在高维预测设置中，可靠地估计测试性能仍然具有挑战性。为了应对这一挑战，提出了一个新颖的性能估计框架。该框架称为Learn2Evaluate，是基于学习曲线的，它通过拟合平滑的单调曲线将测试性能描绘为样本量的函数。与常用的性能估计方法相比，Learn2esvaluate具有多个优势。首先，学习曲线提供了学习者的图形概述。该概述有助于评估添加培训样本的潜在优势，并且比固定子样本大小的性能估计值更完整地比较学习者。其次，学习曲线促进在总样本量而不是子样本大小的情况下估计性能。第三，LEALLE2ALE2允许计算理论上合理且有用的较低置信度结合。此外，可以通过执行偏置校正来拧紧这种结合。通过模拟研究和对OMICS数据的应用来说明LEAL2评论的好处。

交叉验证是一种广泛使用的技术来估计预测误差，但其行为很复杂且不完全理解。理想情况下，人们想认为，交叉验证估计手头模型的预测错误，适合训练数据。我们证明，普通最小二乘拟合的线性模型并非如此。相反，它估计模型的平均预测误差适合于同一人群提取的其他看不见的训练集。我们进一步表明，这种现象发生在大多数流行的预测误差估计中，包括数据拆分，自举和锦葵的CP。接下来，从交叉验证得出的预测误差的标准置信区间可能的覆盖范围远低于所需水平。由于每个数据点都用于训练和测试，因此每个折叠的测量精度之间存在相关性，因此方差的通常估计值太小。我们引入了嵌套的交叉验证方案，以更准确地估计该方差，并从经验上表明，在传统的交叉验证间隔失败的许多示例中，这种修改导致间隔大致正确覆盖。

In many applications, it is of interest to identify a parsimonious set of features, or panel, from multiple candidates that achieves a desired level of performance in predicting a response. This task is often complicated in practice by missing data arising from the sampling design or other random mechanisms. Most recent work on variable selection in missing data contexts relies in some part on a finite-dimensional statistical model, e.g., a generalized or penalized linear model. In cases where this model is misspecified, the selected variables may not all be truly scientifically relevant and can result in panels with suboptimal classification performance. To address this limitation, we propose a nonparametric variable selection algorithm combined with multiple imputation to develop flexible panels in the presence of missing-at-random data. We outline strategies based on the proposed algorithm that achieve control of commonly used error rates. Through simulations, we show that our proposal has good operating characteristics and results in panels with higher classification and variable selection performance compared to several existing penalized regression approaches in cases where a generalized linear model is misspecified. Finally, we use the proposed method to develop biomarker panels for separating pancreatic cysts with differing malignancy potential in a setting where complicated missingness in the biomarkers arose due to limited specimen volumes.

We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We analyze and compare, both empirically and theoretically, the two major variants of our conformal framework: full conformal inference and split conformal inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. As extensions, we develop a method for constructing valid in-sample prediction intervals called rank-one-out conformal inference, which has essentially the same computational efficiency as split conformal inference. We also describe an extension of our procedures for producing prediction bands with locally varying length, in order to adapt to heteroskedascity in the data. Finally, we propose a model-free notion of variable importance, called leave-one-covariate-out or LOCO inference. Accompanying this paper is an R package conformalInference that implements all of the proposals we have introduced. In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package.

预测一组结果 - 而不是独特的结果 - 是统计学习中不确定性定量的有前途的解决方案。尽管有关于构建具有统计保证的预测集的丰富文献，但适应未知的协变量转变（实践中普遍存在的问题）还是一个严重的未解决的挑战。在本文中，我们表明具有有限样本覆盖范围保证的预测集是非信息性的，并提出了一种新型的无灵活分配方法PredSet-1Step，以有效地构建了在未知协方差转移下具有渐近覆盖范围保证的预测集。我们正式表明我们的方法是\ textIt {渐近上可能是近似正确}，对大型样本的置信度有很好的覆盖误差。我们说明，在南非队列研究中，它在许多实验和有关HIV风险预测的数据集中实现了名义覆盖范围。我们的理论取决于基于一般渐近线性估计器的WALD置信区间覆盖范围的融合率的新结合。

重要的加权是调整蒙特卡洛集成以说明错误分布中抽取的一种一般方法，但是当重要性比的右尾巴较重时，最终的估计值可能是高度可变的。当目标分布的某些方面无法通过近似分布捕获，在这种情况下，可以通过修改极端重要性比率来获得更稳定的估计。我们提出了一种新的方法，该方法使用拟合模拟重要性比率的上尾的广义帕累托分布来稳定重要性权重。该方法在经验上的性能要比现有方法稳定重要性采样估计值更好，包括稳定的有效样本量估计，蒙特卡洛误差估计和收敛诊断。提出的帕累托$ \ hat {k} $有限样本收敛率诊断对任何蒙特卡洛估计器都有用。

Model-X条件随机测试是有条件独立性测试的通用框架，解锁了新的可能性，以发现与感兴趣的响应有条件相关的特征，同时控制I型错误率。该测试的一个吸引力的优势是，它可以与任何机器学习模型一起使用来设计强大的测试统计数据。反过来，Model-X文献中的常见实践是使用机器学习模型形成测试统计量，经过培训，以最大程度地提高预测精度，希望能够获得良好的功率测试。但是，这里的理想目标是推动模型（在训练期间）以最大程度地提高测试功能，而不仅仅是预测精度。在本文中，我们通过首次引入新型模型拟合方案来弥合这一差距，这些方案旨在明确提高Model-X测试的功能。这是通过引入新的成本函数来完成的，该功能旨在最大化用于衡量有条件独立性违反的测试统计量。使用合成和真实的数据集，我们证明了我们提出的损失函数与各种基本预测模型（Lasso，弹性网和深神经网络）的组合始终增加所获得的正确发现的数量，同时维持I型错误率下的I型错误率控制。

大型观察数据越来越多地提供健康，经济和社会科学等学科，研究人员对因果问题而不是预测感兴趣。在本文中，从旨在调查参与学校膳食计划对健康指标的实证研究，研究了使用非参数回归的方法估算异质治疗效果的问题。首先，我们介绍了与观察或非完全随机数据进行因果推断相关的设置和相关的问题，以及如何在统计学习工具的帮助下解决这些问题。然后，我们审查并制定现有最先进的框架的统一分类，允许通过非参数回归模型来估算单个治疗效果。在介绍模型选择问题的简要概述后，我们说明了一些关于三种不同模拟研究的方法的性能。我们通过展示一些关于学校膳食计划数据的实证分析的一些方法的使用来结束。

我们提出了一种基于配对构造的模型组件的广义添加剂模型，并以预测为主要目的。该模型组件的设计使我们的模型可以捕获响应协变量之间关系中潜在的复杂相互作用效应。此外，我们的模型不需要连续协变量的离散化，因此适用于许多此类协变量的问题。此外，我们设计了一种受梯度增强启发的拟合算法，以及通过对模型空间和近似值的限制来加快时间对比计算的限制，用于模型选择和模型选择的有效程序。除了我们的模型在更高维度中成为现实的选择绝对必要外，这些技术还可以作为设计有效模型选择算法的其他类型的Copula回归模型的基础。我们已经在模拟研究中探索了我们方法的特征，特别是将其与自然替代方案进行比较，例如逻辑回归，经典增强模型和受到惩罚的逻辑回归。我们还展示了我们在威斯康星州乳腺癌数据集和波士顿住房数据集上的方法。结果表明，即使离散协变量的比例很高，我们的方法的预测性能要么比其他方法更好或可比其他方法媲美。

R包Doubleml实现了Chernozhukov等人的双重/辩护机器学习框架。 （2018）。它提供了基于机器学习方法的因果模型中估计参数的功能。双机器学习框架由三个关键成分组成：Neyman正交性，高质量的机器学习估计和样品拆分。可以通过MLR3生态系统中可用的各种最新机器学习方法来执行滋扰组件的估计。 Doubleml使得可以在各种因果模型中进行推断，包括部分线性和交互式回归模型及其扩展到仪器变量估计。 Doubleml的面向对象的实现为模型规范具有很高的灵活性，并使其易于扩展。本文是对双机器学习框架和R软件包DOUBLEML的介绍。在具有模拟和真实数据集的可再现代码示例中，我们演示了Doubleml用户如何基于机器学习方法执行有效的推断。

我们提出了一种估计具有标称分类数据的高维线性模型的方法。我们的估算器，称为范围，通过使其相应的系数完全相等来融合水平。这是通过对分类变量的系数的阶数统计之间的差异之间的差异来实现这一点，从而聚类系数。我们提供了一种算法，用于精确和有效地计算在具有潜在许多级别的单个变量的情况下的总体上的最小值的全局最小值，并且在多变量情况下在块坐标血管下降过程中使用它。我们表明，利用未知级别融合的Oracle最小二乘解决方案是具有高概率的坐标血缘的极限点，只要真正的级别具有一定的最小分离;已知这些条件在单变量案例中最小。我们展示了在一系列实际和模拟数据集中的范围的有利性能。 R包的R包Catreg实现线性模型的范围，也可以在CRAN上提供逻辑回归的版本。

预测风险评分越来越多地用于指导复杂环境（尤其是医疗保健）中的临床或其他干预措施。直接更新用于指导干预措施的风险评分会导致风险估计。我们建议使用“保留集”（未接受风险评分引导干预措施的人口子集）进行更新，以防止这种情况。由于保留集中的样本并不能从风险预测中受益，因此其规模必须权衡更新的风险评分的性能，同时最大程度地减少被保留样品的数量。我们证明，这种方法的表现优于简单的替代方案，并且通过定义一般的损失函数描述了可以轻松识别最佳保持尺寸（OHS）的条件。我们引入了OHS估计的参数和半参数算法，并证明了它们在近期对先兆子痫的风险评分上的使用。基于这些结果，我们认为保留集是安全，可行且易于实施的手段，可以安全地更新预测风险得分。

在存在分组的协变量的情况下，我们提出了一个增强框架，以允许在组内和之间实施稀疏性。通过使用调整后的自由度同时使用组件和小组梯度提升，可以通过增强来拟合具有与稀疏组套索相似的模型。我们表明，组内和组间稀疏性可以通过混合参数来控制，并讨论稀疏组套索中混合参数的相似性和差异。通过模拟，基因数据以及农业数据，我们显示了该估计器的有效性和预测性竞争力。数据和模拟表明，在存在分组变量的情况下，稀疏组增强的使用与偏差的变量选择较少，并且与组件的增强相比，可预测性较小。此外，我们提出了一种减少偏见通过自由程度来提高组件的偏见的方法。

Statistical risk assessments inform consequential decisions such as pretrial release in criminal justice, and loan approvals in consumer finance. Such risk assessments make counterfactual predictions, predicting the likelihood of an outcome under a proposed decision (e.g., what would happen if we approved this loan?). A central challenge, however, is that there may have been unmeasured confounders that jointly affected past decisions and outcomes in the historical data. This paper proposes a tractable mean outcome sensitivity model that bounds the extent to which unmeasured confounders could affect outcomes on average. The mean outcome sensitivity model partially identifies the conditional likelihood of the outcome under the proposed decision, popular predictive performance metrics (e.g., accuracy, calibration, TPR, FPR), and commonly-used predictive disparities. We derive their sharp identified sets, and we then solve three tasks that are essential to deploying statistical risk assessments in high-stakes settings. First, we propose a doubly-robust learning procedure for the bounds on the conditional likelihood of the outcome under the proposed decision. Second, we translate our estimated bounds on the conditional likelihood of the outcome under the proposed decision into a robust, plug-in decision-making policy. Third, we develop doubly-robust estimators of the bounds on the predictive performance of an existing risk assessment.

Learning curves provide insight into the dependence of a learner's generalization performance on the training set size. This important tool can be used for model selection, to predict the effect of more training data, and to reduce the computational complexity of model training and hyperparameter tuning. This review recounts the origins of the term, provides a formal definition of the learning curve, and briefly covers basics such as its estimation. Our main contribution is a comprehensive overview of the literature regarding the shape of learning curves. We discuss empirical and theoretical evidence that supports well-behaved curves that often have the shape of a power law or an exponential. We consider the learning curves of Gaussian processes, the complex shapes they can display, and the factors influencing them. We draw specific attention to examples of learning curves that are ill-behaved, showing worse learning performance with more training data. To wrap up, we point out various open problems that warrant deeper empirical and theoretical investigation. All in all, our review underscores that learning curves are surprisingly diverse and no universal model can be identified.

Integrative analysis of data from multiple sources is critical to making generalizable discoveries. Associations that are consistently observed across multiple source populations are more likely to be generalized to target populations with possible distributional shifts. In this paper, we model the heterogeneous multi-source data with multiple high-dimensional regressions and make inferences for the maximin effect (Meinshausen, B{\"u}hlmann, AoS, 43(4), 1801--1830). The maximin effect provides a measure of stable associations across multi-source data. A significant maximin effect indicates that a variable has commonly shared effects across multiple source populations, and these shared effects may be generalized to a broader set of target populations. There are challenges associated with inferring maximin effects because its point estimator can have a non-standard limiting distribution. We devise a novel sampling method to construct valid confidence intervals for maximin effects. The proposed confidence interval attains a parametric length. This sampling procedure and the related theoretical analysis are of independent interest for solving other non-standard inference problems. Using genetic data on yeast growth in multiple environments, we demonstrate that the genetic variants with significant maximin effects have generalizable effects under new environments.

无穷小夹刀是一种估计参数模型方差的通用方法，最近也用于某些集合方法。在本文中，我们扩展了无穷小折刀，以估计任意两种模型之间的协方差。这可用于量化模型组合的不确定性，或构建测试统计信息，以比较使用相同训练数据集拟合的模型的不同模型或组合。本文中的具体示例使用了随机森林和M估计剂等模型的增强组合。我们还研究了其在XGBOOST模型的神经网络和集合上的应用。我们通过广泛的模拟及其在北京住房数据中的应用来说明差异估计的疗效，并证明了无穷小折刀协方差估算的理论一致性。

在制定政策指南时，随机对照试验（RCT）代表了黄金标准。但是，RCT通常是狭窄的，并且缺乏更广泛的感兴趣人群的数据。这些人群中的因果效应通常是使用观察数据集估算的，这可能会遭受未观察到的混杂和选择偏见。考虑到一组观察估计（例如，来自多项研究），我们提出了一个试图拒绝偏见的观察性估计值的元偏值。我们使用验证效应，可以从RCT和观察数据中推断出的因果效应。在拒绝未通过此测试的估计器之后，我们对RCT中未观察到的亚组的外推性效应产生了保守的置信区间。假设至少一个观察估计量在验证和外推效果方面是渐近正常且一致的，我们为我们算法输出的间隔的覆盖率概率提供了保证。为了促进在跨数据集的因果效应运输的设置中，我们给出的条件下，即使使用灵活的机器学习方法用于估计滋扰参数，群体平均治疗效应的双重稳定估计值也是渐近的正常。我们说明了方法在半合成和现实世界数据集上的特性，并表明它与标准的荟萃分析技术相比。

In various fields of data science, researchers are often interested in estimating the ratio of conditional expectation functions (CEFR). Specifically in causal inference problems, it is sometimes natural to consider ratio-based treatment effects, such as odds ratios and hazard ratios, and even difference-based treatment effects are identified as CEFR in some empirically relevant settings. This chapter develops the general framework for estimation and inference on CEFR, which allows the use of flexible machine learning for infinite-dimensional nuisance parameters. In the first stage of the framework, the orthogonal signals are constructed using debiased machine learning techniques to mitigate the negative impacts of the regularization bias in the nuisance estimates on the target estimates. The signals are then combined with a novel series estimator tailored for CEFR. We derive the pointwise and uniform asymptotic results for estimation and inference on CEFR, including the validity of the Gaussian bootstrap, and provide low-level sufficient conditions to apply the proposed framework to some specific examples. We demonstrate the finite-sample performance of the series estimator constructed under the proposed framework by numerical simulations. Finally, we apply the proposed method to estimate the causal effect of the 401(k) program on household assets.

In many high-dimensional prediction or classification tasks, complementary data on the features are available, e.g. prior biological knowledge on (epi)genetic markers. Here we consider tasks with numerical prior information that provide an insight into the importance (weight) and the direction (sign) of the feature effects, e.g. regression coefficients from previous studies. We propose an approach for integrating multiple sources of such prior information into penalised regression. If suitable co-data are available, this improves the predictive performance, as shown by simulation and application. The proposed method is implemented in the R package `transreg' (https://github.com/lcsb-bds/transreg).