Graphic Model.pdf

Arrows on the path meet either head to tail or tail

• Notes
• 17

This preview shows page 15 - 17 out of 17 pages.

1.arrows on the path meet either head-to-tail or tail-to-tail at the node and this node is in Z 2.the arrows meet head-to-head at the node, and neither the node, nor any of its descendants, is in Z X1 indep of X3 given X2? X3 indep of X1 given X2? X4 indep of X1 given X2? X1 X4 X2 X3 X and Y are D-separated by Z (and therefore conditionally indep, given Z) iff every path from any variable in X to any variable in Y is blocked by Z A path from variable A to variable B is blocked by Z if it includes a node such that either 1.arrows on the path meet either head-to-tail or tail-to-tail at the node and this node is in Z 2.the arrows meet head-to-head at the node, and neither the node, nor any of its descendants, is in Z X4 indep of X1 given X3? X4 indep of X1 given {X3, X2}? X4 indep of X1 given {}? X1 X4 X2 X3

Subscribe to view the full document.

16 X and Y are D-separated by Z (and therefore conditionally indep, given Z) iff every path from any variable in X to any variable in Y is blocked A path from variable A to variable B is blocked if it includes a node such that either 1.arrows on the path meet either head-to-tail or tail-to-tail at the node and this node is in Z 2.the arrows meet head-to-head at the node, and neither the node, nor any of its descendants, is in Z a indep of b given c? a indep of b given f ? Markov Blanket from [Bishop, 8.2]
17 What You Should Know Bayes nets are convenient representation for encoding dependencies / conditional independence BN = Graph plus parameters of CPD’s Defines joint distribution over variables Can calculate everything else from that Though inference may be intractable Reading conditional independence relations from the graph Each node is cond indep of non-descendents, given only its parents – D-separation ‘Explaining away’ See Bayes Net applet:
• Fall '11
• Mitchell,Tom
• Probability theory, Bayesian network

{[ snackBarMessage ]}

"Before using Course Hero my grade was at 78%. By the end of the semester my grade was at 90%. I could not have done it without all the class material I found."
— Christopher R., University of Rhode Island '15, Course Hero Intern

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern