我们基于从多个数据集的合并信息介绍了一种反事实推断的方法。我们考虑了统计边际问题的因果重新重新制定:鉴于边际结构因果模型(SCM)的集合在不同但重叠的变量集上,请确定与边际相反一致的关节SCMS集。我们使用响应函数配方对分类SCM进行了形式化这种方法,并表明它降低了允许的边际和关节SCM的空间。因此,我们的工作通过其他变量突出了一种通过其他变量的新模式,与统计数据相反。
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This review presents empirical researchers with recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called "causal effects" or "policy evaluation") (2) queries about probabilities of counterfactuals, (including assessment of "regret," "attribution" or "causes of effects") and (3) queries about direct and indirect effects (also known as "mediation"). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both.
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基于AI和机器学习的决策系统已在各种现实世界中都使用,包括医疗保健,执法,教育和金融。不再是牵强的,即设想一个未来,自治系统将推动整个业务决策,并且更广泛地支持大规模决策基础设施以解决社会最具挑战性的问题。当人类做出决定时,不公平和歧视的问题普遍存在,并且当使用几乎没有透明度,问责制和公平性的机器做出决定时(或可能会放大)。在本文中,我们介绍了\ textit {Causal公平分析}的框架,目的是填补此差距,即理解,建模,并可能解决决策设置中的公平性问题。我们方法的主要见解是将观察到数据中存在的差异的量化与基本且通常是未观察到的因果机制收集的因果机制的收集,这些机制首先会产生差异,挑战我们称之为因果公平的基本问题分析(FPCFA)。为了解决FPCFA,我们研究了分解差异和公平性的经验度量的问题,将这种变化归因于结构机制和人群的不同单位。我们的努力最终达到了公平地图,这是组织和解释文献中不同标准之间关系的首次系统尝试。最后,我们研究了进行因果公平分析并提出一本公平食谱的最低因果假设,该假设使数据科学家能够评估不同影响和不同治疗的存在。
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也称为(非参数)结构方程模型(SEMS)的结构因果模型(SCM)被广泛用于因果建模目的。特别是,也称为递归SEM的无循环SCMS,形成了一个研究的SCM的良好的子类,概括了因果贝叶斯网络来允许潜在混淆。在本文中,我们调查了更多普通环境中的SCM,允许存在潜在混杂器和周期。我们展示在存在周期中,无循环SCM的许多方便的性质通常不会持有:它们并不总是有解决方案;它们并不总是诱导独特的观察,介入和反事实分布;边缘化并不总是存在,如果存在边缘模型并不总是尊重潜在的投影;他们并不总是满足马尔可夫财产;他们的图表并不总是与他们的因果语义一致。我们证明,对于SCM一般,这些属性中的每一个都在某些可加工条件下保持。我们的工作概括了SCM的结果,迄今为止仅针对某些特殊情况所知的周期。我们介绍了将循环循环设置扩展到循环设置的简单SCM的类,同时保留了许多方便的无环SCM的性能。用本文,我们的目标是为SCM提供统计因果建模的一般理论的基础。
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估计平均因果效应的理想回归(如果有)是什么?我们在离散协变量的设置中研究了这个问题,从而得出了各种分层估计器的有限样本方差的表达式。这种方法阐明了许多广泛引用的结果的基本统计现象。我们的博览会结合了研究因果效应估计的三种不同的方法论传统的见解:潜在结果,因果图和具有加性误差的结构模型。
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In this review, we discuss approaches for learning causal structure from data, also called causal discovery. In particular, we focus on approaches for learning directed acyclic graphs (DAGs) and various generalizations which allow for some variables to be unobserved in the available data. We devote special attention to two fundamental combinatorial aspects of causal structure learning. First, we discuss the structure of the search space over causal graphs. Second, we discuss the structure of equivalence classes over causal graphs, i.e., sets of graphs which represent what can be learned from observational data alone, and how these equivalence classes can be refined by adding interventional data.
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结构因果模型是珍珠因果理论的基本建模单元;原则上,他们允许我们解决反事实,这些反应性是因果关系阶梯的顶部梯级。但它们通常包含将其应用程序应用于特殊设置的潜在变量。这似乎是本文证明的事实的结果,即使在具有聚节形图所表征的模型中,也是NP - 硬的因果推断。为了处理这种硬度,我们介绍了因果EM算法。其主要目标是从关于分类清单变量的数据重建关于潜在变量的不确定性。然后通过贝叶斯网络的标准算法解决反事实推断。结果是近似计算反事实的一般方法,是它们可识别的或不可识别(在这种情况下,我们提供界限)。我们经验展示,以及通过导出可靠的间隔,我们提供的近似在展开的EM运行中得到准确。这些结果终于争辩说,似乎对趋势的想法似乎不受注意到的趋势概念,即不知道结构方程,通常可以计算反事实界。
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本文介绍了在结构因果模型(SCM)的一般空间上定义的一系列拓扑结构,介绍了因果推断的拓扑学习 - 理论观点。作为框架的说明,我们证明了拓扑因果层次结构定理,表明只有在微薄的SCM集中就可以实现了无实体的假设因果推断。由于弱拓扑结构和统计上可验证假设的开放集之间的已知对应关系,我们的结果表明,原则上的归纳假设足以许可有效的因果推论是统计上无可核实的。类似于无午餐定理的统计推断,目前的结果阐明了因果推断的实质性假设的必然性。我们拓扑方法的额外好处是它很容易容纳具有无限变量的SCM。我们终于建议该框架对探索和评估替代因果归纳的积极项目有所帮助。
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因果关系是理解世界的科学努力的基本组成部分。不幸的是,在心理学和社会科学中,因果关系仍然是禁忌。由于越来越多的建议采用因果方法进行研究的重要性,我们重新制定了心理学研究方法的典型方法,以使不可避免的因果理论与其余的研究渠道协调。我们提出了一个新的过程,该过程始于从因果发现和机器学习的融合中纳入技术的发展,验证和透明的理论形式规范。然后,我们提出将完全指定的理论模型的复杂性降低到与给定目标假设相关的基本子模型中的方法。从这里,我们确定利息量是否可以从数据中估算出来,如果是的,则建议使用半参数机器学习方法来估计因果关系。总体目标是介绍新的研究管道,该管道可以(a)促进与测试因果理论的愿望兼容的科学询问(b)鼓励我们的理论透明代表作为明确的数学对象,(c)将我们的统计模型绑定到我们的统计模型中该理论的特定属性,因此减少了理论到模型间隙通常引起的规范不足问题,以及(d)产生因果关系和可重复性的结果和估计。通过具有现实世界数据的教学示例来证明该过程,我们以摘要和讨论来结论。
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Linear structural causal models (SCMs)-- in which each observed variable is generated by a subset of the other observed variables as well as a subset of the exogenous sources-- are pervasive in causal inference and casual discovery. However, for the task of causal discovery, existing work almost exclusively focus on the submodel where each observed variable is associated with a distinct source with non-zero variance. This results in the restriction that no observed variable can deterministically depend on other observed variables or latent confounders. In this paper, we extend the results on structure learning by focusing on a subclass of linear SCMs which do not have this property, i.e., models in which observed variables can be causally affected by any subset of the sources, and are allowed to be a deterministic function of other observed variables or latent confounders. This allows for a more realistic modeling of influence or information propagation in systems. We focus on the task of causal discovery form observational data generated from a member of this subclass. We derive a set of necessary and sufficient conditions for unique identifiability of the causal structure. To the best of our knowledge, this is the first work that gives identifiability results for causal discovery under both latent confounding and deterministic relationships. Further, we propose an algorithm for recovering the underlying causal structure when the aforementioned conditions are satisfied. We validate our theoretical results both on synthetic and real datasets.
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研究了与隐藏变量有关的非循环图(DAG)相关的因果模型中因果效应的识别理论。然而,由于估计它们输出的识别功能的复杂性,因此未耗尽相应的算法。在这项工作中,我们弥合了识别和估算涉及单一治疗和单一结果的人口水平因果效应之间的差距。我们派生了基于功能的估计,在大类隐藏变量DAG中表现出对所识别的效果的双重稳健性,其中治疗满足简单的图形标准;该类包括模型,产生调整和前门功能作为特殊情况。我们还提供必要的和充分条件,其中隐藏变量DAG的统计模型是非分子饱和的,并且意味着对观察到的数据分布没有平等约束。此外,我们推导了一类重要的隐藏变量DAG,这意味着观察到观察到的数据分布等同于完全观察到的DAG等同于(最高的相等约束)。在这些DAG类中,我们推出了实现兴趣目标的半导体效率界限的估计估计值,该估计是治疗满足我们的图形标准的感兴趣的目标。最后,我们提供了一种完整的识别算法,可直接产生基于权重的估计策略,以了解隐藏可变因果模型中的任何可识别效果。
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We consider the problem of recovering the causal structure underlying observations from different experimental conditions when the targets of the interventions in each experiment are unknown. We assume a linear structural causal model with additive Gaussian noise and consider interventions that perturb their targets while maintaining the causal relationships in the system. Different models may entail the same distributions, offering competing causal explanations for the given observations. We fully characterize this equivalence class and offer identifiability results, which we use to derive a greedy algorithm called GnIES to recover the equivalence class of the data-generating model without knowledge of the intervention targets. In addition, we develop a novel procedure to generate semi-synthetic data sets with known causal ground truth but distributions closely resembling those of a real data set of choice. We leverage this procedure and evaluate the performance of GnIES on synthetic, real, and semi-synthetic data sets. Despite the strong Gaussian distributional assumption, GnIES is robust to an array of model violations and competitive in recovering the causal structure in small- to large-sample settings. We provide, in the Python packages "gnies" and "sempler", implementations of GnIES and our semi-synthetic data generation procedure.
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因果效应估计对于自然和社会科学中的许多任务很重要。但是,如果没有做出强大的,通常无法测试的假设,就无法从观察数据中识别效果。我们考虑了部分识别问题的算法,当未衡量的混淆使鉴定不可能鉴定时,多变量,连续处理的界限治疗效果。我们考虑一个框架,即可观察的证据与基于规范标准在因果模型中编码的约束的含义相匹配。这纯粹是基于生成模型来概括经典方法。将因果关系施放为在受约束优化问题中的目标函数,我们将灵活的学习算法与蒙特卡洛方法相结合,以随机因果节目的名义实施解决方案家族。特别是,我们提出了可以通过因果或观察到的数据模型而没有可能性功能的参数功能的这种约束优化问题的方式,从而降低了任务的计算和统计复杂性。
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We propose a layered hierarchical architecture called UCLA (Universal Causality Layered Architecture), which combines multiple levels of categorical abstraction for causal inference. At the top-most level, causal interventions are modeled combinatorially using a simplicial category of ordinal numbers. At the second layer, causal models are defined by a graph-type category. The non-random ``surgical" operations on causal structures, such as edge deletion, are captured using degeneracy and face operators from the simplicial layer above. The third categorical abstraction layer corresponds to the data layer in causal inference. The fourth homotopy layer comprises of additional structure imposed on the instance layer above, such as a topological space, which enables evaluating causal models on datasets. Functors map between every pair of layers in UCLA. Each functor between layers is characterized by a universal arrow, which defines an isomorphism between every pair of categorical layers. These universal arrows define universal elements and representations through the Yoneda Lemma, and in turn lead to a new category of elements based on a construction introduced by Grothendieck. Causal inference between each pair of layers is defined as a lifting problem, a commutative diagram whose objects are categories, and whose morphisms are functors that are characterized as different types of fibrations. We illustrate the UCLA architecture using a range of examples, including integer-valued multisets that represent a non-graphical framework for conditional independence, and causal models based on graphs and string diagrams using symmetric monoidal categories. We define causal effect in terms of the homotopy colimit of the nerve of the category of elements.
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A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify the presence of hidden confounding factors from a single dataset. Under the assumption of independent causal mechanisms underlying the data generating process, we demonstrate a way to detect unobserved confounders when having multiple observational datasets coming from different environments. We present a theory for testable conditional independencies that are only absent during hidden confounding and examine cases where we violate its assumptions: degenerate & dependent mechanisms, and faithfulness violations. Additionally, we propose a procedure to test these independencies and study its empirical finite-sample behavior using simulation studies and semi-synthetic data based on a real-world dataset. In most cases, our theory correctly predicts the presence of hidden confounding, particularly when the confounding bias is~large.
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This work shows how to leverage causal inference to understand the behavior of complex learning systems interacting with their environment and predict the consequences of changes to the system. Such predictions allow both humans and algorithms to select the changes that would have improved the system performance. This work is illustrated by experiments on the ad placement system associated with the Bing search engine.
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当并非观察到所有混杂因子并获得负面对照时,我们研究因果参数的估计。最近的工作表明,这些方法如何通过两个所谓的桥梁函数来实现识别和有效估计。在本文中,我们使用阴性对照来应对因果推断的主要挑战:这些桥梁功能的识别和估计。先前的工作依赖于这些功能的完整性条件,以识别因果参数并在估计中需要进行独特性假设,并且还集中于桥梁函数的参数估计。相反,我们提供了一种新的识别策略,以避免完整性条件。而且,我们根据最小学习公式为这些功能提供新的估计量。这些估计值适合通用功能类别,例如重现Hilbert空间和神经网络。我们研究了有限样本收敛的结果,既可以估计桥梁功能本身,又要在各种假设组合下对因果参数进行最终估计。我们尽可能避免桥梁上的独特条件。
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反事实推断是一种强大的工具,能够解决备受瞩目的领域中具有挑战性的问题。要进行反事实推断,需要了解潜在的因果机制。但是,仅凭观察和干预措施就不能独特地确定因果机制。这就提出了一个问题,即如何选择因果机制,以便在给定领域中值得信赖。在具有二进制变量的因果模型中已经解决了这个问题,但是分类变量的情况仍未得到解答。我们通过为具有分类变量的因果模型引入反事实排序的概念来应对这一挑战。为了学习满足这些约束的因果机制,并对它们进行反事实推断,我们引入了深层双胞胎网络。这些是深层神经网络,在受过训练的情况下,可以进行双网络反事实推断 - 一种替代绑架,动作和预测方法的替代方法。我们从经验上测试了来自医学,流行病学和金融的多种现实世界和半合成数据的方法,并报告了反事实概率的准确估算,同时证明了反事实订购时不执行反事实的问题。
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动态系统广泛用于科学和工程,以模拟由多个交互组件组成的系统。通常,它们可以在意义上给出因果解释,因为它们不仅模拟了系统组件状态随时间的演变,而且描述了他们的进化如何受到动态的系统的外部干预的影响。我们介绍了结构动态因果模型(SDCMS)的正式框架,其将系统组件的因果语言作为模型的一部分来阐述。 SDCMS表示动态系统作为随机过程的集合,并指定了管理每个组件的动态的基本因果机制,作为任意顺序的随机微分方程的结构化系统。 SDCMS扩展了结构因果模型(SCM)的多功能因果建模框架,也称为结构方程模型(SEM),通过显式允许时间依赖。 SDCM可以被认为是SCM的随机过程版本,其中SCM的静态随机变量由动态随机过程及其衍生物代替。我们为SDCMS理论提供基础,(i)正式定义SDCMS,其解决方案,随机干预和图形表示; (ii)对初始条件的解决方案的存在性和独特性; (iii)随着时间的推移倾向于无穷大,讨论SDCMS平衡的条件下降; (iv)将SDCM的性质与平衡SCM的性质相关联。这封对应关系使人们能够在研究大类随机动力系统的因果语义时利用SCM的大量统计工具和发现方法。该理论用来自不同科学域的几个众所周知的示例进行说明。
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我们研究了在存在潜在变量存在下从数据重建因果图形模型的问题。感兴趣的主要问题是在潜在变量上恢复因果结构,同时允许一般,可能在变量之间的非线性依赖性。在许多实际问题中,原始观测之间的依赖性(例如,图像中的像素)的依赖性比某些高级潜在特征(例如概念或对象)之间的依赖性要小得多,这是感兴趣的设置。我们提供潜在表示和潜在潜在因果模型的条件可通过减少到混合甲骨文来识别。这些结果突出了学习混合模型的顺序的良好研究问题与观察到和解开的基础结构的问题之间的富裕问题之间的有趣连接。证明是建设性的,并导致几种算法用于明确重建全图形模型。我们讨论高效算法并提供说明实践中算法的实验。
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