlying a spatio-temporal datasets from very limited observations is of paramount interest in many scientific fields. However, it remains an open question to know when model discovery algorithms based on sparse regression can actually recover the underlying physical processes. We trace back the poor of performance of Lasso based model discovery algorithms to its potential variable selection inconsistency: meaning that even if the true model is present in the library, it might not be selected. By first revisiting the irrepresentability condition (IRC) of the Lasso, we gain some insights of when this might occur. We then show that the adaptive Lasso will have more chances of verifying the IRC than the Lasso and propose to integrate it within a deep learning model discovery framework with stability selection and error control. Experimental results show we can recover several nonlinear and chaotic canonical PDEs with a single set of hyperparameters from a very limited number of samples at high noise levels.

【4】 Surrogate-based variational data assimilation for tidal modelling 标题：用于潮汐模拟的基于代理的变分数据同化

作者：Rem-Sophia Mouradi,Cédric Goeury,Olivier Thual,Fabrice Zaoui,Pablo Tassi 机构：EDF R&D, National Laboratory for Hydraulics and Environment (LNHE), Quai Watier, Climate, Environment, Coupling and Uncertainties research unit (CECI) at the European, Center for Research and Advanced Training in Scientific Computation (CERFACS), French 链接：https://arxiv.org/abs/2106.11926 摘要：资料同化（DA）被广泛应用于结合物理知识和观测。目前地球科学中常用的方法是进行参数标定。在气候变化的背景下，旧的校准不一定能用于新的情景。这就提出了DA计算成本的问题，因为昂贵的基于物理的数值模型需要重新分析。因此，归约和元建模代表了有趣的观点，例如最近的贡献中提出的集成和变分方法的混合，以结合它们的优势（效率、非线性框架）。然而，它们通常基于montecarlo（MC）类型的采样，这通常需要大量增加集合大小以获得更好的效率，因此在基于集合的方法中也代表了计算负担。为了解决这些问题，提出了两种用替代物代替复杂模型的方法：（i）PODEn4DVAR直接源于PODEn4DVAR，它依赖于基于集成的联合参数状态本征正交分解（POD），提供了一种线性元模型(ii）POD-PCE-3DVAR，其中模型状态被POD缩减，然后使用多项式混沌展开（PCE）学习，产生非线性元模型。这两种元模型都允许编写一个近似的代价函数，其最小值可以解析计算，或通过梯度下降以可忽略不计的代价推导出来。此外，为POD-PCE-3DVAR给出了自适应元模型误差协方差矩阵，从而大大改进了基于元模型的DA分析。提出的方法是面对一个孪生实验，并比较了经典的3DVAR测量为基础的问题。结果是有希望的，特别是优于POD-PCE-3DVAR，显示出良好的收敛性和对噪声的鲁棒性经典3DVAR。 摘要：Data assimilation (DA) is widely used to combine physical knowledge and observations. It is nowadays commonly used in geosciences to perform parametric calibration. In a context of climate change, old calibrations can not necessarily be used for new scenarios. This raises the question of DA computational cost, as costly physics-based numerical models need to be reanalyzed. Reduction and metamodelling represent therefore interesting perspectives, for example proposed in recent contributions as hybridization between ensemble and variational methods, to combine their advantages (efficiency, non-linear framework). They are however often based on Monte Carlo (MC) type sampling, which often requires considerable increase of the ensemble size for better efficiency, therefore representing a computational burden in ensemble-based methods as well. To address these issues, two methods to replace the complex model by a surrogate are proposed and confronted : (i) PODEn3DVAR directly inspired from PODEn4DVAR, relies on an ensemble-based joint parameter-state Proper Orthogonal Decomposition (POD), which provides a linear metamodel ; (ii) POD-PCE-3DVAR, where the model states are POD reduced then learned using Polynomial Chaos Expansion (PCE), resulting in a non-linear metamodel. Both metamodels allow to write an approximate cost function whose minimum can be analytically computed, or deduced by a gradient descent at negligible cost. Furthermore, adapted metamodelling error covariance matrix is given for POD-PCE-3DVAR, allowing to substantially improve the metamodel-based DA analysis. Proposed methods are confronted on a twin experiment, and compared to classical 3DVAR on a measurement-based problem. Results are promising, in particular superior with POD-PCE-3DVAR, showing good convergence to classical 3DVAR and robustness to noise.

【5】 From SIR to SEAIRD: a novel data-driven modeling approach based on the Grey-box System Theory to predict the dynamics of COVID-19 标题：从SIR到SEAIRD：一种新的基于灰盒理论的数据驱动建模方法预测冠状病毒动态

作者：Komi Midzodzi Pékpé,Djamel Zitouni,Gilles Gasso,Wajdi Dhifli,Benjamin C. Guinhouya 机构：C. Guinhouya, Received: date Accepted: date 链接：https://arxiv.org/abs/2106.11918 摘要：COVID-19的常见房室模型是基于先验知识和大量假设的。此外，他们没有系统地纳入无症状病例。我们的研究旨在通过利用灰箱系统理论或灰箱辨识的优点，为数据驱动方法提供一个框架，灰箱辨识以其在部分、不完整或不确定数据下解决问题的鲁棒性而闻名。从一个开源存储库中提取的关于确诊病例和死亡的经验数据被用于开发SEAIRD隔间模型。对COVID-19的行为进行了调整以适应当前的知识。利用常微分方程求解器和优化工具实现并求解了该模型。应用交叉验证技术，计算确定系数$R^2$，以评估模型的拟合优度数据。最后对关键的流行病学参数进行了估计，为SEAIRD模型的建立提供了理论依据。当应用于巴西的案例时，SEAIRD对数据产生了极好的一致性，确定系数为%R^2$$\geq 90\%$。COVID-19传播的概率普遍较高（$\geq 95\%$）。根据20天的模型数据，巴西和法国COVID-19的发病率低至每10万接触者中有3例感染。在同一时间段内，COVID-19的死亡率在法国最高（16.4%），其次是巴西（6.9%），在俄罗斯最低（1美元）。SEAIRD代表了在传染病的动态稳定阶段建模的一种资产，特别是在病理生理学知识非常有限的情况下，对于新病毒。 摘要：Common compartmental modeling for COVID-19 is based on a priori knowledge and numerous assumptions. Additionally, they do not systematically incorporate asymptomatic cases. Our study aimed at providing a framework for data-driven approaches, by leveraging the strengths of the grey-box system theory or grey-box identification, known for its robustness in problem solving under partial, incomplete, or uncertain data. Empirical data on confirmed cases and deaths, extracted from an open source repository were used to develop the SEAIRD compartment model. Adjustments were made to fit current knowledge on the COVID-19 behavior. The model was implemented and solved using an Ordinary Differential Equation solver and an optimization tool. A cross-validation technique was applied, and the coefficient of determination $R^2$ was computed in order to evaluate the goodness-of-fit of the model. %to the data. Key epidemiological parameters were finally estimated and we provided the rationale for the construction of SEAIRD model. When applied to Brazil's cases, SEAIRD produced an excellent agreement to the data, with an %coefficient of determination $R^2$ $\geq 90\%$. The probability of COVID-19 transmission was generally high ($\geq 95\%$). On the basis of a 20-day modeling data, the incidence rate of COVID-19 was as low as 3 infected cases per 100,000 exposed persons in Brazil and France. Within the same time frame, the fatality rate of COVID-19 was the highest in France (16.4\%) followed by Brazil (6.9\%), and the lowest in Russia ($\leq 1\%$). SEAIRD represents an asset for modeling infectious diseases in their dynamical stable phase, especially for new viruses when pathophysiology knowledge is very limited.

【6】 Model-based Pre-clinical Trials for Medical Devices Using Statistical Model Checking 标题：使用统计模型检验的医疗器械基于模型的临床前试验

作者：Haochen Yang,Jicheng Gu,Zhihao Jiang 机构： ShanghaiTech University, Shanghai, China, Shanghai Engineering Research Center of Intelligent Vision and Imaging 链接：https://arxiv.org/abs/2106.11917 摘要：临床试验被认为是医疗器械验证的金标准。然而，由于成本考虑和部分信息，在试验的设计和进行过程中必须做出许多牺牲，这可能会损害试验结果的重要性。在本文中，我们提出了一个基于模型的临床前试验框架使用统计模型检查。生理模型代表了疾病的机理，使得模拟结果的自动判断成为可能。患者参数的抽样和假设检验是通过统计模型检验进行的。该框架使更广泛的假设能够得到保证的统计显著性的检验，这是对临床试验的有益补充。我们在植入型心律转复除颤器的临床前试验中展示了我们的框架。 摘要：Clinical trials are considered as the golden standard for medical device validation. However, many sacrifices have to be made during the design and conduction of the trials due to cost considerations and partial information, which may compromise the significance of the trial results. In this paper, we proposed a model-based pre-clinical trial framework using statistical model checking. Physiological models represent disease mechanism, which enable automated adjudication of simulation results. Sampling of the patient parameters and hypothesis testing are performed by statistical model checker. The framework enables a broader range of hypothesis to be tested with guaranteed statistical significance, which are useful complements to the clinical trials. We demonstrated our framework with a pre-clinical trial on implantable cardioverter defibrillators.

【7】 Credal Self-Supervised Learning 标题：凭证式自我监督学习

作者：Julian Lienen,Eyke Hüllermeier 机构：Department of Computer Science, Paderborn University, Paderborn , Germany, Institute of Informatics, University of Munich (LMU), Munich , Germany 备注：17 pages, 1 figure, 7 tables 链接：https://arxiv.org/abs/2106.11853 摘要：自我训练是一种有效的半监督学习方法。其关键思想是让学习者自己根据当前的假设对未标记的实例迭代生成“伪监督”。结合一致性正则化，伪标记在计算机视觉等领域显示出良好的性能。为了说明伪标签的假设性质，通常以概率分布的形式提供。尽管如此，有人可能会说，即使是概率分布也代表了信息量的过高水平，因为它表明学习者准确地知道基本真理条件概率。因此，在我们的方法中，我们允许学习者以credal集的形式标记实例，即（候选）概率分布集。由于这种表达能力的增强，学习者能够以更灵活、更忠实的方式表达不确定性和知识的缺乏。为了从这类弱标记数据中学习，我们利用了最近在所谓的超集学习领域中提出的方法。在详尽的实证评估中，我们将我们的方法与最先进的自我监督方法进行了比较，结果表明，特别是在包含高度不确定性的低标签场景中，我们的方法具有较高的竞争力。 摘要：Self-training is an effective approach to semi-supervised learning. The key idea is to let the learner itself iteratively generate "pseudo-supervision" for unlabeled instances based on its current hypothesis. In combination with consistency regularization, pseudo-labeling has shown promising performance in various domains, for example in computer vision. To account for the hypothetical nature of the pseudo-labels, these are commonly provided in the form of probability distributions. Still, one may argue that even a probability distribution represents an excessive level of informedness, as it suggests that the learner precisely knows the ground-truth conditional probabilities. In our approach, we therefore allow the learner to label instances in the form of credal sets, that is, sets of (candidate) probability distributions. Thanks to this increased expressiveness, the learner is able to represent uncertainty and a lack of knowledge in a more flexible and more faithful manner. To learn from weakly labeled data of that kind, we leverage methods that have recently been proposed in the realm of so-called superset learning. In an exhaustive empirical evaluation, we compare our methodology to state-of-the-art self-supervision approaches, showing competitive to superior performance especially in low-label scenarios incorporating a high degree of uncertainty.

【8】 Algorithmic Recourse in Partially and Fully Confounded Settings Through Bounding Counterfactual Effects 标题：通过限制反事实效应在部分和完全混淆环境下的算法追索权

作者：Julius von Kügelgen,Nikita Agarwal,Jakob Zeitler,Afsaneh Mastouri,Bernhard Schölkopf 机构：Bernhard Sch¨olkopf , Max Planck Institute for Intelligent Systems T¨ubingen, Germany, Department of Engineering, University of Cambridge, United Kingdom, Graduate Training Centre of Neuroscience, International Max Planck Research School 备注：Preliminary workshop version; work in progress 链接：https://arxiv.org/abs/2106.11849 摘要：算法资源旨在为个人提供可操作的建议，以从自动化决策系统中获得更有利的结果。由于它涉及对在物理世界中进行的干预进行推理，追索权从根本上说是一个因果问题。现有的方法使用从数据中学习到的因果模型，在假设没有隐藏的混杂和建模假设（如加性噪声）的情况下，计算追索行为的影响。在Balke和Pearl（1994）的开创性工作的基础上，我们提出了一种离散随机变量的替代方法，该方法放宽了这些假设，并允许未观察到的混杂和任意结构方程。所提出的方法只需要说明因果图和混淆结构，并限制追索行动的预期反事实效果。如果下限高于某个阈值，即在决策边界的另一边，则期望中保证追索权。 摘要：Algorithmic recourse aims to provide actionable recommendations to individuals to obtain a more favourable outcome from an automated decision-making system. As it involves reasoning about interventions performed in the physical world, recourse is fundamentally a causal problem. Existing methods compute the effect of recourse actions using a causal model learnt from data under the assumption of no hidden confounding and modelling assumptions such as additive noise. Building on the seminal work of Balke and Pearl (1994), we propose an alternative approach for discrete random variables which relaxes these assumptions and allows for unobserved confounding and arbitrary structural equations. The proposed approach only requires specification of the causal graph and confounding structure and bounds the expected counterfactual effect of recourse actions. If the lower bound is above a certain threshold, i.e., on the other side of the decision boundary, recourse is guaranteed in expectation.

【9】 Identifying intercity freight trip ends of heavy trucks from GPS data 标题：利用GPS数据识别重卡城际货运行程终点

作者：Yitao Yang,Bin Jia,Xiao-Yong Yan,Jiangtao Li,Zhenzhen Yang,Ziyou Gao 机构：Key Laboratory of Integrated Transport Big Data Application Technology for Transport Industry, Beijing Jiaotong, Institute of Transportation System Science and Engineering, Beijing Jiaotong University, Beijing , China 链接：https://arxiv.org/abs/2106.11793 摘要：重型卡车的城际货运出行是交通系统规划和城市群管理的重要数据。近几十年来，从GPS数据中提取货运量逐渐成为传统调查的主要替代方法。行程提取的首要任务是确定行程的终点（起点和终点，OD）。在以往的行程终点识别方法中，一些关键参数如速度、时间阈值等大多是基于经验知识来确定的，不可避免地缺乏通用性。本文提出了一种数据驱动的行程终点识别方法。首先，我们通过分析重型卡车的速度分布来定义一个速度阈值，并从原始GPS数据中识别出所有卡车停靠站。其次，通过分析重型卡车在停车位置的停留时间分布，定义了最小和最大时间阈值，并根据这些时间阈值将卡车停车分为三种类型。第三，利用公路网地理信息系统（GIS）数据和货运相关兴趣点（poi）数据，从三种类型的停车场中识别出有效的出行终点。在此步骤中，我们检测POI边界以确定重型卡车是否停在与货运相关的位置。进一步分析了重型卡车城际货运出行的时空特征，并探讨了其在实践中的潜在应用。 摘要：The intercity freight trips of heavy trucks are important data for transportation system planning and urban agglomeration management. In recent decades, the extraction of freight trips from GPS data has gradually become the main alternative to traditional surveys. Identifying the trip ends (origin and destination, OD) is the first task in trip extraction. In previous trip end identification methods, some key parameters, such as speed and time thresholds, have mostly been defined on the basis of empirical knowledge, which inevitably lacks universality. Here, we propose a data-driven trip end identification method. First, we define a speed threshold by analyzing the speed distribution of heavy trucks and identify all truck stops from raw GPS data. Second, we define minimum and maximum time thresholds by analyzing the distribution of the dwell times of heavy trucks at stop location and classify truck stops into three types based on these time thresholds. Third, we use highway network GIS data and freight-related points-of-interest (POIs) data to identify valid trip ends from among the three types of truck stops. In this step, we detect POI boundaries to determine whether a heavy truck is stopping at a freight-related location. We further analyze the spatiotemporal characteristics of intercity freight trips of heavy trucks and discuss their potential applications in practice.

【10】 Simulation-Driven COVID-19 Epidemiological Modeling with Social Media 标题：基于社交媒体的模拟驱动的冠状病毒流行病学建模

作者：Jose Storopoli,Andre Luis Marques Ferreira dos Santos,Alessandra Cristina Guedes Pellini,Breck Baldwin 机构：Department of Computer Science, Universidade Nove de Julho - UNINOVE, São Paulo, Brazil, André Luís Marques Ferreira dos Santos, Department of Business Administration, Medical School 备注：15 pages, 6 figures, 3 tables, 1 algorithm 链接：https://arxiv.org/abs/2106.11686 摘要：现代贝叶斯方法和工作流强调了仿真在模型开发中的重要性。模拟可以帮助研究人员了解模型在受控环境中的行为，并可用于在模型暴露于任何真实数据之前以不同方式对其施加压力。这种改进的理解在流行病学模型中可能是有益的，特别是在处理COVID-19时。不幸的是，很少有研究人员进行任何模拟。我们提出了一个模拟算法，它实现了一个简单的基于agent的疾病传播模型，该模型与COVID-19的标准隔室流行病学模型相结合。我们的算法可以应用于不同的参数化，以反映几种可能的流行场景。此外，我们还模拟了如何将日常症状提及形式的社交媒体信息纳入COVID-19流行病学模型。我们用两个实验来测试我们的社交媒体COVID-19模型。第一种是使用我们基于agent的模拟算法的模拟数据，第二种是使用机器学习tweet分类器来识别从噪声中提到症状的tweet。我们的结果显示了COVID-19模型是如何（1）用于整合社交媒体数据和（2）使用模拟和真实数据进行评估和评估的。 摘要：Modern Bayesian approaches and workflows emphasize in how simulation is important in the context of model developing. Simulation can help researchers understand how the model behaves in a controlled setting and can be used to stress the model in different ways before it is exposed to any real data. This improved understanding could be beneficial in epidemiological models, specially when dealing with COVID-19. Unfortunately, few researchers perform any simulations. We present a simulation algorithm that implements a simple agent-based model for disease transmission that works with a standard compartment epidemiological model for COVID-19. Our algorithm can be applied in different parameterizations to reflect several plausible epidemic scenarios. Additionally, we also model how social media information in the form of daily symptom mentions can be incorporate into COVID-19 epidemiological models. We test our social media COVID-19 model with two experiments. The first using simulated data from our agent-based simulation algorithm and the second with real data using a machine learning tweet classifier to identify tweets that mention symptoms from noise. Our results shows how a COVID-19 model can be (1) used to incorporate social media data and (2) assessed and evaluated with simulated and real data.

【11】 Modal clustering on PPGMMGA projection subspace 标题：PPGMMGA投影子空间上的模态聚类

作者：Luca Scrucca 备注：10 pages, 5 figures, 2 tables 链接：https://arxiv.org/abs/2106.11617 摘要：PPGMMGA是一种投影寻踪（PP）算法，旨在检测和可视化多变量数据中的聚类结构。该算法以负熵作为PP指数，通过拟合高斯混合模型（GMMs）进行密度估计，然后用遗传算法（GAs）进行优化。由于PPGMMGA算法是专门为可视化目的引入的降维技术，因此没有显式地提供集群成员关系。本文提出了一种模式聚类方法来估计投影数据点的聚类。特别地，使用模态EM算法来估计与使用简约GMMs估计的潜在密度的投影子空间中的局部极大值相对应的模态。然后根据识别模式的吸引域对数据点进行聚类。通过对仿真数据和实际数据的分析，验证了该方法的有效性，并对聚类性能进行了评价。 摘要：PPGMMGA is a Projection Pursuit (PP) algorithm aimed at detecting and visualizing clustering structures in multivariate data. The algorithm uses the negentropy as PP index obtained by fitting Gaussian Mixture Models (GMMs) for density estimation, and then optimized using Genetic Algorithms (GAs). Since the PPGMMGA algorithm is a dimension reduction technique specifically introduced for visualization purposes, cluster memberships are not explicitly provided. In this paper a modal clustering approach is proposed for estimating clusters of projected data points. In particular, a modal EM algorithm is employed to estimate the modes corresponding to the local maxima in the projection subspace of the underlying density estimated using parsimonious GMMs. Data points are then clustered according to the domain of attraction of the identified modes. Simulated and real data are discussed to illustrate the proposed method and evaluate the clustering performance.

【12】 Choice of Damping Coefficient in Langevin Dynamics 标题：朗之万动力学中阻尼系数的选择

作者：Robert D. Skeel,Carsten Hartmann 备注：21 pages, 6 figures 链接：https://arxiv.org/abs/2106.11597 摘要：本文考虑了Langevin动力学在采样中的应用，研究了如何选择Langevin动力学中的阻尼参数，以使采样的彻底性最大化。此外，它还考虑了抽样彻底性测度的计算。 摘要：This article considers the application of Langevin dynamics to sampling and investigates how to choose the damping parameter in Langevin dynamics for the purpose of maximizing thoroughness of sampling. Also, it considers the computation of measures of sampling thoroughness.

【13】 Online Ordering Platform City Distribution Based on Genetic Algorithm 标题：基于遗传算法的在线订购平台城市配送

作者：Yu Du 机构：Online Ordering Platform City Distribution Based on Genetic Algorithm DU Yu School of Economics and Management, Beijing Jiaotong University 备注：9 pages, 2 figures 链接：https://arxiv.org/abs/2106.11578 摘要：外卖点菜平台兴起以来，M平台以其优质的服务在行业内处于领先地位。订单量的不断增加导致了平台间为降低配送成本而展开的竞争，配送路径的不合理导致配送成本的急剧上升。通过分析平台配送的现状，研究了M平台上城市配送的车辆路径问题，以配送成本最小为目标。考虑到客户期望交货期和车辆状况的约束，采用三个软时间窗组合不同到达时间的车辆路径问题模型，并采用遗传算法进行求解。结果表明，本文的模型和算法在配送成本和配送时间方面均优于原模型，为M平台在未来城市配送中节约配送成本提供了决策支持。 摘要：Since the rising of the takeaway ordering platform, the M platform has taken the lead in the industry with its high-quality service. The increasing order volume leads the competition between platforms to reduce the distribution cost, which increases rapidly because of the unreasonable distribution route. By analyzing platform distribution's current situation, we study the vehicle routing problem of urban distribution on the M platform and minimize the distribution cost. Considering the constraints of the customer's expected delivery time and vehicle condition, we combine the different arrival times of the vehicle routing problem model using three soft time windows and solve the problem using a genetic algorithm (GA). The results show that our model and algorithm can design the vehicle path superior to the original model in terms of distribution cost and delivery time, thus providing decision support for the M platform to save distribution cost in urban distribution in the future.

【14】 Discrepancy-based Inference for Intractable Generative Models using Quasi-Monte Carlo 标题：基于差异的拟蒙特卡罗难解产生式模型推理

作者：Ziang Niu,Johanna Meier,François-Xavier Briol 机构：Renmin University of China,Leibniz Universit¨at Hannover,University College London, ∗contributed equally, †corresponding author. 链接：https://arxiv.org/abs/2106.11561 摘要：难处理的生成性模型是指可能性不可用但可以抽样的模型。在这种情况下，大多数参数推断方法都需要计算数据和生成模型之间的一些差异。这是例如最小距离估计和近似贝叶斯计算的情况。这些方法需要从模型中为不同的参数值采样大量的实现，当模拟是一个昂贵的操作时，这可能是一个重大的挑战。在本文中，我们建议通过在我们的模型的模拟中加强“样本多样性”来增强这种方法。这将通过使用准蒙特卡罗（QMC）点集来实现。我们的主要结果是样本复杂度边界，它表明，在生成器上的平滑条件下，当使用三种最常见的差异：最大平均差异、Wasserstein距离和Sinkhorn散度时，QMC可以显著减少获得给定精度所需的样本数。此外，还进行了一项模拟研究，该研究强调，在某些理论未涵盖的情况下，有时也可能提高精度。 摘要：Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the generative model. This is for example the case for minimum distance estimation and approximate Bayesian computation. These approaches require sampling a high number of realisations from the model for different parameter values, which can be a significant challenge when simulating is an expensive operation. In this paper, we propose to enhance this approach by enforcing "sample diversity" in simulations of our models. This will be implemented through the use of quasi-Monte Carlo (QMC) point sets. Our key results are sample complexity bounds which demonstrate that, under smoothness conditions on the generator, QMC can significantly reduce the number of samples required to obtain a given level of accuracy when using three of the most common discrepancies: the maximum mean discrepancy, the Wasserstein distance, and the Sinkhorn divergence. This is complemented by a simulation study which highlights that an improved accuracy is sometimes also possible in some settings which are not covered by the theory.

【15】 Extreme Graphical Models with Applications to Functional Neuronal Connectivity 标题：极图模型及其在功能神经元连接中的应用

作者：Andersen Chang,Genevera I. Allen 机构：Department of Statistics, Rice University, Department of Electrical and Computer Engineering, Rice University, Department of Computer Science, Rice University, Department of Pediatrics-Neurology, Baylor College of Medicine 链接：https://arxiv.org/abs/2106.11554 摘要：利用现代钙成像技术，可以在体内同时记录数千个神经元的活动。这些实验有可能为功能连接提供新的见解，功能连接定义为大脑神经元尖峰活动之间的统计关系。作为高维环境下估计条件依赖性的常用工具，图形模型是分析钙成像数据的自然选择。然而，原始的神经元活动记录数据提出了一个独特的挑战：重要的信息在于表明神经元放电的罕见极值观测，而不是与不活动相关的非极值观测。为了解决这个问题，我们开发了一类新的图形模型，称为极值图形模型，它专注于寻找特征之间关于极值的关系。我们的模型假设条件分布是广义正态分布或次正态分布的一个子类，并产生一种曲线指数族图形模型。我们首先导出了极值图形模型的联合多元分布的形式，并给出了它可规范化的条件。然后，我们证明了我们的估计方法在模型选择上的一致性。最后，我们通过一些模拟研究以及一个实际数据实例，研究了极值图形模型的经验性能，并将我们的方法应用于一个真实的钙成像数据集。 摘要：With modern calcium imaging technology, the activities of thousands of neurons can be recorded simultaneously in vivo. These experiments can potentially provide new insights into functional connectivity, defined as the statistical relationships between the spiking activity of neurons in the brain. As a commonly used tool for estimating conditional dependencies in high-dimensional settings, graphical models are a natural choice for analyzing calcium imaging data. However, raw neuronal activity recording data presents a unique challenge: the important information lies in the rare extreme value observations that indicate neuronal firing, as opposed to the non-extreme observations associated with inactivity. To address this issue, we develop a novel class of graphical models, called the extreme graphical model, which focuses on finding relationships between features with respect to the extreme values. Our model assumes the conditional distributions a subclass of the generalized normal or Subbotin distribution, and yields a form of a curved exponential family graphical model. We first derive the form of the joint multivariate distribution of the extreme graphical model and show the conditions under which it is normalizable. We then demonstrate the model selection consistency of our estimation method. Lastly, we study the empirical performance of the extreme graphical model through several simulation studies as well as through a real data example, in which we apply our method to a real-world calcium imaging data set.

【16】 Predictive multiview embedding 标题：预测性多视图嵌入

作者：M. LuValle 备注：12 pages 19 references, 8 figures 链接：https://arxiv.org/abs/2106.11545 摘要：多视图嵌入是一种建模奇怪吸引子的方法，它利用了在真实混沌系统中通常进行测量的方式，使用多维测量来弥补长时间序列的不足。预测性多视图嵌入使这种方法适应了预测新值的问题，并提供了一个自然的框架，用于组合多种信息源，例如自然测量和计算机模型运行，以潜在地改进预测。在这里，我们利用18个月前的月平均预测，展示了预测多视图嵌入如何与简单的统计方法相结合，通过GCM探索四个气候变量的可预测性，建立预测边界，探索吸引子的局部流形结构，结果表明，尽管GCM不能很好地预测某一变量，但将GCM信息与经验数据相结合的混合模型预测该变量的效果明显优于纯经验模型。 摘要：Multiview embedding is a way to model strange attractors that takes advantage of the way measurements are often made in real chaotic systems, using multidimensional measurements to make up for a lack of long timeseries. Predictive multiview embedding adapts this approach to the problem of predicting new values, and provides a natural framework for combining multiple sources of information such as natural measurements and computer model runs for potentially improved prediction. Here, using 18 month ahead prediction of monthly averages, we show how predictive multiview embedding can be combined with simple statistical approaches to explore predictability of four climate variables by a GCM, build prediction bounds, explore the local manifold structure of the attractor, and show that even though the GCM does not predict a particular variable well, a hybrid model combining information from the GCM and empirical data predicts that variable significantly better than the purely empirical model.

【17】 On Selection Criteria for the Tuning Parameter in Robust Divergence 标题：关于鲁棒发散中调谐参数的选择准则

作者：Shonosuke Sugasawa,Shouto Yonekura 机构：Center for Spatial Information Science, The University of Tokyo, Graduate School of Social Sciences, Chiba University, Nospare Inc. 备注：15 pages 链接：https://arxiv.org/abs/2106.11540 摘要：虽然稳健散度（如密度幂散度和$\gamma$-散度）有助于在存在离群值的情况下进行稳健统计推断，但控制稳健程度的调整参数是根据经验法则选择的，这可能导致低效的推断。本文提出了一个基于Hyvarinen分数渐近逼近的选择准则，并将其应用于由鲁棒散度定义的非正规化模型。所提出的选择准则只需要假设密度函数对观测值的一阶和二阶偏导数，无论参数个数多少，都可以很容易地计算出来。通过正态分布和正则线性回归的数值研究，证明了该方法的有效性。 摘要：While robust divergence such as density power divergence and $\gamma$-divergence is helpful for robust statistical inference in the presence of outliers, the tuning parameter that controls the degree of robustness is chosen in a rule-of-thumb, which may lead to an inefficient inference. We here propose a selection criterion based on an asymptotic approximation of the Hyvarinen score applied to an unnormalized model defined by robust divergence. The proposed selection criterion only requires first and second-order partial derivatives of an assumed density function with respect to observations, which can be easily computed regardless of the number of parameters. We demonstrate the usefulness of the proposed method via numerical studies using normal distributions and regularized linear regression.

【18】 Aggregated functional data model applied on clustering and disaggregation of UK electrical load profiles 标题：聚集函数数据模型在英国电力负荷剖面聚类与解聚中的应用

作者：Gabriel Franco,Camila P. E. de Souza,Nancy L. Garcia 机构：University of Campinas (UNICAMP), Campinas, Brazil., Camila P. E. Souza, The University of Western Ontario, London, Canada. 备注：46 pages, 11 figures 链接：https://arxiv.org/abs/2106.11448 摘要：了解消费者层面的电能需求对于规划电网分布和提供非高峰电价具有重要作用，但观察个人消费模式仍然很昂贵。另一方面，聚合负荷曲线通常在变电站级别可用。提出的方法将变电站总负荷分解为估计的平均消耗曲线，称为典型曲线，包括由解释变量给出的信息。此外，基于用户典型曲线和协方差结构的相似性，提出了一种基于模型的变电站聚类方法。该方法应用于英国的一个实际变电站负荷监测数据集，并在八个模拟场景中进行了测试。 摘要：Understanding electrical energy demand at the consumer level plays an important role in planning the distribution of electrical networks and offering of off-peak tariffs, but observing individual consumption patterns is still expensive. On the other hand, aggregated load curves are normally available at the substation level. The proposed methodology separates substation aggregated loads into estimated mean consumption curves, called typical curves, including information given by explanatory variables. In addition, a model-based clustering approach for substations is proposed based on the similarity of their consumers typical curves and covariance structures. The methodology is applied to a real substation load monitoring dataset from the United Kingdom and tested in eight simulated scenarios.

【19】 Local convexity of the TAP free energy and AMP convergence for Z2-synchronization 标题：抽头自由能的局部凸性与Z2同步的AMP收敛性

作者：Michael Celentano,Zhou Fan,Song Mei 机构：edu†Department of Statistics and Data Science, Yale University 备注：56 pages 链接：https://arxiv.org/abs/2106.11428 摘要：本文以高维贝叶斯模型的一个典型例子Z2同步为例，研究了基于TAP方法的均值场变分贝叶斯推理。我们证明了当信号强度$\lambda>1$（弱恢复阈值）时，TAP自由能泛函在Bayes后验定律的平均值附近存在唯一的局部极小值。此外，在这个极小值的局部邻域中的抽头自由能是强凸的。因此，自然梯度/镜像下降算法从局部初始化获得线性收敛到这个最小值，这可以通过近似消息传递（AMP）的有限次迭代获得。这提供了一个严格的基础，通过最小化的TAP自由能在高维的变分推理。我们还分析了AMP的有限样本收敛性，表明AMP在任何$\lambda>1$的抽头极小值处渐近稳定，并且在足够大的$\lambda$的谱初始化下线性收敛到该极小值。这样的保证比状态演化分析得到的结果更强，状态演化分析只描述无限样本极限下固定数量的AMP迭代。我们的证明结合Kac-Rice公式和Sudakov-Fernique-Gaussian比较不等式分析了满足强凸性和稳定性条件的临界点在其局部邻域内的复杂性。 摘要：We study mean-field variational Bayesian inference using the TAP approach, for Z2-synchronization as a prototypical example of a high-dimensional Bayesian model. We show that for any signal strength $\lambda > 1$ (the weak-recovery threshold), there exists a unique local minimizer of the TAP free energy functional near the mean of the Bayes posterior law. Furthermore, the TAP free energy in a local neighborhood of this minimizer is strongly convex. Consequently, a natural-gradient/mirror-descent algorithm achieves linear convergence to this minimizer from a local initialization, which may be obtained by a finite number of iterates of Approximate Message Passing (AMP). This provides a rigorous foundation for variational inference in high dimensions via minimization of the TAP free energy. We also analyze the finite-sample convergence of AMP, showing that AMP is asymptotically stable at the TAP minimizer for any $\lambda > 1$, and is linearly convergent to this minimizer from a spectral initialization for sufficiently large $\lambda$. Such a guarantee is stronger than results obtainable by state evolution analyses, which only describe a fixed number of AMP iterations in the infinite-sample limit. Our proofs combine the Kac-Rice formula and Sudakov-Fernique Gaussian comparison inequality to analyze the complexity of critical points that satisfy strong convexity and stability conditions within their local neighborhoods.

【20】 Nonparametric causal structure learning in high dimensions 标题：高维非参数因果结构学习

作者：Shubhadeep Chakraborty,Ali Shojaie 机构：Department of Biostatistics, University of Washington 链接：https://arxiv.org/abs/2106.11415 摘要：PC算法和FCI算法是一种流行的基于约束的有向无环图（dag）结构学习方法，它们分别适用于潜在变量和选择变量的存在和不存在。这些算法（以及它们的阶独立变量，PC稳定和FCI稳定）对于基于偏相关的稀疏高维dag的学习是一致的。然而，如果数据是联合高斯分布或由线性结构方程模型生成的，则从偏相关推断条件独立性是有效的——这一假设在许多应用中可能会被违背。为了扩大高维因果结构学习的范围，我们提出了PC-稳定和FCI-稳定算法的非参数变体，它们采用条件距离协方差（CdCov）来检验条件独立关系。作为关键的理论贡献，我们证明了当我们实现基于CdCov的条件独立性非参数检验时，PC稳定算法和FCI稳定算法的高维一致性可以推广到DAGs上的一般分布。数值研究表明，对于高斯分布，我们提出的算法的性能几乎与PC稳定和FCI稳定的算法相当，并且在非高斯图形模型中具有优势。 摘要：The PC and FCI algorithms are popular constraint-based methods for learning the structure of directed acyclic graphs (DAGs) in the absence and presence of latent and selection variables, respectively. These algorithms (and their order-independent variants, PC-stable and FCI-stable) have been shown to be consistent for learning sparse high-dimensional DAGs based on partial correlations. However, inferring conditional independences from partial correlations is valid if the data are jointly Gaussian or generated from a linear structural equation model -- an assumption that may be violated in many applications. To broaden the scope of high-dimensional causal structure learning, we propose nonparametric variants of the PC-stable and FCI-stable algorithms that employ the conditional distance covariance (CdCov) to test for conditional independence relationships. As the key theoretical contribution, we prove that the high-dimensional consistency of the PC-stable and FCI-stable algorithms carry over to general distributions over DAGs when we implement CdCov-based nonparametric tests for conditional independence. Numerical studies demonstrate that our proposed algorithms perform nearly as good as the PC-stable and FCI-stable for Gaussian distributions, and offer advantages in non-Gaussian graphical models.

【21】 Robust and Heterogenous Odds Ratio: Estimating Price Sensitivity for Unbought Items 标题：稳健且异质的赔率比：估计未购买物品的价格敏感度

作者：Jean Pauphilet 链接：https://arxiv.org/abs/2106.11389 摘要：问题定义：挖掘对干预的异构响应是数据驱动操作的关键步骤，例如个性化治疗或定价。我们研究如何估计价格敏感性交易水平的数据。从因果推断的角度来看，当（a）对治疗的反应（这里，顾客是否购买产品）是二元的，并且（b）治疗分配被部分观察时（这里，全部信息仅可用于购买的物品），我们估计异质治疗效果。方法/结果：我们提出了一种递归分割方法来估计异质优势比，这是医学和社会科学中广泛使用的治疗效果度量。我们整合了一个对抗性插补步骤，以便即使在存在部分观察到的治疗分配的情况下也能进行稳健的推断。我们在综合数据上验证了我们的方法，并将其应用于政治学、医学和收入管理的三个案例研究。管理含义：我们稳健的异质优势比估计方法是一种简单直观的工具，可以量化患者或客户的异质性并个性化干预，同时解除了许多收入管理数据的中心限制。 摘要：Problem definition: Mining for heterogeneous responses to an intervention is a crucial step for data-driven operations, for instance to personalize treatment or pricing. We investigate how to estimate price sensitivity from transaction-level data. In causal inference terms, we estimate heterogeneous treatment effects when (a) the response to treatment (here, whether a customer buys a product) is binary, and (b) treatment assignments are partially observed (here, full information is only available for purchased items). Methodology/Results: We propose a recursive partitioning procedure to estimate heterogeneous odds ratio, a widely used measure of treatment effect in medicine and social sciences. We integrate an adversarial imputation step to allow for robust inference even in presence of partially observed treatment assignments. We validate our methodology on synthetic data and apply it to three case studies from political science, medicine, and revenue management. Managerial Implications: Our robust heterogeneous odds ratio estimation method is a simple and intuitive tool to quantify heterogeneity in patients or customers and personalize interventions, while lifting a central limitation in many revenue management data.

【22】 ciftiTools: A package for reading, writing, visualizing and manipulating CIFTI files in R 标题：ciftiTools：用于读、写、可视化和操作R中的Cifti文件的软件包

作者：Damon Pham,John Muschelli,Amanda Mejia 机构：Department of Statistics, Indiana University, USA, Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, USA 备注：12 pages, 2 figures 链接：https://arxiv.org/abs/2106.11338 摘要：基于表面的MR数据分析具有公认的优势，包括改进的整个大脑皮层可视化、执行表面平滑以避免与体积平滑相关的问题的能力、改进的受试者间对齐和降低维数。人类连接体项目引入的CIFTI“graydorigin”文件格式进一步推进了基于表面的分析，它将左右半球的表面度量数据与皮质下和小脑灰质数据结合到一个文件中。在灰色坐标空间中进行的分析非常适合利用通过传统分析技术和更先进的贝叶斯统计方法在大脑和受试者之间共享的信息。R统计环境为后者提供了便利，因为它拥有丰富的用于贝叶斯计算和空间建模的先进统计技术。然而，R以前很少支持灰度坐标分析，而且几乎没有任何语言的用于处理CIFTI文件的综合编程工具。在这里，我们介绍了ciftools R包，它为CIFTI和相关数据格式的读取、写入、可视化和操作提供了一个统一的环境。我们举例说明了ciftiols的一套方便且用户友好的工具，用于处理R中的灰度坐标和表面几何数据，并描述了如何利用ciftiols推进基于灰度坐标的功能性MRI数据的统计分析。 摘要：Surface-based analysis of MR data has well-recognized advantages, including improved whole-cortex visualization, the ability to perform surface smoothing to avoid issues associated with volumetric smoothing, improved inter-subject alignment, and reduced dimensionality. The CIFTI ``grayordinate'' file format introduced by the Human Connectome Project further advances surface-based analysis by combining left and right hemispheric surface metric data with subcortical and cerebellar gray matter data into a single file. Analyses performed in grayordinates space are well-suited to leverage information shared across the brain and across subjects through both traditional analysis techniques and more advanced Bayesian statistical methods. The R statistical environment facilitates the latter given its wealth of advanced statistical techniques for Bayesian computation and spatial modeling. Yet little support for grayordinates analysis has been previously available in R, and few comprehensive programmatic tools for working with CIFTI files have been available in any language. Here, we present the ciftiTools R package, which provides a unified environment for reading, writing, visualizing and manipulating CIFTI and related data formats. We illustrate ciftiTools' convenient and user-friendly suite of tools for working with grayordinates and surface geometry data in R, and we describe how ciftiTools is being utilized to advance the statistical analysis of grayordinates-based functional MRI data.

【23】 Variance-Aware Off-Policy Evaluation with Linear Function Approximation 标题：基于线性函数逼近的方差感知非策略评估

作者：Yifei Min,Tianhao Wang,Dongruo Zhou,Quanquan Gu 机构：edu‡Department of Statistics and Data Science, Yale University, UniversityofCalifornia 备注：70 pages, 4 figures 链接：https://arxiv.org/abs/2106.11960 摘要：研究了线性函数逼近强化学习中的非策略评价问题，其目的是基于行为策略收集的离线数据来估计目标策略的价值函数。我们建议加入值函数的方差信息来提高OPE的样本效率。更具体地说，对于时间不均匀的幕式线性马尔可夫决策过程（MDPs），我们提出了一种算法VA-OPE，它利用值函数的估计方差对拟合Q-迭代中的Bellman残差进行加权。我们证明了我们的算法比已知的结果有更严格的误差界。我们还提供了行为策略和目标策略之间分布转移的细粒度描述。大量的数值实验证实了我们的理论。 摘要：We study the off-policy evaluation (OPE) problem in reinforcement learning with linear function approximation, which aims to estimate the value function of a target policy based on the offline data collected by a behavior policy. We propose to incorporate the variance information of the value function to improve the sample efficiency of OPE. More specifically, for time-inhomogeneous episodic linear Markov decision processes (MDPs), we propose an algorithm, VA-OPE, which uses the estimated variance of the value function to reweight the Bellman residual in Fitted Q-Iteration. We show that our algorithm achieves a tighter error bound than the best-known result. We also provide a fine-grained characterization of the distribution shift between the behavior policy and the target policy. Extensive numerical experiments corroborate our theory.

【24】 Robust Regression Revisited: Acceleration and Improved Estimation Rates 标题：稳健回归回顾：加速和改进的估计率

作者：Arun Jambulapati,Jerry Li,Tselil Schramm,Kevin Tian 机构：com‡Stanford University, edu§Stanford University 备注：47 pages 链接：https://arxiv.org/abs/2106.11938 摘要：我们研究了强污染模型下统计回归问题的快速算法，目标是在给定不利污染样本的情况下近似优化广义线性模型（GLM）。这一研究领域的前期工作是基于Prasad等人的稳健梯度下降框架（一种使用有偏梯度查询的一阶方法）或Diakonikolas等人的Sever框架（一种称为平稳点查找器的迭代离群点去除方法）。我们提出了一种用于稳健回归问题的近似线性时间算法，与现有算法相比，该算法具有更好的运行时间或估计保证。对于光滑GLMs的一般情况（如logistic回归），我们证明了Prasad等人的稳健梯度下降框架可以被加速，并且证明了我们的算法扩展到优化Lipschitz GLMs的Moreau包络（如支持向量机），回答了文献中的几个开放性问题。对于稳健线性回归的研究，我们提出了一种比以往的近似线性时间算法获得更高估计率的方法。有趣的是，我们的方法首先在Bakshi和Prasad的平方和算法中引入了一个可辨识性证明，该证明在需要大量多项式运行时间和样本复杂度的情况下实现了最优的错误率。我们在Sever框架下重新解释了他们的证明，在较少的分布假设下得到了一个更快、更有效的算法。 摘要：We study fast algorithms for statistical regression problems under the strong contamination model, where the goal is to approximately optimize a generalized linear model (GLM) given adversarially corrupted samples. Prior works in this line of research were based on the robust gradient descent framework of Prasad et. al., a first-order method using biased gradient queries, or the Sever framework of Diakonikolas et. al., an iterative outlier-removal method calling a stationary point finder. We present nearly-linear time algorithms for robust regression problems with improved runtime or estimation guarantees compared to the state-of-the-art. For the general case of smooth GLMs (e.g. logistic regression), we show that the robust gradient descent framework of Prasad et. al. can be accelerated, and show our algorithm extends to optimizing the Moreau envelopes of Lipschitz GLMs (e.g. support vector machines), answering several open questions in the literature. For the well-studied case of robust linear regression, we present an alternative approach obtaining improved estimation rates over prior nearly-linear time algorithms. Interestingly, our method starts with an identifiability proof introduced in the context of the sum-of-squares algorithm of Bakshi and Prasad, which achieved optimal error rates while requiring large polynomial runtime and sample complexity. We reinterpret their proof within the Sever framework and obtain a dramatically faster and more sample-efficient algorithm under fewer distributional assumptions.

【25】 Provably Efficient Representation Learning in Low-rank Markov Decision Processes 标题：低秩马尔可夫决策过程中可证明有效的表示学习

作者：Weitong Zhang,Jiafan He,Dongruo Zhou,Amy Zhang,Quanquan Gu 机构：UniversityofCalifornia, edu¶Department of Electrical Engineering and Computer Science 备注：27 pages 链接：https://arxiv.org/abs/2106.11935 摘要：深度强化学习（DRL）的成功归功于学习一种适合于潜在探索和开发任务的表征的能力。然而，现有的线性函数逼近可证强化学习算法往往假设特征表示已知且固定。为了了解表示学习如何提高RL的效率，我们研究了一类低秩Markov决策过程（MDPs）的表示学习，其中转换核可以用双线性形式表示。我们提出一个可证明有效的算法称为ReLEX，它可以同时学习表示和执行探索。我们证明了ReLEX算法在没有表示学习的情况下，其性能并不比最新的算法差，并且如果表示函数类在整个状态-动作空间上具有某种温和的覆盖特性，则在样本效率方面会有严格的提高。 摘要：The success of deep reinforcement learning (DRL) is due to the power of learning a representation that is suitable for the underlying exploration and exploitation task. However, existing provable reinforcement learning algorithms with linear function approximation often assume the feature representation is known and fixed. In order to understand how representation learning can improve the efficiency of RL, we study representation learning for a class of low-rank Markov Decision Processes (MDPs) where the transition kernel can be represented in a bilinear form. We propose a provably efficient algorithm called ReLEX that can simultaneously learn the representation and perform exploration. We show that ReLEX always performs no worse than a state-of-the-art algorithm without representation learning, and will be strictly better in terms of sample efficiency if the function class of representations enjoys a certain mild "coverage'' property over the whole state-action space.

【26】 Dangers of Bayesian Model Averaging under Covariate Shift 标题：协变量漂移下贝叶斯模型平均的危险性

作者：Pavel Izmailov,Patrick Nicholson,Sanae Lotfi,Andrew Gordon Wilson 机构：†New York University, ‡Stevens Capital Management 链接：https://arxiv.org/abs/2106.11905 摘要：神经网络的近似贝叶斯推理被认为是标准训练的一种稳健的替代方法，通常对分布外的数据具有良好的性能。然而，贝叶斯神经网络（BNNs）通过全批量哈密顿montecarlo进行高保真近似推理，在协变量漂移下泛化能力较差，甚至不如经典估计。我们解释了这个令人惊讶的结果，说明了贝叶斯模型平均值在协变量变化下实际上是有问题的，特别是在输入特征中的线性依赖性导致缺乏后收缩的情况下。此外，我们还说明了为什么相同的问题不影响许多近似推理程序，或经典的最大后验概率（MAP）训练。最后，我们提出了新的先验知识，以提高BNN的稳健性，许多来源的协变量转移。 摘要：Approximate Bayesian inference for neural networks is considered a robust alternative to standard training, often providing good performance on out-of-distribution data. However, Bayesian neural networks (BNNs) with high-fidelity approximate inference via full-batch Hamiltonian Monte Carlo achieve poor generalization under covariate shift, even underperforming classical estimation. We explain this surprising result, showing how a Bayesian model average can in fact be problematic under covariate shift, particularly in cases where linear dependencies in the input features cause a lack of posterior contraction. We additionally show why the same issue does not affect many approximate inference procedures, or classical maximum a-posteriori (MAP) training. Finally, we propose novel priors that improve the robustness of BNNs to many sources of covariate shift.

【27】 Local policy search with Bayesian optimization 标题：基于贝叶斯优化的本地策略搜索

作者：Sarah Müller,Alexander von Rohr,Sebastian Trimpe 机构：Max Planck Institute for Intelligent Systems, Stuttgart, Germany, Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Germany, IAV GmbH, Gifhorn, Germany, Institute for Ophthalmic Research, University of Tübingen, Tübingen, Germany 链接：https://arxiv.org/abs/2106.11899 摘要：强化学习（Reinforcement learning，RL）的目标是通过与环境的交互来寻找最优策略。因此，学习复杂的行为需要大量的样本，这在实践中是禁止的。然而，用于局部搜索的策略梯度往往是从随机扰动中获得的，而不是系统地推理和主动地选择信息样本。这些随机样本产生高方差估计，因此在样本复杂度方面是次优的。主动选择信息样本是贝叶斯优化的核心，它从过去的样本中构造一个目标的概率替代物来推理后续的信息样本。在这篇论文中，我们提议将两个世界结合起来。我们开发了一个利用目标函数及其梯度的概率模型的算法。基于该模型，该算法决定在何处查询含噪的零阶预言，以提高梯度估计。该算法是一种新型的策略搜索方法，并与现有的黑盒算法进行了比较。比较表明，改进的样本复杂度和减少方差在广泛的经验评价综合目标。此外，我们强调了在流行的RL基准上进行主动采样的好处。 摘要：Reinforcement learning (RL) aims to find an optimal policy by interaction with an environment. Consequently, learning complex behavior requires a vast number of samples, which can be prohibitive in practice. Nevertheless, instead of systematically reasoning and actively choosing informative samples, policy gradients for local search are often obtained from random perturbations. These random samples yield high variance estimates and hence are sub-optimal in terms of sample complexity. Actively selecting informative samples is at the core of Bayesian optimization, which constructs a probabilistic surrogate of the objective from past samples to reason about informative subsequent ones. In this paper, we propose to join both worlds. We develop an algorithm utilizing a probabilistic model of the objective function and its gradient. Based on the model, the algorithm decides where to query a noisy zeroth-order oracle to improve the gradient estimates. The resulting algorithm is a novel type of policy search method, which we compare to existing black-box algorithms. The comparison reveals improved sample complexity and reduced variance in extensive empirical evaluations on synthetic objectives. Further, we highlight the benefits of active sampling on popular RL benchmarks.

【28】 Dynamic Customer Embeddings for Financial Service Applications 标题：金融服务应用程序的动态客户嵌入

作者：Nima Chitsazan,Samuel Sharpe,Dwipam Katariya,Qianyu Cheng,Karthik Rajasethupathy 备注：ICML Workshop on Representation Learning for Finance and E-Commerce Applications 链接：https://arxiv.org/abs/2106.11880 摘要：随着金融服务（FS）公司经历了技术驱动的剧烈变化，新数据流的可用性为更全面地了解客户提供了机会。我们提出了动态客户嵌入（DCE），这是一个利用客户的数字活动和广泛的金融环境来学习FS行业中客户的密集表示的框架。我们的方法检查移动或网络数字会话中的客户操作和页面浏览，会话本身的顺序，以及登录时整个组织中常见财务功能的快照。我们在三个预测问题中使用真实世界的数据测试我们的客户嵌入：1）客户在下一个数字会话中的意图，2）客户在会话后呼叫呼叫中心的概率，以及3）数字会话被欺骗的概率。DCE在所有三个下游问题上都表现出了性能提升。 摘要：As financial services (FS) companies have experienced drastic technology driven changes, the availability of new data streams provides the opportunity for more comprehensive customer understanding. We propose Dynamic Customer Embeddings (DCE), a framework that leverages customers' digital activity and a wide range of financial context to learn dense representations of customers in the FS industry. Our method examines customer actions and pageviews within a mobile or web digital session, the sequencing of the sessions themselves, and snapshots of common financial features across our organization at the time of login. We test our customer embeddings using real world data in three prediction problems: 1) the intent of a customer in their next digital session, 2) the probability of a customer calling the call centers after a session, and 3) the probability of a digital session to be fraudulent. DCE showed performance lift in all three downstream problems.

【29】 Asymptotics for semi-discrete entropic optimal transport 标题：半离散熵最优运输问题的渐近性

作者：Jason M. Altschuler,Jonathan Niles-Weed,Austin J. Stromme 机构：MIT, NYU 链接：https://arxiv.org/abs/2106.11862 摘要：我们计算了连续到离散或半离散环境下熵最优运输问题最优解代价的精确二阶渐近性。与离散或连续情形相比，我们证明了这种展开式中的一阶项消失，而二阶项不消失，因此在半离散情形下，在逆正则化参数中，非正则解和正则解之间的代价差是二次的，前导常数显式依赖于测度之间最优无规映射不连续点的密度值。我们通过证明对偶问题解的新的点态收敛速度来发展这些结果，这可能是独立的。 摘要：We compute exact second-order asymptotics for the cost of an optimal solution to the entropic optimal transport problem in the continuous-to-discrete, or semi-discrete, setting. In contrast to the discrete-discrete or continuous-continuous case, we show that the first-order term in this expansion vanishes but the second-order term does not, so that in the semi-discrete setting the difference in cost between the unregularized and regularized solution is quadratic in the inverse regularization parameter, with a leading constant that depends explicitly on the value of the density at the points of discontinuity of the optimal unregularized map between the measures. We develop these results by proving new pointwise convergence rates of the solutions to the dual problem, which may be of independent interest.

【30】 Machine learning for risk assessment in gender-based crime 标题：机器学习在性别犯罪风险评估中的应用

作者：Ángel González-Prieto,Antonio Brú,Juan Carlos Nuño,José Luis González-Álvarez 机构： Universidad Aut´onoma de Madrid, Universidad Complutense de Madrid, Universidad Polit´ecnica de Madrid 备注：17 pages, 5 figures, 4 tables. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible 链接：https://arxiv.org/abs/2106.11847 摘要：基于性别的犯罪是当代社会最令人关注的祸害之一。为了从根本上消除这一威胁，世界各国政府投入了大量的经济和人力资源。尽管作出了这些努力，但准确预测性别暴力受害者再次受到攻击的风险仍然是一个非常困难的开放问题。开发新的方法来发布准确、公平和快速的预测，将使警察部队能够选择最适当的措施来防止再次犯罪。在这项工作中，我们建议应用机器学习（ML）技术来建立模型，准确预测性别暴力罪犯的再犯风险。这项工作贡献的相关性有三个方面：（i）提出的最大似然法优于现有的基于经典统计技术的风险评估算法；（ii）这项研究是通过一个官方专用数据库进行的，有40000多份关于性别暴力的报告，以及（iii）提出了两个新的质量指标，用于评估模型提供的有效警察保护及其产生的投入资源过载。此外，我们提出了一个混合模型，将统计预测方法与ML方法相结合，允许当局实现从先前存在的模型到基于ML的模型的平稳过渡。这种混合性质使决策过程能够在警察系统的效率和所采取的保护措施的积极性之间取得最佳平衡。 摘要：Gender-based crime is one of the most concerning scourges of contemporary society. Governments worldwide have invested lots of economic and human resources to radically eliminate this threat. Despite these efforts, providing accurate predictions of the risk that a victim of gender violence has of being attacked again is still a very hard open problem. The development of new methods for issuing accurate, fair and quick predictions would allow police forces to select the most appropriate measures to prevent recidivism. In this work, we propose to apply Machine Learning (ML) techniques to create models that accurately predict the recidivism risk of a gender-violence offender. The relevance of the contribution of this work is threefold: (i) the proposed ML method outperforms the preexisting risk assessment algorithm based on classical statistical techniques, (ii) the study has been conducted through an official specific-purpose database with more than 40,000 reports of gender violence, and (iii) two new quality measures are proposed for assessing the effective police protection that a model supplies and the overload in the invested resources that it generates. Additionally, we propose a hybrid model that combines the statistical prediction methods with the ML method, permitting authorities to implement a smooth transition from the preexisting model to the ML-based model. This hybrid nature enables a decision-making process to optimally balance between the efficiency of the police system and aggressiveness of the protection measures taken.

【31】 Emphatic Algorithms for Deep Reinforcement Learning 标题：深度强化学习的重点算法

作者：Ray Jiang,Tom Zahavy,Zhongwen Xu,Adam White,Matteo Hessel,Charles Blundell,Hado van Hasselt 机构： Department of ComputingScience, University of Alberta 备注：None 链接：https://arxiv.org/abs/2106.11779 摘要：非策略学习允许我们从不同行为策略产生的经验中学习可能的行为策略。时间差分（TD）学习算法在与函数逼近和非策略采样相结合时会变得不稳定，这被称为“致命的三元组”。强调时间差分（ETD（$\lambda$）算法通过对TD（$\lambda$）更新进行适当加权，确保了线性情况下的收敛性。在本文中，我们将强调方法的应用扩展到深度强化学习代理。我们发现，单纯地将ETD（$\lambda$）应用于流行的深度强化学习算法（使用前向视图多步返回）会导致较差的性能。然后，我们推导出新的重点算法用于此类算法的上下文中，并且我们证明它们在设计用于突出TD方法的不稳定性的小问题中提供了显著的好处。最后，我们在街机学习环境的经典Atari游戏中大规模应用这些算法时，观察到了性能的提高。 摘要：Off-policy learning allows us to learn about possible policies of behavior from experience generated by a different behavior policy. Temporal difference (TD) learning algorithms can become unstable when combined with function approximation and off-policy sampling - this is known as the ''deadly triad''. Emphatic temporal difference (ETD($\lambda$)) algorithm ensures convergence in the linear case by appropriately weighting the TD($\lambda$) updates. In this paper, we extend the use of emphatic methods to deep reinforcement learning agents. We show that naively adapting ETD($\lambda$) to popular deep reinforcement learning algorithms, which use forward view multi-step returns, results in poor performance. We then derive new emphatic algorithms for use in the context of such algorithms, and we demonstrate that they provide noticeable benefits in small problems designed to highlight the instability of TD methods. Finally, we observed improved performance when applying these algorithms at scale on classic Atari games from the Arcade Learning Environment.

【32】 Privacy Amplification via Iteration for Shuffled and Online PNSGD 标题：混洗PNSGD和在线PNSGD的迭代隐私放大

作者：Matteo Sordello,Zhiqi Bu,Jinshuo Dong 机构：Department of Statistics, University of Pennsylvania, Graduate Group in AMCS, University of Pennsylvania, IDEAL Institute, Northwestern University 链接：https://arxiv.org/abs/2106.11767 摘要：本文考虑了Feldman等人提出的迭代隐私放大框架，Asoodeh等人通过收缩系数对其进行了简化。本文主要研究了投影噪声随机梯度下降（PNSGD）算法在隐藏中间更新情况下的隐私保证问题。现有文献中的一个局限性是只研究了早期停止的PNSGD，而对于更广泛应用的PNSGD在随机数据集上的应用还没有结果。此外，当以在线方式接收新数据时，关于如何降低注入噪声的方案还没有被提出。在这项工作中，我们首先证明了随机PNSGD的隐私保证，当每个样本大小$n$的噪声是固定的，但当$n$增加时，它会以预定的速率减少，以达到隐私损失的收敛。然后，我们分析了在线设置，并为注入噪声的大小提供了一个更快的衰减方案，这也保证了隐私丢失的收敛性。 摘要：In this paper, we consider the framework of privacy amplification via iteration, which is originally proposed by Feldman et al. and subsequently simplified by Asoodeh et al. in their analysis via the contraction coefficient. This line of work focuses on the study of the privacy guarantees obtained by the projected noisy stochastic gradient descent (PNSGD) algorithm with hidden intermediate updates. A limitation in the existing literature is that only the early stopped PNSGD has been studied, while no result has been proved on the more widely-used PNSGD applied on a shuffled dataset. Moreover, no scheme has been yet proposed regarding how to decrease the injected noise when new data are received in an online fashion. In this work, we first prove a privacy guarantee for shuffled PNSGD, which is investigated asymptotically when the noise is fixed for each sample size $n$ but reduced at a predetermined rate when $n$ increases, in order to achieve the convergence of privacy loss. We then analyze the online setting and provide a faster decaying scheme for the magnitude of the injected noise that also guarantees the convergence of privacy loss.

【33】 A Deep Latent Space Model for Graph Representation Learning 标题：一种用于图表示学习的深度潜在空间模型

作者：Hanxuan Yang,Qingchao Kong,Wenji Mao 链接：https://arxiv.org/abs/2106.11721 摘要：图表示学习是关系数据建模的一个基本问题，对许多下游应用程序都有好处。传统的基于贝叶斯的图模型和最近发展起来的基于深度学习的GNN都存在着不实用性和不可解释性的问题，因此提出了无向图的组合模型。由于现实世界中有很大一部分图是有向图（其中无向图是特例），本文提出了一种有向图的深潜空间模型（DLSM），将传统的基于潜变量的生成模型引入到深度学习框架中。我们提出的模型由一个图卷积网络（GCN）编码器和一个随机译码器组成，这两个译码器通过分层变分自动编码器结构分层连接。通过利用节点随机因子对群落异质性程度进行具体建模，该模型在群落结构和异质性程度上都具有较好的解释性。为了快速推理，采用了随机梯度变分贝叶斯（SGVB）的非迭代识别模型，比传统的基于MCMC的方法具有更大的可扩展性。在真实数据集上的实验表明，该模型在学习可解释节点嵌入的同时，在链路预测和社区检测任务上都达到了最先进的性能。源代码位于https://github.com/upperr/DLSM. 摘要：Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from impracticability or lack interpretability, thus combined models for undirected graphs have been proposed to overcome the weaknesses. As a large portion of real-world graphs are directed graphs (of which undirected graphs are special cases), in this paper, we propose a Deep Latent Space Model (DLSM) for directed graphs to incorporate the traditional latent variable based generative model into deep learning frameworks. Our proposed model consists of a graph convolutional network (GCN) encoder and a stochastic decoder, which are layer-wise connected by a hierarchical variational auto-encoder architecture. By specifically modeling the degree heterogeneity using node random factors, our model possesses better interpretability in both community structure and degree heterogeneity. For fast inference, the stochastic gradient variational Bayes (SGVB) is adopted using a non-iterative recognition model, which is much more scalable than traditional MCMC-based methods. The experiments on real-world datasets show that the proposed model achieves the state-of-the-art performances on both link prediction and community detection tasks while learning interpretable node embeddings. The source code is available at https://github.com/upperr/DLSM.

【34】 Active Learning under Pool Set Distribution Shift and Noisy Data 标题：池集分布漂移和噪声数据下的主动学习

作者：Andreas Kirsch,Tom Rainforth,Yarin Gal 机构： Department of Computer Science 链接：https://arxiv.org/abs/2106.11719 摘要：主动学习对于更有效的深度学习至关重要。贝叶斯主动学习的研究重点是减少模型参数的不确定性。然而，我们发现，BALD会被与任务无关的分布外数据或垃圾数据卡住。我们研究了一种新的*预期预测信息增益（EPIG）*来处理池集的分布变化。EPIG减少了从测试数据分布中取样的未标记的评估集*上的*预测*的不确定性，该测试数据分布的分布可能不同于池集分布。在此基础上，我们提出了一种新的用于贝叶斯神经网络的EPIG-BALD获取函数，该函数选择样本来提高测试数据分布的性能，而不是选择样本来降低模型的不确定性，包括测试数据分布中密度较低的分布外区域。我们的方法在高维数据集上优于现有的贝叶斯主动学习方法，并且在现有方法失败的情况下避免了分布外的垃圾数据。 摘要：Active Learning is essential for more label-efficient deep learning. Bayesian Active Learning has focused on BALD, which reduces model parameter uncertainty. However, we show that BALD gets stuck on out-of-distribution or junk data that is not relevant for the task. We examine a novel *Expected Predictive Information Gain (EPIG)* to deal with distribution shifts of the pool set. EPIG reduces the uncertainty of *predictions* on an unlabelled *evaluation set* sampled from the test data distribution whose distribution might be different to the pool set distribution. Based on this, our new EPIG-BALD acquisition function for Bayesian Neural Networks selects samples to improve the performance on the test data distribution instead of selecting samples that reduce model uncertainty everywhere, including for out-of-distribution regions with low density in the test data distribution. Our method outperforms state-of-the-art Bayesian active learning methods on high-dimensional datasets and avoids out-of-distribution junk data in cases where current state-of-the-art methods fail.

【35】 Learning Dynamical Systems from Noisy Sensor Measurements using Multiple Shooting 标题：利用多次打靶法从噪声传感器测量中学习动态系统

作者：Armand Jordana,Justin Carpentier,Ludovic Righetti 机构：Tandon School of Engineering, New York University, Brooklyn, NY, Inria, Département d’informatique de l’ENS, École normale supérieure, CNRS, PSL Research, University, Paris, France 链接：https://arxiv.org/abs/2106.11712 摘要：动态系统建模在捕捉和理解复杂的物理现象中起着至关重要的作用。当物理模型不够精确或难以用解析公式描述时，可以使用神经网络等通用函数逼近器直接从传感器测量中获取系统动力学。到目前为止，学习这些神经网络参数的现有方法对大多数感兴趣的动力系统的固有不稳定性非常敏感，这反过来又妨碍了对很长序列的研究。在这项工作中，我们介绍了一个通用的和可扩展的方法，基于多重射击学习潜在的间接观测动态系统的表现。我们在直接从原始图像观察到的系统上实现了最先进的性能。此外，我们证明了我们的方法对噪声测量是鲁棒的，并且可以处理复杂的动力学系统，例如混沌系统。 摘要：Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function approximators such as neural networks to capture the system dynamics directly from sensor measurements. As for now, current methods to learn the parameters of these neural networks are highly sensitive to the inherent instability of most dynamical systems of interest, which in turn prevents the study of very long sequences. In this work, we introduce a generic and scalable method based on multiple shooting to learn latent representations of indirectly observed dynamical systems. We achieve state-of-the-art performances on systems observed directly from raw images. Further, we demonstrate that our method is robust to noisy measurements and can handle complex dynamical systems, such as chaotic ones.

【36】 A Unified Framework for Conservative Exploration 标题：保守探索的统一框架

作者：Yunchang Yang,Tianhao Wu,Han Zhong,Evrard Garcelon,Matteo Pirotta,Alessandro Lazaric,Liwei Wang,Simon S. Du 机构：Center for Data Sience, Peking University, University of Science and Technology of China, Facebook AI Research, Key Laboratory of Machine Perception, MOE, School of EECS, Peking University, University of Washington 链接：https://arxiv.org/abs/2106.11692 摘要：我们研究土匪和强化学习（RL）受保守约束，其中代理人被要求执行至少以及一个给定的基线策略。这种设置特别适用于现实世界的领域，包括数字营销、医疗保健、生产、金融等。对于多武装强盗、线性强盗和表格RL，在以前的工作中提出了专门的算法和理论分析。在本文中，我们提出了一个保守bandits和RL的统一框架，其中我们的核心技术是计算从运行基线策略中获得的必要和充分的预算。对于下界，我们的框架给出了一个黑盒约简，它将非保守环境中的某个下界转化为保守环境中的一个新下界。我们加强了现有的保守多武装土匪的下界，得到了保守线性土匪、表RL和低秩MDP的新下界。对于上界，我们的框架通过简单的分析将一个非保守的置信上限（UCB）算法转化为一个保守的算法。对于多武装土匪，线性土匪和表RL，我们的新上界收紧或匹配现有的显着更简单的分析。我们还得到了保守低秩MDP的一个新的上界。 摘要：We study bandits and reinforcement learning (RL) subject to a conservative constraint where the agent is asked to perform at least as well as a given baseline policy. This setting is particular relevant in real-world domains including digital marketing, healthcare, production, finance, etc. For multi-armed bandits, linear bandits and tabular RL, specialized algorithms and theoretical analyses were proposed in previous work. In this paper, we present a unified framework for conservative bandits and RL, in which our core technique is to calculate the necessary and sufficient budget obtained from running the baseline policy. For lower bounds, our framework gives a black-box reduction that turns a certain lower bound in the nonconservative setting into a new lower bound in the conservative setting. We strengthen the existing lower bound for conservative multi-armed bandits and obtain new lower bounds for conservative linear bandits, tabular RL and low-rank MDP. For upper bounds, our framework turns a certain nonconservative upper-confidence-bound (UCB) algorithm into a conservative algorithm with a simple analysis. For multi-armed bandits, linear bandits and tabular RL, our new upper bounds tighten or match existing ones with significantly simpler analyses. We also obtain a new upper bound for conservative low-rank MDP.

【37】 Repulsive Deep Ensembles are Bayesian 标题：排斥深度系综是贝叶斯系综

作者：Francesco D'Angelo,Vincent Fortuin 机构：ETH Zürich, Zürich, Switzerland 链接：https://arxiv.org/abs/2106.11642 摘要：深度集成由于其概念上的简单性和高效性，最近在深度学习社区中获得了广泛的应用。然而，保持用梯度下降法独立训练的集合成员之间的功能多样性是一个挑战。当添加更多集成成员时，这可能导致病态，例如集成性能饱和，这会收敛到单个模型的性能。此外，这不仅影响其预测的质量，而且更影响集合的不确定性估计，从而影响其对分布外数据的性能。我们假设这一限制可以通过阻止不同的系综成员崩溃为相同的功能来克服。为此，我们在深层系综的更新规则中引入了一个核化排斥项。我们证明，这种简单的修改不仅加强和保持了成员之间的多样性，而且更重要的是，将最大后验概率推理转化为适当的贝叶斯推理。也就是说，我们提出的斥力系综的训练动力学遵循一个具有真实后验概率的KL散度的Wasserstein梯度流。我们研究了权重空间和函数空间中的排斥项，并对它们与标准集合和贝叶斯基线在合成和真实预测任务中的性能进行了实证比较。 摘要：Deep ensembles have recently gained popularity in the deep learning community for their conceptual simplicity and efficiency. However, maintaining functional diversity between ensemble members that are independently trained with gradient descent is challenging. This can lead to pathologies when adding more ensemble members, such as a saturation of the ensemble performance, which converges to the performance of a single model. Moreover, this does not only affect the quality of its predictions, but even more so the uncertainty estimates of the ensemble, and thus its performance on out-of-distribution data. We hypothesize that this limitation can be overcome by discouraging different ensemble members from collapsing to the same function. To this end, we introduce a kernelized repulsive term in the update rule of the deep ensembles. We show that this simple modification not only enforces and maintains diversity among the members but, even more importantly, transforms the maximum a posteriori inference into proper Bayesian inference. Namely, we show that the training dynamics of our proposed repulsive ensembles follow a Wasserstein gradient flow of the KL divergence with the true posterior. We study repulsive terms in weight and function space and empirically compare their performance to standard ensembles and Bayesian baselines on synthetic and real-world prediction tasks.

【38】 Heterogeneous Treatment Effects in Regression Discontinuity Designs 标题：回归不连续设计中的异质性处理效应

作者：Ágoston Reguly 机构：Heterogeneous Treatment Effectsin Regression Discontinuity Design´Agoston RegulyCentral European UniversityJune 2 3 备注：36 pages, 8 tables, 8 figures 链接：https://arxiv.org/abs/2106.11640 摘要：提出了一种有监督的机器学习算法来揭示经典回归不连续（RD）设计中治疗效果的异质性。扩展Athey和Imbens（2016），我开发了一个构建诚实的“回归不连续树”的标准，其中树的每个叶子包含一个治疗的RD估计（由公共截止规则指定），条件是一些治疗前协变量的值。哪些协变量与获取治疗效果异质性相关是先验未知的，算法的任务是在不使推理失效的情况下发现它们。我通过Monte Carlo模拟研究了该方法的性能，并将其应用于Pop Eleches和Urquiola（2013）编制的数据集，以揭示罗马尼亚上更好中学的影响中的各种异质性来源。 摘要：The paper proposes a supervised machine learning algorithm to uncover treatment effect heterogeneity in classical regression discontinuity (RD) designs. Extending Athey and Imbens (2016), I develop a criterion for building an honest ``regression discontinuity tree'', where each leaf of the tree contains the RD estimate of a treatment (assigned by a common cutoff rule) conditional on the values of some pre-treatment covariates. It is a priori unknown which covariates are relevant for capturing treatment effect heterogeneity, and it is the task of the algorithm to discover them, without invalidating inference. I study the performance of the method through Monte Carlo simulations and apply it to the data set compiled by Pop-Eleches and Urquiola (2013) to uncover various sources of heterogeneity in the impact of attending a better secondary school in Romania.

【39】 Uniform-PAC Bounds for Reinforcement Learning with Linear Function Approximation 标题：线性函数逼近强化学习的一致PAC界

作者：Jiafan He,Dongruo Zhou,Quanquan Gu 机构：and 备注：30 pages 链接：https://arxiv.org/abs/2106.11612 摘要：研究了线性函数逼近下的强化学习。现有算法只能保证高概率遗憾和/或近似正确（PAC）样本复杂度，不能保证收敛到最优策略。为了克服现有算法的局限性，本文提出了一种新的算法FLUTE，该算法能以高概率均匀收敛到最优策略。一致PAC保证是文献中关于强化学习的最有力的保证，它可以直接表示PAC和高概率后悔界，使我们的算法优于现有的线性函数逼近算法。该算法的核心是一种新的极大极小值函数估计算法和一种从历史观测数据中选取训练样本的多级划分方案。这两种技术都是新的和独立的兴趣。 摘要：We study reinforcement learning (RL) with linear function approximation. Existing algorithms for this problem only have high-probability regret and/or Probably Approximately Correct (PAC) sample complexity guarantees, which cannot guarantee the convergence to the optimal policy. In this paper, in order to overcome the limitation of existing algorithms, we propose a new algorithm called FLUTE, which enjoys uniform-PAC convergence to the optimal policy with high probability. The uniform-PAC guarantee is the strongest possible guarantee for reinforcement learning in the literature, which can directly imply both PAC and high probability regret bounds, making our algorithm superior to all existing algorithms with linear function approximation. At the core of our algorithm is a novel minimax value function estimator and a multi-level partition scheme to select the training samples from historical observations. Both of these techniques are new and of independent interest.

【40】 Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models 标题：分布梯度匹配在不确定神经动力学模型学习中的应用

作者：Lenart Treven,Philippe Wenk,Florian Dörfler,Andreas Krause 机构：Learning and Adaptive Systems Group & Automatic Control Lab, ETH Z¨urich, Switzerland, ETH Z¨urich and Max Planck ETH Center for Learning Systems, Florian D¨orfler 链接：https://arxiv.org/abs/2106.11609 摘要：微分方程，特别是神经微分方程，是连续时间系统辨识中的关键技术。虽然许多确定性学习算法是基于伴随方法的数值积分设计的，但许多下游任务，如主动学习、强化学习探索、鲁棒控制或滤波，都需要对预测不确定性进行精确估计。在这项工作中，我们提出了一种新的方法来估计认知不确定的神经常微分方程，避免了数值积分的瓶颈。我们直接在状态空间中建模不确定性，而不是在ODE参数中建模不确定性。我们的算法-分布梯度匹配（DGM）-联合训练一个更平滑的模型和一个动力学模型，并通过最小化Wasserstein损失来匹配它们的梯度。我们的实验表明，与传统的基于数值积分的近似推理方法相比，我们的方法训练速度更快，预测以前看不到的轨迹速度更快，并且在神经ODEs的情况下，更准确。 摘要：Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the adjoint method, many downstream tasks such as active learning, exploration in reinforcement learning, robust control, or filtering require accurate estimates of predictive uncertainties. In this work, we propose a novel approach towards estimating epistemically uncertain neural ODEs, avoiding the numerical integration bottleneck. Instead of modeling uncertainty in the ODE parameters, we directly model uncertainties in the state space. Our algorithm - distributional gradient matching (DGM) - jointly trains a smoother and a dynamics model and matches their gradients via minimizing a Wasserstein loss. Our experiments show that, compared to traditional approximate inference methods based on numerical integration, our approach is faster to train, faster at predicting previously unseen trajectories, and in the context of neural ODEs, significantly more accurate.

【41】 Continuous-Depth Neural Models for Dynamic Graph Prediction 标题：动态图预测的连续深度神经模型

作者：Michael Poli,Stefano Massaroli,Clayton M. Rabideau,Junyoung Park,Atsushi Yamashita,Hajime Asama,Jinkyoo Park 机构： 2The University of Tokyo 3Syntensor 备注：Extended version of the workshop paper "Graph Neural Ordinary Differential Equations". arXiv admin note: substantial text overlap with arXiv:1911.07532 链接：https://arxiv.org/abs/2106.11581 摘要：介绍了连续深度图神经网络的结构。神经图微分方程（Neural-graph-differential equations，Neural-GDEs）被形式化为GNNs的对应形式，其中输入输出关系由GNN层的连续统一体决定，混合了离散拓扑结构和微分方程。该框架与静态GNN模型兼容，并通过混合动力系统理论扩展到动态和随机环境。在这里，神经GDE通过利用基本的动力学几何结构来提高性能，进一步引入了适应不规则采样数据的能力。结果证明了所提出的模型在交通量预测、遗传调控网络预测等方面的有效性。 摘要：We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN layers, blending discrete topological structures and differential equations. The proposed framework is shown to be compatible with static GNN models and is extended to dynamic and stochastic settings through hybrid dynamical system theory. Here, Neural GDEs improve performance by exploiting the underlying dynamics geometry, further introducing the ability to accommodate irregularly sampled data. Results prove the effectiveness of the proposed models across applications, such as traffic forecasting or prediction in genetic regulatory networks.

【42】 A stochastic linearized proximal method of multipliers for convex stochastic optimization with expectation constraints 标题：具有期望约束的凸随机优化问题的随机线性化乘子近似法

作者：Liwei Zhang,Yule Zhang,Jia Wu,Xiantao Xiao 机构：the date of receipt and acceptance should be inserted later 链接：https://arxiv.org/abs/2106.11577 摘要：研究了一类具有不等式凸期望约束的凸期望函数的极小化问题。本文提出了一种可计算的随机逼近型算法，即随机线性化近似乘子法来求解这类凸随机优化问题。该算法可以粗略地看作是随机逼近法和传统的近似乘子法的混合。在温和的条件下，我们证明了在适当选择算法参数的情况下，该算法对于目标约简和约束违反都具有$O（K^{-1/2}）$的预期收敛速度，其中$K$表示迭代次数。此外，我们还证明了该算法具有高概率的$O（\log（K）K^{-1/2}）$约束冲突界和$O（\log^{3/2}（K）K^{-1/2}）$目标界。初步的数值结果验证了该算法的有效性。 摘要：This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal method of multipliers, to solve this convex stochastic optimization problem. This algorithm can be roughly viewed as a hybrid of stochastic approximation and the traditional proximal method of multipliers. Under mild conditions, we show that this algorithm exhibits $O(K^{-1/2})$ expected convergence rates for both objective reduction and constraint violation if parameters in the algorithm are properly chosen, where $K$ denotes the number of iterations. Moreover, we show that, with high probability, the algorithm has $O(\log(K)K^{-1/2})$ constraint violation bound and $O(\log^{3/2}(K)K^{-1/2})$ objective bound. Some preliminary numerical results demonstrate the performance of the proposed algorithm.

【43】 Instance-Optimal Compressed Sensing via Posterior Sampling 标题：基于后验采样的实例最优压缩感知

作者：Ajil Jalal,Sushrut Karmalkar,Alexandros G. Dimakis,Eric Price 机构： 1University of Texas atAustin, Department of Electrical and Computer Engineering 2University of Texas at Austin, Department of ComputerScience 链接：https://arxiv.org/abs/2106.11438 摘要：我们描述了从已知先验分布提取的信号的压缩感知的测量复杂性，即使先验的支持是整个空间（而不是，比方说，稀疏向量）。对于高斯测量和信号的{any}先验分布，我们证明了后验采样估计器达到了接近最优的恢复保证。此外，只要分布估计（例如，来自可逆生成模型的估计）接近Wasserstein距离的真实分布，该结果对模型失配具有鲁棒性。我们利用Langevin动力学实现了深生成先验的后验抽样估计，并通过实证发现它比MAP产生了更为精确的多样性估计。 摘要：We characterize the measurement complexity of compressed sensing of signals drawn from a known prior distribution, even when the support of the prior is the entire space (rather than, say, sparse vectors). We show for Gaussian measurements and \emph{any} prior distribution on the signal, that the posterior sampling estimator achieves near-optimal recovery guarantees. Moreover, this result is robust to model mismatch, as long as the distribution estimate (e.g., from an invertible generative model) is close to the true distribution in Wasserstein distance. We implement the posterior sampling estimator for deep generative priors using Langevin dynamics, and empirically find that it produces accurate estimates with more diversity than MAP.

【44】 A Note on the Polynomial Ergodicity of the One-Dimensional Zig-Zag process 标题：关于一维Zig-Zag过程的多项式遍历性的注记

作者：G. Vasdekis,G. O. Roberts 备注：6 pages 链接：https://arxiv.org/abs/2106.11357 摘要：证明了重尾目标上一维Zig-Zag过程的多项式遍历性，并给出了该过程在以学生分布为目标时多项式收敛的精确阶。 摘要：We prove polynomial ergodicity for the one-dimensional Zig-Zag process on heavy tailed targets and identify the exact order of polynomial convergence of the process when targeting Student distributions.

【45】 Feedback Shaping: A Modeling Approach to Nurture Content Creation 标题：反馈塑造：培育内容创作的建模方法

作者：Ye Tu,Chun Lo,Yiping Yuan,Shaunak Chatterjee 机构：LinkedIn Corporation 备注：None 链接：https://arxiv.org/abs/2106.11312 摘要：社交媒体平台通过诸如newsfeed之类的推荐系统将内容创造者和内容消费者聚集在一起。到目前为止，此类推荐系统的重点主要是对内容消费者偏好进行建模，并对其体验进行优化。然而，同样重要的是，通过优先考虑创作者的兴趣来培育内容创作，因为高质量的内容形成了可持续参与和对话的种子，带来了新的消费者，同时保留了现有的消费者。在这项工作中，我们提出了一种建模方法来预测内容消费者的反馈如何激励创作者。然后，我们利用此模型通过重塑反馈分布来优化内容创建者的新闻提要体验，从而形成更活跃的内容生态系统。实际上，我们讨论了如何平衡消费者和创作者的用户体验，以及如何利用强大的网络效应进行在线A/B测试。我们在LinkedIn newsfeed上展示了一个已部署的用例，在该用例中，我们使用这种方法显著改进了内容创建，同时又不损害消费者的体验。 摘要：Social media platforms bring together content creators and content consumers through recommender systems like newsfeed. The focus of such recommender systems has thus far been primarily on modeling the content consumer preferences and optimizing for their experience. However, it is equally critical to nurture content creation by prioritizing the creators' interests, as quality content forms the seed for sustainable engagement and conversations, bringing in new consumers while retaining existing ones. In this work, we propose a modeling approach to predict how feedback from content consumers incentivizes creators. We then leverage this model to optimize the newsfeed experience for content creators by reshaping the feedback distribution, leading to a more active content ecosystem. Practically, we discuss how we balance the user experience for both consumers and creators, and how we carry out online A/B tests with strong network effects. We present a deployed use case on the LinkedIn newsfeed, where we used this approach to improve content creation significantly without compromising the consumers' experience.

【46】 Complexity-Free Generalization via Distributionally Robust Optimization 标题：基于分布式鲁棒优化的无复杂度泛化

作者：Henry Lam,Yibo Zeng 机构：Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 链接：https://arxiv.org/abs/2106.11180 摘要：在数据驱动优化和机器学习中，获得泛化界的方法大多建立在经验风险最小化（ERM）的基础上，而经验风险最小化在很大程度上依赖于假设类的函数复杂性。在本文中，我们提出了一种从分布式鲁棒优化（DRO）中获得这些解的界的替代方法，DRO是一种基于最坏情况分析和模糊集概念的数据驱动优化框架，用于捕获统计不确定性。与ERM中假设类的复杂性不同，我们的DRO界依赖于模糊集的几何结构及其与真损失函数的相容性。值得注意的是，当使用最大平均差异作为DRO距离度量时，我们的分析意味着，据我们所知，文献中的第一个推广界完全依赖于真实损失函数，完全没有任何复杂度度量或假设类的界限。 摘要：Established approaches to obtain generalization bounds in data-driven optimization and machine learning mostly build on solutions from empirical risk minimization (ERM), which depend crucially on the functional complexity of the hypothesis class. In this paper, we present an alternate route to obtain these bounds on the solution from distributionally robust optimization (DRO), a recent data-driven optimization framework based on worst-case analysis and the notion of ambiguity set to capture statistical uncertainty. In contrast to the hypothesis class complexity in ERM, our DRO bounds depend on the ambiguity set geometry and its compatibility with the true loss function. Notably, when using maximum mean discrepancy as a DRO distance metric, our analysis implies, to the best of our knowledge, the first generalization bound in the literature that depends solely on the true loss function, entirely free of any complexity measures or bounds on the hypothesis class.

【47】 On Stein Variational Neural Network Ensembles 标题：关于Stein变分神经网络集成

作者：Francesco D'Angelo,Vincent Fortuin,Florian Wenzel 机构：ETH Zürich, Zürich, Switzerland, Humboldt University of Berlin, Berlin, Germany 链接：https://arxiv.org/abs/2106.10760 摘要：深层神经网络的集合最近取得了巨大的成功，但它们并没有提供一个恰当的贝叶斯证明。此外，虽然它们允许对多个假设的预测进行平均，但它们不能保证它们的多样性，从而导致函数空间中的冗余解。相比之下，基于粒子的推理方法，如Stein变分梯度下降（SVGD），提供了一个贝叶斯框架，但依赖于核的选择来度量集合成员之间的相似性。在这项工作中，我们研究了不同的SVGD方法在权值空间，函数空间，以及在混合设置。我们比较了SVGD方法和其他基于集成的方法的理论特性，并评估了它们在合成任务和实际任务中的实证性能。我们发现使用函数核和混合核的SVGD可以克服深系综的限制。它改进了函数多样性和不确定性估计，更接近真实贝叶斯后验概率。此外，我们还表明，与标准的确定性更新相比，使用随机SVGD更新可以进一步提高性能。 摘要：Ensembles of deep neural networks have achieved great success recently, but they do not offer a proper Bayesian justification. Moreover, while they allow for averaging of predictions over several hypotheses, they do not provide any guarantees for their diversity, leading to redundant solutions in function space. In contrast, particle-based inference methods, such as Stein variational gradient descent (SVGD), offer a Bayesian framework, but rely on the choice of a kernel to measure the similarity between ensemble members. In this work, we study different SVGD methods operating in the weight space, function space, and in a hybrid setting. We compare the SVGD approaches to other ensembling-based methods in terms of their theoretical properties and assess their empirical performance on synthetic and real-world tasks. We find that SVGD using functional and hybrid kernels can overcome the limitations of deep ensembles. It improves on functional diversity and uncertainty estimation and approaches the true Bayesian posterior more closely. Moreover, we show that using stochastic SVGD updates, as opposed to the standard deterministic ones, can further improve the performance.

【48】 A measure of the importance of roads based on topography and traffic intensity 标题：根据地形和交通强度衡量道路重要性的一种方法

作者：Krzysztof J. Szajowski,Kinga Włodarczyk 机构： Wrocław University of Science and Technology 备注：35 pages, 7 figures 链接：https://arxiv.org/abs/2101.09382 摘要：考虑了街道交通的数学模型，该模型允许评估其各个路段对街道系统功能的重要性。基于合作博弈方法和可靠性理论，构造了适合的测度。主要目的是分析评估道路碎片重要性（等级）的方法，包括其功能。将考虑这些要素对整个系统有效无障碍的相关性。 摘要：Mathematical models of street traffic allowing assessment of the importance of their individual segments for the functionality of the street system is considering. Based on methods of cooperative games and the reliability theory the suitable measure is constructed. The main goal is to analyze methods for assessing the importance (rank) of road fragments, including their functions. A relevance of these elements for effective accessibility for the entire system will be considered.