Counterfactual Probabilities: Computational Methods, Bounds and Applications

By Alexander Balke, Judea Pearl. 1994

Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, and determination of liability. In this paper we present methods for computing the probabilities of such queries using the formulation proposed in [Balke and Pearl, 1994], where the antecedent of the query is interpreted as an external action that forces the proposition A to be true. When a prior probability is available on the causal mechanisms governing the domain, counterfactual probabilities can be evaluated precisely. However, when causal knowledge is specified as conditional probabilities on the observables, only bounds can computed. This paper develops techniques for evaluating these bounds, and demonstrates their use in two applications: (1) the determination of treatment efficacy from studies in which subjects may choose their own treatment, and (2) the determination of liability in product-safety litigation.

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Citations in the corpus

Improving the accuracy of medical diagnosis with causal machine learning (2020, methodology): “We now derive expressions for the expected disablement and expected suf ﬁ ciency for these models using twin-networks method for computing counterfactuals introduced in 64,71 .”
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].”
Woulda, Coulda, Shoulda: Counterfactually-Guided Policy Search (2018, background): “The central idea of CF-GPS is that, instead of running an agent on scenarios sampled de novo from a model, we infer scenarios in hindsight from given off-policy data, and then evaluate and improve the agent on these speciﬁc scenarios using given or learned causal mechanisms (Balke & Pearl, 1994).”
COPHY: Counterfactual Learning of Physical Dynamics (2019, background): “…given observations without explicitly observing the effect of the intervention on data is a hard task and requires modeling of the causal relationships between the variable on which the intervention is performed and the variable whose alternative future should be predicted (Balke & Pearl, 1994).”
Identiﬁability of Path-Speciﬁc Effects ∗ (2005, methodology): “The parallel worlds model is a generalization of the twin network model, first appearing in[Balke and Pearl, 1994], to more than two possible worlds.”
On the Testability of Causal Models With Latent and Instrumental Variables (1995, methodology): “This feature constitutes a graphi cal definition of the notion of instrumental variables, which plays an important role in econometric modeling [Bowden & Turkington 1984) and in randomized trials [Imbens & Angrist 1994, Balke & Pearl 1994b) Instrumental variables is a technique invented by the…”
Causes and explanations: A structural-model approach (2000, background): “We can make sense out of probabilistic counterfactual statements, even conditional ones (the probability that X would be 3 if Y 1 were 2, given that Y is in fact 1) in this framework (see [Balke and Pearl 1994]), by putting a probability on the set of possible contexts.”
Causes and Explanations: A Structural-Model Approach: Part 1: Causes (2013, background): “We can make sense out of probabilistic counterfactual statements, even conditional ones (the probability that X would be 3 if Y1 were 2, given that Y is in fact 1) in this framework (see [Balke and Pearl 1994 ]), by putting a probability on the set of possible contexts.”
Mendelian randomization: Using genes as instruments for making causal inferences in epidemiology (2008, unknown): “Third, non-parametric methods can be used to obtain bounds for the causal effect, at least when the instrument, exposure and disease are all categorical variables [9, 117], though this approach may prove less useful with the continuous exposures common in epidemiology [9, 117].”
Influence Diagrams for Causal Modelling and Inference (2002, methodology): “In the alternative approach of Balke & Pearl (1994), one starts by boldly assuming the simultaneous existence, and joint distribution, of the collection of complementary quantities.”
Reinforcement Learning: An Introduction (1998, background): “For example, it is closely related to the idea of “interventions” and “counterfactuals” in probabilistic graphical (Bayesian) models (e.g., Pearl, 1995; Balke and Pearl, 1994).”
The Mediation Formula: A Guide to the Assessment of Causal Pathways in Nonlinear Models (2011, methodology): “The structural methodology presented in this paper adheres to this philosophy and it has produced indeed a principled solution to the mediation problem, based on the counterfactual reading of structural equations (Balke and Pearl, 1994a,b; Pearl, 2009a, Chapter 7).”
Bounds on Treatment Effects from Studies with Imperfect Compliance (1997, methodology): “This may be accomplished by a procedure detailed in (Balke and Pearl 1994), which is based on linear programming optimization coupled with the fact that the domain of U can be partitioned into sixteen equivalence classes, each representing one of four possible mappings from Z to D conjoined with one”
Causes of Effects and Effects of Causes (2015, background): “We further investigate the circumstances under which such bounds can emerge, and the philosophical dilemma associated with determining individual cases from statistical data.”
What Counterfactuals Can Be Tested (2007, methodology): “The first attempt to construct such a graph was made in [Balke & Pearl, 1994a] where atwin network graph was constructed forγ which mention exactly two submodels.”