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Causal reasoning with ancestral graphs
, 2008
"... Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One promin ..."
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Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate postintervention probabilities to preintervention probabilities that are estimable from observational data. However, such causal diagrams are seldom fully testable given observational data. In consequence, many causal discovery algorithms based on datamining can only output an equivalence class of causal diagrams (rather than a single one). This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a (partial) ancestral graph. We present two main results. The first result extends Pearl (1995)’s celebrated docalculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl’s calculus—the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (1993).
Simpson's Paradox: An Anatomy
, 1999
"... This report discusses the reversal effect known as Simpson's paradox from a causaltheoretic viewpoint. It analyzes the reasons why the effect has been (and still is) considered paradoxical and why its resolution has been so late in coming. The report is extracted from a forthcoming book Caus ..."
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This report discusses the reversal effect known as Simpson's paradox from a causaltheoretic viewpoint. It analyzes the reasons why the effect has been (and still is) considered paradoxical and why its resolution has been so late in coming. The report is extracted from a forthcoming book Causality [Pearl, 2000], and assumes some familiarity with causal diagrams and the do(\Delta)(orset(\Delta)) notation (e.g., [Pearl, 1995]). 0.1 A Tale of a NonParadox Simpson's paradox [Simpson, 1951# Blyth, 1972], first encountered by Pearson in 1899 [Aldrich, 1995], refers to the phenomenon whereby an event C increases the probability of E in a given population p and, at the same time, decreases the probability of E in every subpopulation of p. In other words, if F and :F are two complementary properties describing two subpopulations, we mightwell encounter the inequalities P (EjC) ?P(Ej:C)# (1) P (EjC# F ) !P(Ej:C#F )# (2) P (EjC# :F ) !P(Ej:C#:F ): (3) Although such order reversal might n...
2003]: ‘On World Poverty: Its Causes and Effects
 Food and Agricultural Organization (FAO) of the United Nations, Research Bulletin
, 2003
"... Recent advances in modeling directed acyclic graphs are used to sortout causal patterns among a set of thirteen measures deemed relevant to the incidence of world poverty. Crosssection measures of the percent of population living on one and two dollars or less per day from eighty low income countr ..."
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Recent advances in modeling directed acyclic graphs are used to sortout causal patterns among a set of thirteen measures deemed relevant to the incidence of world poverty. Crosssection measures of the percent of population living on one and two dollars or less per day from eighty low income countries are exposed to a battery of tests of conditional independence with respect to measures of economic and political freedom, income inequality, income per person, agricultural income, child mortality, birth rate, life expectancy, relative size of rural population, illiteracy rate, foreign aid as a percentage of national income, international trade as a percentage of national income and percentage of population that is undernourished. Motivation for the method of analysis precedes results. Results are presented as a graph that shows our measures of economic and political freedom, income inequality, illiteracy and agricultural income to be exogenous movers of poverty when measured as the percent of the population living on two dollars or less per day. Foreign aid and international trade are not connected to the other variables in the graph. Results on our measure of extreme poverty (people living on one dollar or less per day) show that such populations are immune from improvements in economic progress of the general economy. The “rising tide lifts all boats ” argument apparently doesn’t cover the extreme poor of our sample.
On The Identification Of Nonparametric Structural Models
, 1997
"... In this paper we study the identifiability of nonparametric models, that is, models in which both the functional forms of the equations and the probability distributions of the disturbances remain unspecified. Identifiability in such models does not mean uniqueness of parameters but rather uniquenes ..."
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In this paper we study the identifiability of nonparametric models, that is, models in which both the functional forms of the equations and the probability distributions of the disturbances remain unspecified. Identifiability in such models does not mean uniqueness of parameters but rather uniqueness of the set of predictions of interest to the investigator. For example, predicting the effects of changes, interventions, and control. We provide sufficient and necessary conditions for identifying a set of causal predictions of the type: "Find the distribution of Y , assuming that X is controlled by external intervention", where Y and X are arbitrary variables of interest. Whenever identifiable, such predictions can be expressed in closed algebraic form, in terms of observed distributions. We also show how the identifying criteria can be verified qualitatively, by inspection, using the graphical representation of the structural model. When compared to standard identifiability tests of lin...
Statistical Models for Causation
, 2005
"... We review the basis for inferring causation by statistical modeling. Parameters should be stable under interventions, and so should error distributions. There are also statistical conditions on the errors. Stability is difficult to establish a priori, and the statistical conditions are equally probl ..."
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We review the basis for inferring causation by statistical modeling. Parameters should be stable under interventions, and so should error distributions. There are also statistical conditions on the errors. Stability is difficult to establish a priori, and the statistical conditions are equally problematic. Therefore, causal relationships are seldom to be inferred from a data set by running statistical algorithms, unless there is substantial prior knowledge about the mechanisms that generated the data. We begin with linear models (regression analysis) and then turn to graphical models, which may in principle be nonlinear.
From Imaging and Stochastic Control to a Calculus of Actions
"... This paper highlights relationships among stochastic control theory, Lewis' notion of "imaging", and the representation of actions in AI systems. We show that the language of causal graphs offers a practical solution to the frame problem and its two satellites: the ramification and co ..."
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This paper highlights relationships among stochastic control theory, Lewis' notion of "imaging", and the representation of actions in AI systems. We show that the language of causal graphs offers a practical solution to the frame problem and its two satellites: the ramification and concurrency problems. Finally, we present a symbolic machinery that admits both probabilistic and causal information and produces probabilistic statements about the effect of actions and the impact of observations. 1 Representing and Revising Probability Functions Engineers consider the theory of stochastic control as the basic paradigm in the design and analysis of systems operating in uncertain environments. Knowledge in stochastic control theory is represented by a function P (s), which measures the probability assigned to each state s of the world, at any given time. Given P (s), it is possible to calculate the probability of any conceivable event E, by simply summing up P (s) over all states that entai...
Causal Inference in Sociological Studies
, 2001
"... Acknowledgments: The authors would like to thank Melissa Hardy, David Harding, and Felix Elwert for comments on an earlier draft of this paper. 1. ..."
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Acknowledgments: The authors would like to thank Melissa Hardy, David Harding, and Felix Elwert for comments on an earlier draft of this paper. 1.
ReEvaluating the Evaluation of Training Programs
"... substantial help in recreating the original data set. We are also grateful to Joshua Angrist, George Cave, David Cutler, Lawrence Katz, Caroline MinterHoxby, and participants at the HarvardMIT labor seminar, the Harvard econometrics and labor lunch seminars, the MIT labor lunch seminar, and a semi ..."
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substantial help in recreating the original data set. We are also grateful to Joshua Angrist, George Cave, David Cutler, Lawrence Katz, Caroline MinterHoxby, and participants at the HarvardMIT labor seminar, the Harvard econometrics and labor lunch seminars, the MIT labor lunch seminar, and a seminar at the Manpower Development Research Corporation (MDRC) for many suggestions and comments. All remaining errors are the authors’
Editorial Causality, Unintended Consequences and Deducing Shared Causes
"... Despite warnings against inferring causality from observed correlations or statistical dependence, some articles do. Observed correlation is neither necessary nor sufficient to infer causality as defined by the term’s everyday usage. For example, a deterministic causal process creates pseudorandom n ..."
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Despite warnings against inferring causality from observed correlations or statistical dependence, some articles do. Observed correlation is neither necessary nor sufficient to infer causality as defined by the term’s everyday usage. For example, a deterministic causal process creates pseudorandom numbers; yet, we observe no correlation between the numbers. Child height correlates with spelling ability because age causes both. Moreover, order is problematic—we hear train whistles before observing trains, yet trains cause whistles. Scientific methods specifically prohibit inferring causal theories from specific observations (i.e., effects) because, in part, many credible causes are perfectly consistent with available observations. Moreover, actions inferred from effects have more unintended consequences than actions based on sound deductive causal theories because causal theories predict multiple effects. However, an often overlooked but key feature of these theories is that we describe the cause with more variables than the effect. Consequently, inductive processes might appear deductive as the number of effects increases relative to the number of potential causes. For example, in real criminal trials, jurors judge whether sufficient evidence exists to infer guilt. In contrast, determining guilt in criminal mystery novels is deductive because the number of clues (i.e., effects) is large relative to the number of potential suspects (i.e., causes). We can make inferential tasks resemble deductive tasks by increasing the number of effects (i.e., variables) relative to the number of potential causes and seeking a shared cause for all observed effects. Moreover, under some conditions, the method of seeking shared causes might approach deductive reasoning when the number of causes is strictly limited. At least, the resulting number of possible causal theories is far less than the number generated from repeated observations of a single effect (i.e., variable).