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Descendants of Colliders Conditioning on descendants of a collider also induces association in between the parents of the collider.

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Flow of Causation The flow of association is symmetric, whereas the flow of causation is not. Under the causal edges assumption (Assumption 3.3), causation only flows in a single direction. Causation only flows along directed paths. Association flows along any path that does not

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low of association is symmetric, whereas the flow of causation is not. Under the causal edges assumption (Assumption 3.3), causation only flows in a single direction. Causation only flows along <span>directed paths. Association flows along any path that does not contain an immorality <span>

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al expression. In this chapter, that means to reduce an expression from one that uses potential outcome notation to one that uses only statistical notation such as π , π , π , expectations, and <span>conditioning. This means that we can calculate the causal effect from just the observational distribution π(π, π, π) <span>

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Conditional exchangeability is the main assumption necessary for causal inference. Armed with this assumption, we can identify the causal effect within levels of π

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the fundamental problem of causal inference It is fundamental because if we cannot observe both π π (1) and π π (0) , then we cannot observe the causal effect π π (1) β π π (0) .

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stable unit-treatment value assumption (SUTVA)

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Assumption 3.2 (Minimality Assumption) 1. Given its parents in the DAG, a node π is independent of all its non-descendants (Assumption 3.1). 2. Adjacent nodes in the DAG are dependent.

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Positivity is the condition that all subgroups of the data with different covariates have some probability of receiving any value of treatment

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SUTVA is satisfied if unit (individual) π βs outcome is simply a function of unit π βs treatment.

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In machine learning, we often only care about predicting the observed outcome π , so there is no need for potential outcomes, which means machine learning does not have to deal with this fundamental problem that we must deal with in causal in

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s in π that a DAG implies. It does not even tell us that if π and π are adjacent in the DAG, then π and π are dependent. And this additional information is very commonly assumed in causal DAGs. <span>To get this guaranteed dependence between adjacent nodes, we will generally assume a slightly stronger assumption than the local Markov assumption: minimality <span>

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An βestimatorβ is a function that takes a dataset as input and outputs an estimate.

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Consistency is the assumption that the outcome we observe π is actually the potential outcome under the observed treatment π

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