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on 08-May-2022 (Sun)
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Open itWe refer to the flow of association along directed paths as causal association. A common type of non-causal association that makes total association not causation is confounding association. In the graph in Figure 3.20, we depict the confounding association in red
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Open itCausal graphs are special in that we additionally assume that the edges have causal meaning (causal edges assumption, Assumption 3.3). This assumption is what introduces causality into our models, and it makes one type of path take on a whole new meaning: directed paths. This assumption endows directed paths with the unique role of carrying causation along them. Additionally, this assumption is asymmetric; “ 𝑋 is a cause of 𝑌 ” is not the same as saying
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Open itThe Positivity-Unconfoundedness Tradeoff Although conditioning on more covariates could lead to a higher chance of satisfying unconfoundedness, it can lead to a higher chance of violating positivity. As we increase the dimension of the covariates, we make the subgroups for any level 𝑥 of the covariates smaller.
Original toplevel document (pdf)
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Open itAs we discussed in Section 4.2, the graph for the interventional distribution 𝑃(𝑌 | do(𝑡)) is the same as the graph for the observational distribution 𝑃(𝑌, 𝑇, 𝑋) , but with the incoming edges to 𝑇 removed.
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Open itened node has no causal parents is that the intervened node is set to a constant value, so it no longer depends on any of the variables it depends on in the observational setting (its parents). <span>The graph with edges removed is known as the manipulated graph <span>
Original toplevel document (pdf)
cannot see any pdfsFlashcard 7082274327820
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Open itThis non-causal association flows along the 𝑇 ← 𝑋 → 𝑌 path
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