https://machinelearning.subwiki.org/w/index.php?action=history&feed=atom&title=Do_operator
Do operator - Revision history
2026-07-31T03:36:22Z
Revision history for this page on the wiki
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https://machinelearning.subwiki.org/w/index.php?title=Do_operator&diff=1666&oldid=prev
IssaRice at 23:11, 14 February 2019
2019-02-14T23:11:49Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:11, 14 February 2019</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given [[random variable]]s <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math> (this notation assumes that the random variables corresponding to the individual values are clear from context). The notation <math>\Pr_x(y)</math> is also used.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given [[random variable]]s <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math> (this notation assumes that the random variables corresponding to the individual values are clear from context). The notation <math>\Pr_x(y)</math> is also used.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>. Note also that in the expression <math>\mathit{do}(X=x)</math>, the subexpression <math>X=x</math> does not mean the event where the random variable <math>X</math> takes on the value <math>x</math>, i.e. the event <math>\{\omega\in\Omega : X(\omega) = x\}</math>. Thus, inside a ''do'' operator, the standard notational convention of probability theory does not hold.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>. Note also that in the expression <math>\mathit{do}(X=x)</math>, the subexpression <math>X=x</math> does not mean the event where the random variable <math>X</math> takes on the value <math>x</math>, i.e. the event <math>\{\omega\in\Omega : X(\omega) = x\}</math>. Thus, inside a ''do'' operator, the standard notational convention of probability theory does not hold<ins style="font-weight: bold; text-decoration: none;">. To stress the point, suppose the event <math>X=x</math> can be specified in another way, such as by the event <math>Z=z</math>. In this case, since <math>X=x</math> and <math>Z=z</math> are exactly the same set, the probabilities involving them, such as <math>\Pr(X=x)</math> vs <math>\Pr(Z=z)</math> and <math>\Pr(Y=y \mid X=x)</math> vs <math>\Pr(Y=y \mid Z=z)</math>, should all be the same, but I don't think <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> and <math>\Pr(Y=y \mid \mathit{do}(Z=z))</math> need be the same (check this)</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td></tr>
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IssaRice
https://machinelearning.subwiki.org/w/index.php?title=Do_operator&diff=1665&oldid=prev
IssaRice at 23:07, 14 February 2019
2019-02-14T23:07:42Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:07, 14 February 2019</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given [[random variable]]s <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math> (this notation assumes that the random variables corresponding to the individual values are clear from context). The notation <math>\Pr_x(y)</math> is also used.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given [[random variable]]s <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math> (this notation assumes that the random variables corresponding to the individual values are clear from context). The notation <math>\Pr_x(y)</math> is also used.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math><ins style="font-weight: bold; text-decoration: none;">. Note also that in the expression <math>\mathit{do}(X=x)</math>, the subexpression <math>X=x</math> does not mean the event where the random variable <math>X</math> takes on the value <math>x</math>, i.e. the event <math>\{\omega\in\Omega : X(\omega) = x\}</math>. Thus, inside a ''do'' operator, the standard notational convention of probability theory does not hold</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td></tr>
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IssaRice
https://machinelearning.subwiki.org/w/index.php?title=Do_operator&diff=1664&oldid=prev
IssaRice at 23:04, 14 February 2019
2019-02-14T23:04:29Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:04, 14 February 2019</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==History==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Pearl: "An equivalent notation, using <math>\mathit{set}(x)</math> instead of <math>\mathit{do}(x)</math>, was used in Pearl (1995a). The <math>\mathit{do}(x)</math> notation was first used in Goldszmidt and Pearl (1992) and is gaining in popular support. Lauritzen (2001) used <math>P ( y \mid X \leftarrow x)</math>. The expression <math>P(y \mid \mathit{do}(x))</math> is equivalent in intent to <math>P(Y_x = y)</math> in the potential-outcome model introduced by Neyman (1923) and Rubin (1974) and to the expression <math>P[(X = x) \mathbin{\Box\!\!\rightarrow} (Y = y)]</math> in the counter-factual theory of Lewis (1973b)."<ref>Judea Pearl. ''Causality''. p. 70, footnote 2</ref></ins></div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==References==</ins></div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Causal inference]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Causal inference]]</div></td></tr>
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IssaRice
https://machinelearning.subwiki.org/w/index.php?title=Do_operator&diff=1352&oldid=prev
IssaRice at 00:24, 15 January 2019
2019-01-15T00:24:56Z
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td></tr>
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IssaRice
https://machinelearning.subwiki.org/w/index.php?title=Do_operator&diff=786&oldid=prev
IssaRice at 23:32, 23 September 2018
2018-09-23T23:32:53Z
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given [[random variable]]s <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math> (this notation assumes that the random variables corresponding to the individual values are clear from context).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given [[random variable]]s <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math> (this notation assumes that the random variables corresponding to the individual values are clear from context)<ins style="font-weight: bold; text-decoration: none;">. The notation <math>\Pr_x(y)</math> is also used</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td></tr>
</table>
IssaRice
https://machinelearning.subwiki.org/w/index.php?title=Do_operator&diff=376&oldid=prev
IssaRice at 20:36, 2 June 2018
2018-06-02T20:36:21Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:36, 2 June 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given random <del style="font-weight: bold; text-decoration: none;">variables </del><math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math> (this notation assumes that the random variables corresponding to the individual values are clear from context).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given <ins style="font-weight: bold; text-decoration: none;">[[</ins>random <ins style="font-weight: bold; text-decoration: none;">variable]]s </ins><math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math> (this notation assumes that the random variables corresponding to the individual values are clear from context).</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[Do calculus|''do'' calculus]].</div></td></tr>
</table>
IssaRice
https://machinelearning.subwiki.org/w/index.php?title=Do_operator&diff=374&oldid=prev
IssaRice at 20:33, 2 June 2018
2018-06-02T20:33:08Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:33, 2 June 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3">Line 3:</td>
<td colspan="2" class="diff-lineno">Line 3:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[''do'' calculus]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The ''do'' operator is used extensively in the [[<ins style="font-weight: bold; text-decoration: none;">Do calculus|</ins>''do'' calculus]].</div></td></tr>
</table>
IssaRice
https://machinelearning.subwiki.org/w/index.php?title=Do_operator&diff=373&oldid=prev
IssaRice at 20:32, 2 June 2018
2018-06-02T20:32:54Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:32, 2 June 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2">Line 2:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The ''do'' operator is used extensively in the [[''do'' calculus]].</ins></div></td></tr>
</table>
IssaRice
https://machinelearning.subwiki.org/w/index.php?title=Do_operator&diff=372&oldid=prev
IssaRice at 20:30, 2 June 2018
2018-06-02T20:30:25Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:30, 2 June 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given random variables <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given random variables <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</math> <ins style="font-weight: bold; text-decoration: none;">(this notation assumes that the random variables corresponding to the individual values are clear from context)</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td></tr>
</table>
IssaRice
https://machinelearning.subwiki.org/w/index.php?title=Do_operator&diff=371&oldid=prev
IssaRice at 20:29, 2 June 2018
2018-06-02T20:29:36Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:29, 2 June 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given random variables <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x</math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The '''''do'' operator''' is used in causal inference to denote an intervention. Given random variables <math>X,Y</math>, we write <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> to mean the [[probability]] that <math>Y=y</math> given we intervene and set <math>X</math> to be <math>x<ins style="font-weight: bold; text-decoration: none;"></math>. In some texts, this is abbreviated to <math>\Pr(y\mid\hat x)</ins></math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In general <math>\Pr(Y=y \mid \mathit{do}(X=x))</math> is not the same as conditioning on <math>X=x</math>, i.e. <math>\Pr(Y=y \mid X=x)</math>.</div></td></tr>
</table>
IssaRice