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Are Bayesian networks typically faithful?

贝叶斯网络通常满足忠实性吗?

Faithfulness is a common assumption in causal inference, often motivated by the fact that the faithful parameters of linear Gaussian and discrete Bayesian networks are typical, and the folklore belief that this should also hold for other classes of Bayesian networks. We address this open question by showing that among all Bayesian networks over a given DAG, the faithful Bayesian networks are indeed `typical': they constitute a dense, open set with respect to the total…

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Causal Graphs, Markov Properties and Do-calculus for Stochastic Differential Equations

随机微分方程的因果图、马尔可夫性质与 do 演算

Stochastic differential equations (SDEs) are widely used to model continuous-time dynamical systems, but graphical causal models for them are not yet well-understood. We consider systems of causal SDEs that are equipped with an explicit causal semantics. We pose solvability conditions for systems of causal SDEs such that they have well-defined observational and interventional distributions - even after marginalisation - and provide a general class of Lipschitz semimartingale…

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Testing Partially-Identifiable Causal Queries Using Ternary Tests

使用三结果检验检验部分可识别的因果命题

We consider hypothesis testing of binary causal queries using observational data. Since the mapping of causal models to the observational distribution that they induce is not one-to-one, in general, causal queries are often only partially identifiable. When binary statistical tests are used for testing partially-identifiable causal queries, their results do not translate in a straightforward manner to the causal hypothesis testing problem. We propose using ternary…

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Revisiting the Berkeley Admissions data: Statistical Tests for Causal Hypotheses

重访伯克利录取数据:因果假设的统计检验

Reasoning about fairness through correlation-based notions is rife with pitfalls. The 1973 University of California, Berkeley graduate school admissions case from Bickel et. al. (1975) is a classic example of one such pitfall, namely Simpson's paradox. The discrepancy in admission rates among males and female applicants, in the aggregate data over all departments, vanishes when admission rates per department are examined. We reason about the Berkeley graduate school…

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Evaluating and Correcting Performative Effects of Decision Support Systems via Causal Domain Shift

通过因果域迁移评估并校正决策支持系统的施为效应

When predicting a target variable $Y$ from features $X$, the prediction $\hat{Y}$ can be performative: an agent might act on this prediction, affecting the value of $Y$ that we eventually observe. Performative predictions are deliberately prevalent in algorithmic decision support, where a Decision Support System (DSS) provides a prediction for an agent to affect the value of the target variable. When deploying a DSS in high-stakes settings (e.g. healthcare, law, predictive…

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