Causal effect identifiability under partial-observability

Abstract

© International Conference on Machine Learning, ICML 2020. All rights reserved.Causal effect identifiability is concerned with es_tablishing the effect of intervening on a set of variables on another set of variables from observa_tional or interventional distributions under causal assumptions that are usually encoded in the form of a causal graph. Most of the results of this liter_ature implicitly assume that every variable mod_eled in the graph is measured in the available distributions. In practice, however, the data col_lections of the different studies considered do not measure the same variables, consistently. In this paper, we study the causal effect identifiability problem when the available distributions encom_pass different sets of variables, which we refer to as identification under partial-observability. We study a number of properties of the factors that comprise a causal effect under various levels of abstraction, and then characterize the relationship between them with respect to their status relative to the identification of a targeted intervention. We establish a sufficient graphical criterion for deter_mining whether the effects are identifiable from partially-observed distributions. Finally, building on these graphical properties, we develop an algo_rithm that returns a formula for a causal effect in terms of the available distributions.