Warning: "continue" targeting switch is equivalent to "break". Did you mean to use "continue 2"? in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 726

Warning: "continue" targeting switch is equivalent to "break". Did you mean to use "continue 2"? in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 729

Deprecated: Function get_magic_quotes_gpc() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 421

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/cookbook/recipecheck.php on line 80

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/cookbook/recipecheck.php on line 94

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Warning: Use of undefined constant MathJaxInlineCallback - assumed 'MathJaxInlineCallback' (this will throw an Error in a future version of PHP) in /cgihome/cis520/html/dynamic/2018/wiki/cookbook/MathJax.php on line 84

Warning: Use of undefined constant MathJaxEquationCallback - assumed 'MathJaxEquationCallback' (this will throw an Error in a future version of PHP) in /cgihome/cis520/html/dynamic/2018/wiki/cookbook/MathJax.php on line 88

Warning: Use of undefined constant MathJaxLatexeqrefCallback - assumed 'MathJaxLatexeqrefCallback' (this will throw an Error in a future version of PHP) in /cgihome/cis520/html/dynamic/2018/wiki/cookbook/MathJax.php on line 94

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Function create_function() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 484

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/cookbook/wikipublisher/wikipublisher.php on line 1020

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/cookbook/wikipublisher/wikipublisher.php on line 1056

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/cookbook/wikipublisher/wikipublisher.php on line 1074

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/cookbook/analyze.php on line 89

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/scripts/skins.php on line 118

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/scripts/pagelist.php on line 436

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/scripts/pagelist.php on line 486

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/scripts/pagelist.php on line 488

Deprecated: Function get_magic_quotes_gpc() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 421

Deprecated: Function get_magic_quotes_gpc() is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 421

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/scripts/upload.php on line 345

Deprecated: Array and string offset access syntax with curly braces is deprecated in /cgihome/cis520/html/dynamic/2018/wiki/scripts/upload.php on line 384

Warning: Cannot modify header information - headers already sent by (output started at /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php:484) in /cgihome/cis520/html/dynamic/2018/wiki/pmwiki.php on line 1304
CIS520 Machine Learning | Lectures / Weak Union
Recent Changes - Search:

Home

Weak Union

 

Prove

{$ (X \bot Y,W | Z) \rightarrow (X \bot Y | Z,W) $}

Use Conditional Independence definition: {$ (A \bot B | C) \rightarrow p(A|B,C) = p(A|C) $}

on each of the two parts of the theorem

{$ (X \bot Y,W | Z) \rightarrow p(X|Y,W,Z) = p(X|Z) $}

{$ (X \bot Y | Z,W) \rightarrow P(X|Y,W,Z) = P(X|Z,W)$}

but {$ p(X|Z) = P(X|Z,W)$}

Why?

{$ p(X|Z)$} is the expectation over Y and W of {$ p(X|Y,W,Z) $}, and {$P(X|Z,W)$} is the expectation over Y of the same quantity. But since we assumed X is conditionally independent of Y and W, taking the expectation over Y or W or both does not change the value. Back to Lectures

Edit - History - Print - Recent Changes - Search
Page last modified on 24 November 2013 at 03:10 PM