Probabilities of causation: Bounds and identification

By Jin Tian, Judea Pearl. 2000

264 citations recorded by the source corpus.

This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structural‐semantical definitions of the probabilities of necessary or sufficient causation (or both), we show how to bound these quantities from data obtained in experimental and observational studies, under general assumptions concerning the data‐generating process. In particular, we strengthen the results of Pearl [39] by presenting sharp bounds based on combined experimental and nonexperimental data under no process assumptions, as well as under the mild assumptions of exogeneity (no confounding) and monotonicity (no prevention). These results delineate more precisely the basic assumptions that must be made before statistical measures such as the excess‐risk‐ratio could be used for assessing attributional quantities such as the probability of causation.

Subfields: Artificial Intelligence

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Citations in the corpus

Causal Modeling-Based Discrimination Discovery and Removal: Criteria, Bounds, and Algorithms (2019, background): “In fact, it is known that P ðyx; yx0 Þ is unidentifiable from the observational data even in the Markovian model [37].”
Algorithmic recourse under imperfect causal knowledge: a probabilistic approach (2020, background): “An alternative approach could address causal sufficiency violations by relying on latent variable models to estimate confounders from multiple causes [61] or proxy variables [31], or to work with bounds on causal effects instead [4, 49].”
Causal inference in statistics: An overview (2009, background): “…powerful in refining assumptions (Angrist et al., 1996; Heckman and Vytlacil, 2005), deriving consistent estimands (Robins, 1986), bounding probabilities of necessary and sufficient causation (Tian and Pearl, 2000), and combining data from experimental and nonexperimental studies (Pearl, 2000a).”
PC-Fairness: A Unified Framework for Measuring Causality-based Fairness (2019, background): “According to [13], P (v) can be expressed as the summation over the probabilities of certain values u of U that satisfy following corresponding requirements: for each V ∈ V, we must have fV (paV , uV ) = v where v, paV are specified by v and uV is specified by u.”
Causes and Explanations: A Structural-Model Approach. Part I: Causes (2000, methodology): “In [Pearl 2000], a notion of contributory cause is defined as well as actual cause.”
3. The Foundations of Causal Inference (2010, background): “…powerful in refining assumptions (Angrist et al. 1996; Heckman and Vytlacil 2005), deriving consistent estimands (Robins 1986), bounding probabilities of necessary and sufficient causation (Tian and Pearl 2000), and combining data from experimental and nonexperimental studies (Pearl 2000a:302).”
Algorithmic Transparency via Quantitative Input Influence: Theory and Experiments with Learning Systems (2016, background): “In [39], Tian and Pearl discuss measures of causal strength for individual binary inputs and outputs in a probabilistic setting.”
Counterfactual Off-Policy Evaluation with Gumbel-Max Structural Causal Models (2019, background): “In particular, the monotonicity assumption (Pearl, 2000; Tian & Pearl, 2000) is sufficient to identify the Probability of Necessity and related quantities used in epidemiology (Cuellar & Kennedy, 2018; Yamada & Kuroki, 2017) to identify the answers to counterfactual queries with respect to a binary…”
Statistics and causal inference: A review (2003, background): “, 1996), deriving consistent estimands (Robins, 1986), bounding probabilities of necessary and sufficient causation (Tian and Pearl, 2000), and combining data from experimental and nonexperimental studies (Pearl, 2000).”
Anti-discrimination learning: a causal modeling-based framework (2017, background): “A potential solution may be to employ the bound for the probability of necessity and sufficiency [34], which was developed within the causal modeling framework for estimating the probability of causation.”
Causes of Effects and Effects of Causes (2015, methodology): “Portions of this paper are based on Pearl (2000a, 2011, 2012).”