尽管在机器学习的方法论核心中是一个问题，但如何比较分类器仍未达成一致的共识。每个比较框架都面临着（至少）三个基本挑战：质量标准的多样性，数据集的多样性以及选择数据集选择的随机性/任意性。在本文中，我们通过采用决策理论的最新发展，为生动的辩论增添了新的观点。我们最终的框架基于所谓的偏好系统，通过广义的随机优势概念对分类器进行排名，该概念强大地绕过了繁琐的，甚至通常是自相矛盾的，对聚合的依赖。此外，我们表明，可以通过解决易于手柄的线性程序和通过适应的两样本观察随机化测试进行统计测试来实现广泛的随机优势。这确实产生了一个有力的框架，可以同时相对于多个质量标准进行分类器的统计比较。我们在模拟研究和标准基准数据集中说明和研究我们的框架。

The quality of consequences in a decision making problem under (severe) uncertainty must often be compared among different targets (goals, objectives) simultaneously. In addition, the evaluations of a consequence's performance under the various targets often differ in their scale of measurement, classically being either purely ordinal or perfectly cardinal. In this paper, we transfer recent developments from abstract decision theory with incomplete preferential and probabilistic information to this multi-target setting and show how -- by exploiting the (potentially) partial cardinal and partial probabilistic information -- more informative orders for comparing decisions can be given than the Pareto order. We discuss some interesting properties of the proposed orders between decision options and show how they can be concretely computed by linear optimization. We conclude the paper by demonstrating our framework in an artificial (but quite real-world) example in the context of comparing algorithms under different performance measures.

While methods for comparing two learning algorithms on a single data set have been scrutinized for quite some time already, the issue of statistical tests for comparisons of more algorithms on multiple data sets, which is even more essential to typical machine learning studies, has been all but ignored. This article reviews the current practice and then theoretically and empirically examines several suitable tests. Based on that, we recommend a set of simple, yet safe and robust non-parametric tests for statistical comparisons of classifiers: the Wilcoxon signed ranks test for comparison of two classifiers and the Friedman test with the corresponding post-hoc tests for comparison of more classifiers over multiple data sets. Results of the latter can also be neatly presented with the newly introduced CD (critical difference) diagrams.

本文提出了一个贝叶斯模型，以比较任何度量的多个数据集上的多种算法。该模型基于Bradley-Terry模型，该模型计算出一种算法在不同数据集上的性能要好于另一个算法的次数。由于其贝叶斯基础，贝叶斯布拉德利·特里模型（BBT）的特征与经常主义的方法不同，可以比较多个数据集上的多种算法，例如Demsar（2006）对平均等级的测试，以及Benavoli等人。 （2016）多个成对的Wilcoxon测试，具有P-调整程序。特别是，贝叶斯的方法允许对算法发表更多细微的陈述，而不是声称差异是统计学意义的。贝叶斯的方法还允许定义何时出于实际目的或实际等效区域（绳索）等效的何时等效。与Benavoli等人提出的贝叶斯签名的等级比较程序不同。 （2017年），我们的方法可以为任何度量标准定义绳索，因为它基于概率声明，而不是基于该度量的差异。本文还提出了一个局部绳索概念，该概念评估了在某些交叉验证中对某些其他算法的平均值的平均度量之间的正差异是否应真正被视为基于效应大小的第一种算法比第二个算法更好。该局部绳索提案与贝叶斯的使用无关，可以根据等级的常见方式使用。可以使用实现BBT的R软件包和Python程序。

Selecting a minimal feature set that is maximally informative about a target variable is a central task in machine learning and statistics. Information theory provides a powerful framework for formulating feature selection algorithms -- yet, a rigorous, information-theoretic definition of feature relevancy, which accounts for feature interactions such as redundant and synergistic contributions, is still missing. We argue that this lack is inherent to classical information theory which does not provide measures to decompose the information a set of variables provides about a target into unique, redundant, and synergistic contributions. Such a decomposition has been introduced only recently by the partial information decomposition (PID) framework. Using PID, we clarify why feature selection is a conceptually difficult problem when approached using information theory and provide a novel definition of feature relevancy and redundancy in PID terms. From this definition, we show that the conditional mutual information (CMI) maximizes relevancy while minimizing redundancy and propose an iterative, CMI-based algorithm for practical feature selection. We demonstrate the power of our CMI-based algorithm in comparison to the unconditional mutual information on benchmark examples and provide corresponding PID estimates to highlight how PID allows to quantify information contribution of features and their interactions in feature-selection problems.

本文开发了新型的保形方法，以测试是否从与参考集相同的分布中采样了新的观察结果。以创新的方式将感应性和偏置的共形推断融合，所描述的方法可以以原则性的方式基于已知的分布式数据的依赖侧信息重新权重标准p值，并且可以自动利用最强大的优势来自任何一级和二进制分类器的模型。该解决方案可以通过样品分裂或通过新颖的转置交叉验证+方案来实现，该方案与现有的交叉验证方法相比，由于更严格的保证，这也可能在共形推理的其他应用中有用。在研究错误的发现率控制和在具有几个可能的离群值的多个测试框架内的虚假发现率控制和功率之后，提出的解决方案被证明通过模拟以及用于图像识别和表格数据的应用超过了标准的共形P值。

Virtually all machine learning tasks are characterized using some form of loss function, and "good performance" is typically stated in terms of a sufficiently small average loss, taken over the random draw of test data. While optimizing for performance on average is intuitive, convenient to analyze in theory, and easy to implement in practice, such a choice brings about trade-offs. In this work, we survey and introduce a wide variety of non-traditional criteria used to design and evaluate machine learning algorithms, place the classical paradigm within the proper historical context, and propose a view of learning problems which emphasizes the question of "what makes for a desirable loss distribution?" in place of tacit use of the expected loss.

We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task? And how can clustering results be validated? Connectivity-based versus prototype-based approaches are reflected in the context of several popular methods: single-linkage, spectral embedding, k-means, and Gaussian mixtures are discussed as well as the density-based protocols (H)DBSCAN, Jarvis-Patrick, CommonNN, and density-peaks.

我们基于电子价值开发假设检测理论，这是一种与p值不同的证据，允许毫不费力地结合来自常见场景中的几项研究的结果，其中决定执行新研究可能取决于以前的结果。基于E-V值的测试是安全的，即它们在此类可选的延续下保留I型错误保证。我们将增长速率最优性（GRO）定义为可选的连续上下文中的电力模拟，并且我们展示了如何构建GRO E-VARIABLE，以便为复合空缺和替代，强调模型的常规测试问题，并强调具有滋扰参数的模型。 GRO E值采取具有特殊前瞻的贝叶斯因子的形式。我们使用几种经典示例说明了该理论，包括一个样本安全T检验（其中右哈尔前方的右手前锋为GE）和2x2差价表（其中GRE之前与标准前沿不同）。分享渔业，奈曼和杰弗里斯·贝叶斯解释，电子价值观和相应的测试可以提供所有三所学校的追随者可接受的方法。

无论是在功能选择的领域还是可解释的AI领域，都有基于其重要性的“排名”功能的愿望。然后可以将这种功能重要的排名用于：（1）减少数据集大小或（2）解释机器学习模型。但是，在文献中，这种特征排名没有以系统的，一致的方式评估。许多论文都有不同的方式来争论哪些具有重要性排名最佳的特征。本文通过提出一种新的评估方法来填补这一空白。通过使用合成数据集，可以事先知道特征重要性得分，从而可以进行更系统的评估。为了促进使用新方法的大规模实验，在Python建造了一个名为FSEVAL的基准测定框架。该框架允许并行运行实验，并在HPC系统上的计算机上分布。通过与名为“权重和偏见”的在线平台集成，可以在实时仪表板上进行交互探索图表。该软件作为开源软件发布，并在PYPI平台上以包裹发行。该研究结束时，探索了一个这样的大规模实验，以在许多方面找到参与算法的优势和劣势。

机器学习通常以经典的概率理论为前提，这意味着聚集是基于期望的。现在有多种原因可以激励人们将经典概率理论作为机器学习的数学基础。我们系统地检查了一系列强大而丰富的此类替代品，即各种称为光谱风险度量，Choquet积分或Lorentz规范。我们提出了一系列的表征结果，并演示了使这个光谱家族如此特别的原因。在此过程中，我们证明了所有连贯的风险度量的自然分层，从它们通过利用重新安排不变性Banach空间理论的结果来诱导的上层概率。我们凭经验证明了这种新的不确定性方法如何有助于解决实用的机器学习问题。

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often referred to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of attempts so far at handling uncertainty in general and formalizing this distinction in particular.

我们查看模型可解释性的特定方面：模型通常需要限制在大小上才能被认为是可解释的，例如，深度5的决策树比深度50中的一个更容易解释。但是，较小的模型也倾向于高偏见。这表明可解释性和准确性之间的权衡。我们提出了一种模型不可知论技术，以最大程度地减少这种权衡。我们的策略是首先学习甲骨文，这是培训数据上高度准确的概率模型。 Oracle预测的不确定性用于学习培训数据的抽样分布。然后，对使用此分布获得的数据样本进行了可解释的模型，通常会导致精确度明显更高。我们将抽样策略作为优化问题。我们的解决方案1具有以下关键的有利属性：（1）它使用固定数量的七个优化变量，而与数据的维度（2）无关，它是模型不可知的 - 因为可解释的模型和甲骨文都可能属于任意性模型家族（3）它具有模型大小的灵活概念，并且可以容纳向量大小（4）它是一个框架，使其能够从优化领域的进度中受益。我们还提出了以下有趣的观察结果：（a）通常，小型模型大小的最佳训练分布与测试分布不同； （b）即使可解释的模型和甲骨文来自高度截然不同的模型家族，也存在这种效果：我们通过使用封闭的复发单位网络作为甲骨文来提高决策树的序列分类精度，从而在文本分类任务上显示此效果。使用字符n-grams； （c）对于模型，我们的技术可用于确定给定样本量的最佳训练样本。

大多数机器学习算法由一个或多个超参数配置，必须仔细选择并且通常会影响性能。为避免耗时和不可递销的手动试验和错误过程来查找性能良好的超参数配置，可以采用各种自动超参数优化（HPO）方法，例如，基于监督机器学习的重新采样误差估计。本文介绍了HPO后，本文审查了重要的HPO方法，如网格或随机搜索，进化算法，贝叶斯优化，超带和赛车。它给出了关于进行HPO的重要选择的实用建议，包括HPO算法本身，性能评估，如何将HPO与ML管道，运行时改进和并行化结合起来。这项工作伴随着附录，其中包含关于R和Python的特定软件包的信息，以及用于特定学习算法的信息和推荐的超参数搜索空间。我们还提供笔记本电脑，这些笔记本展示了这项工作的概念作为补充文件。

由于其出色的经验表现，随机森林是过去十年中使用的机器学习方法之一。然而，由于其黑框的性质，在许多大数据应用中很难解释随机森林的结果。量化各个特征在随机森林中的实用性可以大大增强其解释性。现有的研究表明，一些普遍使用的特征对随机森林的重要性措施遭受了偏见问题。此外，对于大多数现有方法，缺乏全面的规模和功率分析。在本文中，我们通过假设检验解决了问题，并提出了一个自由化特征 - 弥散性相关测试（事实）的框架，以评估具有偏见性属性的随机森林模型中给定特征的重要性，我们零假设涉及该特征是否与所有其他特征有条件地独立于响应。关于高维随机森林一致性的一些最新发展，对随机森林推断的这种努力得到了赋予的能力。在存在功能依赖性的情况下，我们的事实测试的香草版可能会遇到偏见问题。我们利用偏置校正的不平衡和调节技术。我们通过增强功率的功能转换将合奏的想法进一步纳入事实统计范围。在相当普遍的具有依赖特征的高维非参数模型设置下，我们正式确定事实可以提供理论上合理的随机森林具有P值，并通过非催化分析享受吸引人的力量。新建议的方法的理论结果和有限样本优势通过几个模拟示例和与Covid-19的经济预测应用进行了说明。

经典的错误发现率（FDR）控制程序提供了强大而可解释的保证，而它们通常缺乏灵活性。另一方面，最近的机器学习分类算法是基于随机森林（RF）或神经网络（NN）的算法，具有出色的实践表现，但缺乏解释和理论保证。在本文中，我们通过引入新的自适应新颖性检测程序（称为Adadetect）来使这两个相遇。它将多个测试文献的最新作品范围扩展到高维度的范围，尤其是Yang等人的范围。 （2021）。显示AD​​ADETECT既可以强烈控制FDR，又具有在特定意义上模仿甲骨文之一的力量。理论结果，几个基准数据集上的数值实验以及对天体物理数据的应用，我们的方法的兴趣和有效性得到了证明。特别是，虽然可以将AdadEtect与任何分类器结合使用，但它在带有RF的现实世界数据集以及带有NN的图像上特别有效。

Network-based analyses of dynamical systems have become increasingly popular in climate science. Here we address network construction from a statistical perspective and highlight the often ignored fact that the calculated correlation values are only empirical estimates. To measure spurious behaviour as deviation from a ground truth network, we simulate time-dependent isotropic random fields on the sphere and apply common network construction techniques. We find several ways in which the uncertainty stemming from the estimation procedure has major impact on network characteristics. When the data has locally coherent correlation structure, spurious link bundle teleconnections and spurious high-degree clusters have to be expected. Anisotropic estimation variance can also induce severe biases into empirical networks. We validate our findings with ERA5 reanalysis data. Moreover we explain why commonly applied resampling procedures are inappropriate for significance evaluation and propose a statistically more meaningful ensemble construction framework. By communicating which difficulties arise in estimation from scarce data and by presenting which design decisions increase robustness, we hope to contribute to more reliable climate network construction in the future.

Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension $d$ while letting the sample size $n$ increase to infinity. Recently, much effort has been dedicated towards understanding how these methods behave in high-dimensional settings, where $d$ and $n$ both increase to infinity together. This often leads to different inference procedures, depending on the assumptions about the dimensionality, leaving the practitioner in a bind: given a dataset with 100 samples in 20 dimensions, should they calibrate by assuming $n \gg d$, or $d/n \approx 0.2$? This paper considers the goal of dimension-agnostic inference; developing methods whose validity does not depend on any assumption on $d$ versus $n$. We introduce an approach that uses variational representations of existing test statistics along with sample splitting and self-normalization to produce a new test statistic with a Gaussian limiting distribution, regardless of how $d$ scales with $n$. The resulting statistic can be viewed as a careful modification of degenerate U-statistics, dropping diagonal blocks and retaining off-diagonal blocks. We exemplify our technique for some classical problems including one-sample mean and covariance testing, and show that our tests have minimax rate-optimal power against appropriate local alternatives. In most settings, our cross U-statistic matches the high-dimensional power of the corresponding (degenerate) U-statistic up to a $\sqrt{2}$ factor.

分类链是一种用于在多标签分类中建模标签依赖性的有效技术。但是，该方法需要标签的固定静态顺序。虽然理论上，任何顺序都足够了，实际上，该订单对最终预测的质量具有大量影响。动态分类链表示每个实例对分类的想法，可以动态选择预测标签的顺序。这种方法的天真实现的复杂性是禁止的，因为它需要训练一系列分类器，以满足标签的每种可能置换。为了有效地解决这个问题，我们提出了一种基于随机决策树的新方法，该方法可以动态地选择每个预测的标签排序。我们凭经验展示了下一个标签的动态选择，通过在否则不变的随机决策树模型下使用静态排序。 ％和实验环境。此外，我们还展示了基于极端梯度提升树的替代方法，其允许更具目标的动态分级链训练。我们的结果表明，该变体优于随机决策树和其他基于树的多标签分类方法。更重要的是，动态选择策略允许大大加速培训和预测。

We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD). We present two distributionfree tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.