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# Whenever Lifted Conviction Engendering.

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At whatever time Lifted Conviction Engendering SRI Global College of Wisconsin SRI Worldwide College of Wisconsin UC Berkeley Rodrigo de Salvo Braz Sriraam Natarajan Hung Bui Jude Shavlik Stuart Russell Slides online http://www.ai.sri.com/~braz/and go to "Presentations"
Transcripts
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At whatever time Lifted Belief Propagation SRI International University of Wisconsin SRI International University of Wisconsin UC Berkeley Rodrigo de Salvo Braz Sriraam Natarajan Hung Bui Jude Shavlik Stuart Russell

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Slides online http://www.ai.sri.com/~braz/and go to âPresentationsâ

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What we are doing Regular lifted induction (de Salvo Braz et al, MLNs, Milch) smashs models (thoroughly parts them) before surmising begins Needs to consider whole model before giving an outcome In this work, we interleave part and derivation , getting definite limits on question as we go We more often than not won\'t smash or consider whole model before yielding answer

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Outline Background Relational Probabilistic Models Propositionalization Belief Propagation Lifted Belief Propagation and shattering Anytime Lifted Belief Propagation Intuition Box proliferation Example Final Remarks Connection to Theorem Proving Conclusion Future headings

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Background

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Relational Probabilistic Model Compact representation for graphical models A parameterized component (parfactor) remains for every one of its instantiations 8 Y ï¦ 1 (clever( Y )) 8 X,Y ï¦ 2 (interesting( Y ),likes( X , Y )), X â  Y remains for ï¦ 1 (entertaining( a )), ï¦ 1 (amusing( b )), ï¦ 1 (clever( c )),â¦, ï¦ 2 (amusing( a ),preferences( b , a )), ï¦ 2 (entertaining( a ),preferences( c , a )),â¦, ï¦ 2 (amusing( z ),loves( a , z )),â¦

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Propositionalization 8 Y ï¦ 1 (clever( Y )) 8 X , Y ï¦ 2 (clever( Y ),likes( X , Y )), X â  Y P(funny( fred ) | likes( tom , fred )) = ? Confirmation likes( tom , fred ) ï¦ 2 likes( alice , fred ) ï¦ 2 Query amusing( fred ) ï¦ 1 ï¦ 2 preferences( weave , fred ) â¦ ï¦ 2 likes( zoe , fred )

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Belief Propagation Propagates messages the distance to question 8 Y ï¦ 1 (clever( Y )) 8 X , Y ï¦ 2 (entertaining( Y ),likes( X , Y )), X â  Y P(funny( fred ) | likes( tom , fred )) = ? Confirmation sends an alternate message on the grounds that it has proof on it loves( tom , fred ) ï¦ 2 likes( alice , fred ) ï¦ 2 Query interesting( fred ) ï¦ 1 ï¦ 2 preferences( sway , fred ) â¦ gatherings of indistinguishable messages ï¦ 2 likes( zoe , fred )

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Lifted Belief Propagation Groups indistinguishable messages and figures them once 8 Y ï¦ 1 (amusing( Y )) 8 X,Y ï¦ 2 (clever( Y ),likes( X , Y )), X â  Y P(funny( fred ) | likes( tom , fred )) = ? Proof Evidence likes( tom , fred ) likes( tom , fred ) Query likes( alice , fred ) interesting( fred ) clever( fred ) likes( Person , fred ) preferences( sway , fred ) â¦ messages exponentiated by the quantity of individual indistinguishable messages likes( zoe , fred ) group of symmetric arbitrary variables

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The Need for Shattering Lifted BP relies on upon bunches of variables being symmetric , that is, sending and accepting indistinguishable messages. At the end of the day, it speaks the truth partitioning arbitrary variables in cases neighbors( X , Y ) amusing( Y ) likes( X , Y ) cohorts( X , Y ) Evidence: neighbors( tom , fred ), schoolmates( mary , fred )

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The Need for Shattering Evidence on neighbors( tom , fred ) makes it unmistakable from others in âneighborsâ bunch neighbors( tom , fred ) interesting( fred ) likes( tom , fred ) colleagues( tom , fred ) neighbors( X , fred ) likes( X , fred ) colleagues( X , fred ) neighbors( X , Y ) clever( Y ) likes( X , Y ) colleagues( X , Y ) Even groups without confirmation should be part in light of the fact that particular messages make their destinations particular too x Even bunches without proof should be part Y not fred X not tom

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The Need for Shattering In general lifted BP, we just get the chance to group flawlessly exchangeable items (everybody who is not tom or mary âbehaves the sameâ). On the off chance that they are simply comparative , despite everything they should be considered independently . neighbors( tom , fred ) clever( fred ) likes( tom , fred ) schoolmates( tom , fred ) neighbors( mary , fred ) likes( mary , fred ) colleagues( mary , fred ) X not in { tom , mary } neighbors( X , fred ) likes( X , fred ) cohorts( X , fred ) Evidence on schoolmates( mary , fred ) further parts groups Evidence on colleagues( mary , fred ) further parts bunches Y not fred neighbors( X , Y ) entertaining( Y ) likes( X , Y ) schoolmates( X , Y )

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Anytime Lifted Belief Propagation

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Intuition for Anytime Lifted BP in( House , Town ) next( House , Another ) seismic tremor( Town ) lives( Another , Neighbor ) Alarm can go off because of a quake alert( House ) saw( Neighbor , Someone ) veiled( Someone ) theft( House ) A âpriorâ variable makes caution going off improbable without those reasons Alarm can go off because of thievery in( House , Item ) partOf( Entrance , House ) broken( Entrance ) missing( Item )

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Intuition for Anytime Lifted BP in( House , Town ) next( House , Another ) tremor( Town ) lives( Another , Neighbor ) alert( House ) saw( Neighbor , Someone ) covered( Someone ) robbery( House ) Given a home in sf with home2 and home3 by it with neighbors jim and mary , every seeing person1 and person2 , a few things in home , including a missing ring and non-missing money , crushed front yet not broken spirit passages to home, a quake in sf , what is the likelihood that home âs alert goes off? in( House , Item ) partOf( Entrance , House ) broken( Entrance ) missing( Item )

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Lifted Belief Propagation Message ignoring whole model before acquiring inquiry answer next( home , home2 ) in( home , sf ) Complete shattering before conviction engendering begins lives( home2 , jim ) â¦ seismic tremor( sf ) saw( jim , person1 ) covered( person1 ) next( home , home3 ) caution( home ) lives( home2 , mary ) saw( mary , person2 ) robbery( home ) conceal( person2 ) in( home , money ) partOf( front , home ) â¦ missing( money ) broken( front ) in( home , Item ) in( home , ring ) partOf( back , home ) Item not in { ring , cash,â¦} â¦ missing( ring ) missing( Item ) broken( back )

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Intuition for Anytime Lifted BP next( home , home2 ) Evidence in( home , sf ) lives( home2 , jim ) â¦ quake( sf ) saw( jim , person1 ) Given tremor, we as of now have a decent lower bound, paying little mind to thievery branch Query veiled( person1 ) next( home , home3 ) alert( home ) lives( home2 , mary ) saw( mary , person2 ) theft( home ) conceal( person2 ) Wasted shattering! Squandered shattering! Squandered shattering! Squandered shattering! Squandered shattering! in( home , money ) partOf( front , home ) â¦ missing( money ) broken( front ) in( home , Item ) in( home , ring ) partOf( back , home ) Item not in { ring , cash,â¦} â¦ missing( ring ) missing( Item ) broken( back )

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Using just a segment of a model By utilizing just a segment, I donât need to smash different parts of the model. In what capacity can utilize just a bit? An answer for propositional models as of now exists: box spread.

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Box Propagation A method for getting limits on inquiry without looking at whole system. [0, 1] A

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Box Propagation A method for getting limits on inquiry without looking at whole system. [0.36, 0.67] [0, 1] A B f 1

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Box Propagation A method for getting limits on question without looking at whole system. [0,1] [0.1, 0.6] [0.38, 0.50] [0.05, 0.5] f 2 ... A B f 1 [0,1] f 3 ... [0.32, 0.4]

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Box Propagation A method for getting limits on question without looking at whole system. [0.2,0.8] [0.3, 0.4] [0.41, 0.44] [0.17, 0.3] f 2 ... A B f 1 [0,1] f 3 ... [0.32, 0.4]

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Box Propagation A method for getting limits on question without looking at whole system. 0.45 0.32 0.42 0.21 f 2 ... A B f 1 0.3 f 3 ... 0.36 Convergence after all messages are gathered

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Anytime Lifted BP Incremental shattering + box engendering

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Anytime Lifted Belief Propagation Start from question alone [0,1] caution( home ) The calculation meets expectations by picking a bunch variable and incorporating the components in its sweeping

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Anytime Lifted Belief Propagation in( home , Town ) seismic tremor( Town ) [0.1, 0.9] alert( home ) theft( home ) ï¦ (caution( home ), in( home , Town ), quake( Town )) subsequent to bringing together caution( home ) and alert( House ) in ï¦ (caution( House ), in( House , Town ), tremor( Town )) creating imperative House = home Again, through unification Blanket elements alone can focus a bound on inquiry (if alert dependably has a likelihood of going off of no less than 0.1 and at most 0.9 regarless of robbery or quakes)

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Anytime Lifted Belief Propagation ï¦ (in( home , sf )) in( home , sf ) seismic tremor( sf ) Cluster in( home , Town ) brings together with in( home , sf ) in ï¦ (in( home , sf )) (which speaks to proof) part group around Town = sf [0.1, 0.9] alert( home ) thievery( home ) in( home , Town ) Bound continues as before in light of the fact that we still havenât considered confirmation on tremors Town â  sf quake( Town )

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Anytime Lifted Belief Propagation in( home , sf ) ï¦ ( quake( sf ) speaks to the confirmation that there was a seismic tremor( sf ) [0.8, 0.9] alert( home ) robbery( home ) Now question bound gets to be tight No compelling reason to further extend (and break) different branches If bound is adequate, there is no compelling reason to further grow (and break) different branches in( home , Town ) Town â  sf seismic tremor( Town )

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Anytime Lifted Belief Propagation in( home , sf ) tremor( sf ) [0.85, 0.9] partOf( front , home ) caution( home ) robbery( home ) broken( front ) in( home , Town ) We can continue growing voluntarily for smaller boundsâ¦ Now inquiry bound gets to

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