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OSL : Online Structure Learning using Background Knowledge Axiomatization Evangelos Michelioudakis 1 , Anastasios Skarlatidis 1 , Georgios Paliouras 1 and Alexander Artikis 2 , 1 1 Institute of Informatics and Telecommunications, NCSR

  1. OSL α : Online Structure Learning using Background Knowledge Axiomatization Evangelos Michelioudakis 1 , Anastasios Skarlatidis 1 , Georgios Paliouras 1 and Alexander Artikis 2 , 1 1 Institute of Informatics and Telecommunications, NCSR “Demokritos” 2 Department of Maritime Studies, University of Piraeus September 20, 2016

  2. Motivation ◮ Targets: ◮ Learning in temporal domains ◮ Handle uncertainty and complex relational structure ◮ Handle large (streaming) training data ◮ Approach: ◮ Markov Logic Networks, Event Calculus ( MLN − EC ) ◮ Online structure learning ( OSL α ) ◮ Starting point: Online Structure Learning (OSL) algorithm � Online strategy for updating the model × Cannot handle a search space having large domain of constants × Does not exploit background knowledge × Does not support first-order logic functions 1 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  3. Running Example: Activity Recognition ◮ Recognize human activities in multimedia content ◮ Video frames are annotated by humans I ndividual Activities C omplex Activities 340 enter ( id 0 ) 340 walking ( id 0 ) 340 coord ( id 0 )=( 20 . 88 , − 11 . 90 ) 340 walking ( id 1 ) 340 coord ( id 1 )=( 22 . 88 , − 14 . 80 ) 340 moving ( id 0 , id 1 ) · · · · · · 345 inactive ( id 0 ) 345 coord ( id 1 )=( 32 . 74 , − 5 . 24 ) 345 exit ( id 1 ) 2 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  4. − EC : Probabilistic Event Calculus based on MLNs MLN I NPUT ◮ T RANSFORMATION ◮ I NFERENCE ◮ O UTPUT � Composite Compact Event Knowledge Markov Logic Networks Definitions Base Recognised Composite Events Event Calculus Axioms Simple, Derived Event Stream 3 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  5. OSL α : Online Structure Learning using Background Knowledge Axiomatizaiton OSL α Data Stream/Training Examples Learnt Hypothesis H t : . . . 0 . 51 HoldsAt ( move ( id 1 , id 2 ) , t +1) ⇐ Micro-Batch D t HappensAt ( walking ( id 1 ) , t ) ∧ HappensAt ( walking ( ID 1 ) , 99) HappensAt ( walking ( id 2 ) , t ) HappensAt ( walking ( ID 2 ) , 99) OrientationMove ( ID 1 , ID 2 , 99) Close ( ID 1 , ID 2 , 34 , 99) Next (99 , 100) HoldsAt ( move ( ID 1 , ID 2 ) , 100) . . . MLN − EC Axioms : HoldsAt ( f, t +1) ⇐ InitiatedAt ( f, t ) HoldsAt ( f, t +1) ⇐ HoldsAt ( f, t ) ∧ ¬ TerminatedAt ( f, t ) ¬ HoldsAt ( f, t +1) ⇐ TerminatedAt ( f, t ) ¬ HoldsAt ( f, t +1) ⇐ ¬ HoldsAt ( f, t ) ∧ ¬ InitiatedAt ( f, t ) 4 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  6. OSL α : Online Structure Learning using Background Knowledge Axiomatizaiton OSL α Data Stream/Training Examples EC Axioms : Learnt Hypothesis H t : − MLN . . . 0 . 51 HoldsAt ( move ( id 1 , id 2 ) , t +1) ⇐ HoldsAt ( f, t +1) ⇐ Micro-Batch D t HappensAt ( walking ( id 1 ) , t ) ∧ HappensAt ( walking ( ID 1 ) , 99) HappensAt ( walking ( id 2 ) , t ) InitiatedAt ( f, t ) HappensAt ( walking ( ID 2 ) , 99) OrientationMove ( ID 1 , ID 2 , 99) HoldsAt ( f, t +1) ⇐ Close ( ID 1 , ID 2 , 34 , 99) Next (99 , 100) HoldsAt ( f, t ) ∧ HoldsAt ( move ( ID 1 , ID 2 ) , 100) ¬ TerminatedAt ( f, t ) . . . MLN − EC Axioms : HoldsAt ( f, t +1) ⇐ ¬ HoldsAt ( f, t +1) ⇐ InitiatedAt ( f, t ) TerminatedAt ( f, t ) HoldsAt ( f, t +1) ⇐ HoldsAt ( f, t ) ∧ ¬ TerminatedAt ( f, t ) ¬ HoldsAt ( f, t +1) ⇐ ¬ HoldsAt ( f, t +1) ⇐ ¬ HoldsAt ( f, t ) ∧ TerminatedAt ( f, t ) ¬ InitiatedAt ( f, t ) ¬ HoldsAt ( f, t +1) ⇐ ¬ HoldsAt ( f, t ) ∧ ¬ InitiatedAt ( f, t ) 4 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  7. OSL α : Online Structure Learning using Background Knowledge Axiomatizaiton OSL α Data Stream/Training Examples Learnt Hypothesis H t : . . . 0 . 51 HoldsAt ( move ( id 1 , id 2 ) , t +1) ⇐ Inference Micro-Batch D t HappensAt ( walking ( id 1 ) , t ) ∧ HappensAt ( walking ( ID 1 ) , 99) HappensAt ( walking ( id 2 ) , t ) HappensAt ( walking ( ID 2 ) , 99) OrientationMove ( ID 1 , ID 2 , 99) Close ( ID 1 , ID 2 , 34 , 99) Next (99 , 100) HoldsAt ( move ( ID 1 , ID 2 ) , 100) . . . EC Axioms : MLN − HoldsAt ( f, t +1) ⇐ InitiatedAt ( f, t ) HoldsAt ( f, t +1) ⇐ HoldsAt ( f, t ) ∧ ¬ TerminatedAt ( f, t ) ¬ HoldsAt ( f, t +1) ⇐ TerminatedAt ( f, t ) ¬ HoldsAt ( f, t +1) ⇐ ¬ HoldsAt ( f, t ) ∧ ¬ InitiatedAt ( f, t ) 4 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  8. OSL α : Online Structure Learning using Background Knowledge Axiomatizaiton OSL α Data Stream/Training Examples Learnt Hypothesis H t : . . . 0 . 51 HoldsAt ( move ( id 1 , id 2 ) , t +1) ⇐ Hypergraph Inference Micro-Batch D t HappensAt ( walking ( id 1 ) , t ) ∧ HappensAt ( walking ( ID 1 ) , 99) HappensAt ( walking ( id 2 ) , t ) HappensAt ( walking ( ID 2 ) , 99) OrientationMove ( ID 1 , ID 2 , 99) Close ( ID 1 , ID 2 , 34 , 99) Next (99 , 100) HoldsAt ( move ( ID 1 , ID 2 ) , 100) . . . EC Axioms : MLN − HoldsAt ( f, t +1) ⇐ InitiatedAt ( f, t ) HoldsAt ( f, t +1) ⇐ HoldsAt ( f, t ) ∧ ¬ TerminatedAt ( f, t ) ¬ HoldsAt ( f, t +1) ⇐ TerminatedAt ( f, t ) ¬ HoldsAt ( f, t +1) ⇐ ¬ HoldsAt ( f, t ) ∧ ¬ InitiatedAt ( f, t ) 4 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  9. OSL α : Online Structure Learning using Background Knowledge Axiomatizaiton OSL α Data Stream/Training Examples Learnt Hypothesis H t : . . . 0 . 51 HoldsAt ( move ( id 1 , id 2 ) , t +1) ⇐ Hypergraph Inference Micro-Batch D t HappensAt ( walking ( id 1 ) , t ) ∧ HappensAt ( walking ( ID 1 ) , 99) HappensAt ( walking ( id 2 ) , t ) HappensAt ( walking ( ID 2 ) , 99) OrientationMove ( ID 1 , ID 2 , 99) Close ( ID 1 , ID 2 , 34 , 99) Next (99 , 100) HoldsAt ( move ( ID 1 , ID 2 ) , 100) . . . Paths to EC Axioms : MLN − Clauses HoldsAt ( f, t +1) ⇐ InitiatedAt ( f, t ) HoldsAt ( f, t +1) ⇐ HoldsAt ( f, t ) ∧ ¬ TerminatedAt ( f, t ) ¬ HoldsAt ( f, t +1) ⇐ TerminatedAt ( f, t ) Clause Evaluation ¬ HoldsAt ( f, t +1) ⇐ ¬ HoldsAt ( f, t ) ∧ ¬ InitiatedAt ( f, t ) 4 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  10. OSL α : Online Structure Learning using Background Knowledge Axiomatizaiton OSL α Data Stream/Training Examples Learnt Hypothesis H t : . . . 0 . 51 HoldsAt ( move ( id 1 , id 2 ) , t +1) ⇐ Hypergraph Inference Micro-Batch D t HappensAt ( walking ( id 1 ) , t ) ∧ HappensAt ( walking ( ID 1 ) , 99) HappensAt ( walking ( id 2 ) , t ) HappensAt ( walking ( ID 2 ) , 99) OrientationMove ( ID 1 , ID 2 , 99) Close ( ID 1 , ID 2 , 34 , 99) Next (99 , 100) HoldsAt ( move ( ID 1 , ID 2 ) , 100) . . . Paths to EC Axioms : MLN − Clauses HoldsAt ( f, t +1) ⇐ InitiatedAt ( f, t ) HoldsAt ( f, t +1) ⇐ HoldsAt ( f, t ) ∧ ¬ TerminatedAt ( f, t ) ¬ HoldsAt ( f, t +1) ⇐ TerminatedAt ( f, t ) Weight Clause Learning Evaluation ¬ HoldsAt ( f, t +1) ⇐ ¬ HoldsAt ( f, t ) ∧ ¬ InitiatedAt ( f, t ) 4 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  11. OSL α : Online Structure Learning using Background Knowledge Axiomatizaiton OSL α Data Stream/Training Examples Learnt Hypothesis H t : . . . 0 . 51 HoldsAt ( move ( id 1 , id 2 ) , t +1) ⇐ Hypergraph Inference Micro-Batch D t HappensAt ( walking ( id 1 ) , t ) ∧ HappensAt ( walking ( ID 1 ) , 99) HappensAt ( walking ( id 2 ) , t ) HappensAt ( walking ( ID 2 ) , 99) + OrientationMove ( ID 1 , ID 2 , 99) Close ( ID 1 , ID 2 , 34 , 99) Next (99 , 100) HoldsAt ( move ( ID 1 , ID 2 ) , 100) . . . Paths to EC Axioms : MLN − Clauses HoldsAt ( f, t +1) ⇐ . . . InitiatedAt ( f, t ) Micro-Batch D t +1 HoldsAt ( f, t +1) ⇐ HappensAt ( exit ( ID 1 ) , 200) HoldsAt ( f, t ) ∧ HappensAt ( walking ( ID 2 ) , 200) ¬ TerminatedAt ( f, t ) ¬ OrientationMove ( ID 1 , ID 2 , 200) ¬ Close ( ID 1 , ID 2 , 34 , 200) ¬ HoldsAt ( f, t +1) ⇐ Next (200 , 201) TerminatedAt ( f, t ) Weight Clause ¬ HoldsAt ( move ( ID 1 , ID 2 ) , 201) Learning Evaluation ¬ HoldsAt ( f, t +1) ⇐ . . . ¬ HoldsAt ( f, t ) ∧ ¬ InitiatedAt ( f, t ) . . . 4 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  12. Reduced Hypergraph and Relational Pathfinding AUXWalking HappensAt WalkingID2 HappensAt Close 34 WalkingID1 99 AUXWalking ID2 Next OrientationMove 100 ID1 HoldsAt MoveID1ID2 AUXMove 5 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  13. Template Guided Search HoldsAt ( f, t 1 ) ⇐ Wrongly predicted atom: InitiatedAt ( f, t 0 ) ∧ ¬ HoldsAt ( MoveID 1 ID 2 , 100 ) Next ( t 0 , t 1 ) 6 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

  14. Template Guided Search HoldsAt ( f, t 1 ) ⇐ Wrongly predicted atom: InitiatedAt ( f, t 0 ) ∧ ¬ HoldsAt ( MoveID 1 ID 2 , 100 ) Next ( t 0 , t 1 ) HoldsAt ( MoveID 1 ID 2 , 100 ) ⇐ InitiatedAt ( MoveID 1 ID 2 , t 0 ) ∧ Next ( t 0 , 100 ) 6 / 18 Evangelos Michelioudakis OSL α : Online Structure Learning using Background Knowledge Axiomatization

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