Epsilon-Identifiability of Causal Quantities

Ang Li; Scott Mueller; Xin Shu; Judea Pearl

cs.AIJan 27, 2023

Epsilon-Identifiability of Causal Quantities

Authors: Ang Li, Scott Mueller, Xin Shu, Judea Pearl

Organizations: Cognitive Systems Laboratory, Department of Computer Science, University of California, Los Angeles, Los Angeles, California, USA.

Abstract

Identifying the effects of causes and causes of effects is vital in virtually every scientific field. Often, however, the needed probabilities may not be fully identifiable from the available data sources. This paper shows how approximate identifiability is still possible for several probabilities of causation. We term this epsilon-identifiability and demonstrate its usefulness in cases where the behavior of certain subpopulations can be restricted within sufficiently narrow bounds. In particular, we show how unidentifiable causal effects and counterfactual probabilities can be epsilon-identified when such allowances are made. Often, these allowances are easily measured and reasonably assumed. Finally, epsilon-identifiability is applied to the unit selection problem.

Figures & tables

Panel of Figure 1 — Figure 1: Causal graphs with confounders.

	Medicine	No medicine
Recovered	$780$	$210$
Not recovered	$480$	$30$

Table 1: Results of an observational study with

1500

individuals who have access to the medicine, where

1260

individuals chose to receive the medicine and

240

individuals chose not to.

	Discount	No discount
Bought the purchase	$900$	$750$
No purchase	$600$	$750$

Table 2: Results of an experimental study with

1500

randomly selected customers were forced to apply the discount, and

1500

randomly selected customers were forced not to.

Causal Identifiability

Causal identifiability asks when data and stated assumptions uniquely determine causal structures, effects, or counterfactuals.

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Computational Identifiability

Lucius E. J. Bynum, Rajesh Ranganath, Kyunghyun Cho

New York University

Causal Effect Estimation Parameter Identifiability Causal Identifiability Causal Inference Query Identifiability

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Identification conditions describe the computability of a target query or parameter of interest as a function of the type and amount of information available. In causal identification, this information is often expressed in the form of a causal graph, and data are observed or collected for some subset of variables in the graph. Target queries may be for a single effect alone or for a class of effects in a given model. The derivation of an identification algorithm then defines mathematically the process by which the desired causal effect(s) can be uniquely determined, theoretically, in expectation. Identifiability in expectation, or 'theoretical identifiability,' generally assumes asymptotic properties, infinite data, or other mathematically idealized conditions. In this paper, we explore a fundamental distinction between this theoretical, idealized notion of identifiability and a proposed alternative that is computation-bound. The framework we propose - 'computational identifiability' - is to instead define a finite computational search procedure for an empirical estimator. If this process finds an estimator empirically, within a desired error tolerance, then identifiability is satisfied, conditional on the specified assumptions of the search (i.e., a prior distribution over the parameters) and conditional on the search procedure itself. Through several experiments, we demonstrate how this framework allows us to answer fine-grained, practical identification questions, such as identification with small finite samples, with ambiguous graphical criteria, with mixed observational-interventional data, and across counterfactual data and estimands. Code is available at https://github.com/lbynum/metadentify.

Abstract

Causal Identifiability

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