UMD CMSC 828G  Principles of Data Mining (29 pages)
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Principles of Data Mining
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Lecture Notes
 Pages:
 29
 School:
 University of Maryland, College Park
 Course:
 Cmsc 828g  Advanced Topics in Information Processing:DataIntensive Computing with MapReduce
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CMSC828G Principles of Data Mining Readings handouts Today s Lecture d Separation minimal I Maps Bayesian Networks Markov Networks Upcoming Due Dates H2 due today P2 due 3 14 Lecture 12 Summary of Last Class We defined the following concepts The Markov Independences of a DAG G I Xi NonDesc Xi Pai G is an I Map of a distribution P If P satisfies the Markov independencies implied by G We proved the factorization theorem if G is an I Map of P then P X1 X n P X i Pai i slides courtesy of Nir Friedman see references Conditional Independencies Let Markov G be the set of Markov Independencies implied by G The factorization theorem shows P X1 Xn P Xi Pai G is an I Map of P i We can also show the opposite Thm of P P X1 Xn P Xi Pai G is an I Map i Proof Outline Example X Z Y P X Y Z P X P Y X P Z X P Z X Y P X Y P X P Y X P Z X Implied Independencies Does a graph G imply additional independencies as a consequence of Markov G We can define a logic of independence statements Some axioms I X Y Z I Y X Z I X Y1 Y2 Z I X Y1 Z d seperation A procedure d sep X Y Z G that given a DAG G and sets X Y and Z returns either yes or no Goal d sep X Y Z G yes iff I X Y Z follows from Markov G Paths Intuition dependency must flow along paths in the graph A path is a sequence of neighboring variables Examples R E A B C A E R Earthquake Radio Burglary Alarm Call Paths We want to know when a path is active creates dependency between end nodes blocked cannot create dependency end nodes We want to classify situations in which paths are active Path Blockage Three cases Blocked Common cause E E Unblocked Active R A R A Path Blockage Three cases Common cause Blocked E Unblocked Active E Intermediate cause A A C C Path Blockage Three cases Common cause Blocked E Intermediate cause Common Effect Unblocked Active E B A B C A E C B A C Path Blockage General Case A path is active given evidence Z if Whenever we have the configuration A C B B or one of its descendents are in Z No other nodes in the path
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