Online Learning of Weighted Relational Rules for Complex Event - - PowerPoint PPT Presentation

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Online Learning of Weighted Relational Rules for Complex Event - - PowerPoint PPT Presentation

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Online Learning of Weighted Relational Rules for Complex Event Recognition Nikos Katzouris 1 ,Evangelos Michelioudakis 3,1 , Alexander Artikis 2,1 and Georios Paliouras 1 http://cer.iit.demokritos.gr 1 National Center for Scientific Research

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Online Learning of Weighted Relational Rules for Complex Event Recognition

Nikos Katzouris1,Evangelos Michelioudakis3,1, Alexander Artikis2,1 and Georios Paliouras1

http://cer.iit.demokritos.gr

1National Center for Scientific Research Demokritos, Athens, Greece 2University of piraeus, Piraeus, Greece, 3National University of Athens, Athens, Greece

ECML-PKDD 2018

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The problem Setting

Input ◮ Recognition ◮ Output

Event Recognition System Complex Event Definitions

Simple Events . . . . . . . . . . . .

initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(active(Y ), T), holdsAt(close(X , Y , 25), T). terminatedAt(meet(X , Y ), T) ← happensAt(walking(X ), T), not holdsAt(close(X , Y , 25), T). Event Calculus as a Reasoning Engine holdsAt(F, T + 1) ← initiatedAtF, T) holdsAtAt(F, T + 1) ← holdsAt(F, T), not terminatedAt(F, T). Very efficient inference: Artikis et al. An Event Calculus for Event Recognition, TKDE, 2015. happensAt(active(id0 ), 10) holdsAt(coord(id0 , 20.88, 11.90), 10) happensAt(active(id1 ), 10) holdsAt(coord(id1 , 22.34, 15.23), 10)

. . .

Complex Events . . . . . . . . . . . .

holdsAt(meet(id0 , id1 ), 11) holdsAt(meet(id0 , id1 ), 12) holdsAt(meet(id0 , id1 ), 13)

. . .

Learn this From These

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The problem Setting

Input ◮ Recognition ◮ Output

Event Recognition System Complex Event Definitions

Simple Events . . . . . . . . . . . .

initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(active(Y ), T), holdsAt(close(X , Y , 25), T). terminatedAt(meet(X , Y ), T) ← happensAt(walking(X ), T), not holdsAt(close(X , Y , 25), T). Event Calculus as a Reasoning Engine holdsAt(F, T + 1) ← initiatedAtF, T) holdsAtAt(F, T + 1) ← holdsAt(F, T), not terminatedAt(F, T). Very efficient inference: Artikis et al. An Event Calculus for Event Recognition, TKDE, 2015. happensAt(active(id0 ), 10) holdsAt(coord(id0 , 20.88, 11.90), 10) happensAt(active(id1 ), 10) holdsAt(coord(id1 , 22.34, 15.23), 10)

. . .

Complex Events . . . . . . . . . . . .

holdsAt(meet(id0 , id1 ), 11) holdsAt(meet(id0 , id1 ), 12) holdsAt(meet(id0 , id1 ), 13)

. . .

Learn this From These

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The problem Setting

Input ◮ Recognition ◮ Output

Event Recognition System Complex Event Definitions

Simple Events . . . . . . . . . . . .

initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(active(Y ), T), holdsAt(close(X , Y , 25), T). terminatedAt(meet(X , Y ), T) ← happensAt(walking(X ), T), not holdsAt(close(X , Y , 25), T). Event Calculus as a Reasoning Engine holdsAt(F, T + 1) ← initiatedAtF, T) holdsAtAt(F, T + 1) ← holdsAt(F, T), not terminatedAt(F, T). Very efficient inference: Artikis et al. An Event Calculus for Event Recognition, TKDE, 2015. happensAt(active(id0 ), 10) holdsAt(coord(id0 , 20.88, 11.90), 10) happensAt(active(id1 ), 10) holdsAt(coord(id1 , 22.34, 15.23), 10)

. . .

Complex Events . . . . . . . . . . . .

holdsAt(meet(id0 , id1 ), 11) holdsAt(meet(id0 , id1 ), 12) holdsAt(meet(id0 , id1 ), 13)

. . .

Learn this From These

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The problem Setting

Input ◮ Recognition ◮ Output

Event Recognition System Complex Event Definitions

Simple Events . . . . . . . . . . . .

initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(active(Y ), T), holdsAt(close(X , Y , 25), T). terminatedAt(meet(X , Y ), T) ← happensAt(walking(X ), T), not holdsAt(close(X , Y , 25), T). Event Calculus as a Reasoning Engine holdsAt(F, T + 1) ← initiatedAtF, T) holdsAtAt(F, T + 1) ← holdsAt(F, T), not terminatedAt(F, T). Very efficient inference: Artikis et al. An Event Calculus for Event Recognition, TKDE, 2015. happensAt(active(id0 ), 10) holdsAt(coord(id0 , 20.88, 11.90), 10) happensAt(active(id1 ), 10) holdsAt(coord(id1 , 22.34, 15.23), 10)

. . .

Complex Events . . . . . . . . . . . .

holdsAt(meet(id0 , id1 ), 11) holdsAt(meet(id0 , id1 ), 12) holdsAt(meet(id0 , id1 ), 13)

. . .

Learn this From These

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The problem Setting

Input ◮ Recognition ◮ Output

Event Recognition System Complex Event Definitions

Simple Events . . . . . . . . . . . .

initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(active(Y ), T), holdsAt(close(X , Y , 25), T). terminatedAt(meet(X , Y ), T) ← happensAt(walking(X ), T), not holdsAt(close(X , Y , 25), T). Event Calculus as a Reasoning Engine holdsAt(F, T + 1) ← initiatedAtF, T) holdsAtAt(F, T + 1) ← holdsAt(F, T), not terminatedAt(F, T). Very efficient inference: Artikis et al. An Event Calculus for Event Recognition, TKDE, 2015. happensAt(active(id0 ), 10) holdsAt(coord(id0 , 20.88, 11.90), 10) happensAt(active(id1 ), 10) holdsAt(coord(id1 , 22.34, 15.23), 10)

. . .

Complex Events . . . . . . . . . . . .

holdsAt(meet(id0 , id1 ), 11) holdsAt(meet(id0 , id1 ), 12) holdsAt(meet(id0 , id1 ), 13)

. . .

Learn this From These

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Learning Requirements

◮ Event recognition applications deal with noisy data streams.

◮ Resilience to noise → Statistical Relational Learning. ◮ Learning should be online.

◮ Single-pass. ◮ Learn from past mistakes.

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Contribution of this Work

Two online learners from previous work: ◮ OLED

◮ Katzouris N. et al. Online Learning of Event Definitions, TPLP, 2016.

◮ ✓ Efficient structure learning using Hoeffding bounds. ◮ ✗ Crisp learner. ◮ OSLα

◮ Micheloudakis V., et al. OSLa: Online Structure Learning using

Background Knowledge Axiomatization, ECML, 2016.

◮ MLN learner. ◮ ✓ Efficient weight learning. ◮ ✗ Inefficient structure learning.

◮ Blindly generates too many rules.

Current work: ◮ WoLED (OLED + weight learning)

◮ MLN learner ◮ ✓ Efficient structure learning. ◮ ✓ Efficient weight learning.

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OLED

initiatedAt(meet(X , Y ), T) ← initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T). initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(inactive(Y ), T). initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(inactive(Y ), T), holdsAt(close(X , Y , 25), T).

. . .

initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), holdsAt(close(X , Y , 25), T). initiatedAt(meet(X , Y ), T) ← happensAt(inactive(Y ), T).

...

initiatedAt(meet(X , Y ), T) ← holdsAt(orientation(X , Y , 45), T initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(inactive(Y ), T), holdsAt(close(X , Y , 25), T), holdsAt(close(Y , X , 25), T), not happensAt(inactive(X ), T), not happensAt(abrupt(X ), T), not happensAt(running(X ), T), happensAt(inactive(Y ), T), not happensAt(active(Y ), T), not happensAt(running(Y ), T), not happensAt(abrupt(Y ), T), holdsAt(orientation(X , Y , 45), T).

. . . . . . . . .

Bottom Clause ⊥ :

Used O( 1 ǫ2 ln 1 δ ) examples Used O( 1 ǫ2 ln 1 δ ) examples Used O( 1 ǫ2 ln 1 δ ) examples

◮ Learns a rule with online hill-climbing.

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OLED

initiatedAt(meet(X , Y ), T) ← initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T). initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(inactive(Y ), T). initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(inactive(Y ), T), holdsAt(close(X , Y , 25), T).

. . .

initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), holdsAt(close(X , Y , 25), T). initiatedAt(meet(X , Y ), T) ← happensAt(inactive(Y ), T).

...

initiatedAt(meet(X , Y ), T) ← holdsAt(orientation(X , Y , 45), T initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(inactive(Y ), T), holdsAt(close(X , Y , 25), T), holdsAt(close(Y , X , 25), T), not happensAt(inactive(X ), T), not happensAt(abrupt(X ), T), not happensAt(running(X ), T), happensAt(inactive(Y ), T), not happensAt(active(Y ), T), not happensAt(running(Y ), T), not happensAt(abrupt(Y ), T), holdsAt(orientation(X , Y , 45), T).

. . . . . . . . .

Bottom Clause ⊥ :

Used O( 1 ǫ2 ln 1 δ ) examples Used O( 1 ǫ2 ln 1 δ ) examples Used O( 1 ǫ2 ln 1 δ ) examples

◮ Uses Hoeffding tests to make (ǫ, δ)-optimal decisions.

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WoLED

−0.829 initiatedAt(meet(X , Y ), T) ← 0.2 initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T). 0.5 initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(inactive(Y ), T). 1.82 initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(inactive(Y ), T), holdsAt(close(X , Y , 25), T).

. . .

0.1 initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), holdsAt(close(X , Y , 25), T). 0.0 initiatedAt(meet(X , Y ), T) ← happensAt(inactive(Y ), T).

...

−1.3 initiatedAt(meet(X , Y ), T) ← holdsAt(orientation(X , Y , 45), T initiatedAt(meet(X , Y ), T) ← happensAt(active(X ), T), happensAt(inactive(Y ), T), holdsAt(close(X , Y , 25), T), holdsAt(close(Y , X , 25), T), not happensAt(inactive(X ), T), not happensAt(abrupt(X ), T), not happensAt(running(X ), T), happensAt(inactive(Y ), T), not happensAt(active(Y ), T), not happensAt(running(Y ), T), not happensAt(abrupt(Y ), T), holdsAt(orientation(X , Y , 45), T).

. . . . . . . . .

Bottom Clause ⊥ :

Used O( 1 ǫ2 ln 1 δ ) examples Used O( 1 ǫ2 ln 1 δ ) examples Used O( 1 ǫ2 ln 1 δ ) examples

◮ The WoLED algorithm:

◮ Simultaneous structure & weight learning. ◮ Weight learning with AdaGrad.

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The AdaGrad Weight Update Rule

w t+1

i

= sign(w t

i − η

C t

i

∆gt

i ) max{0, |w t i − η

C t

i

∆gt

i | − λ η

C t

i

}

Current weight

  • f the i-th rule

Previous weight

  • f the i-th rule

Learning rate Rule’s current mistakes Term proportional to the rule’s accumulated past mistakes Regularization rate

  • ∆gt

i (i-th rule’s mistakes at time t): difference in rule’s true groundings

in the true state and the MAP-inferred state.

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WoLED Overview

WoLED

MAP Inference Theory Expansion Weights Update Hoeffding Tests/Rule Expansion Pruning Background Knowledge holdsAt(F, T + 1) ← initiatedAt(F, T). holdsAt(F, T + 1) ← holdsAt(F, T), not terminatedAt(F, T). Mode Declarations head(initiatedAt(move(+id, +id), +time)) head(terminatedAt(move(+id, +id), +time)) body(happensAt(walking(+id, +id), +time)) body(not happensAt(walking(+id, +id), +time)) body(distLessThan(+id, +id, #dist, +time)) body(dirLessThan(+id, +id, #dist, +time)) Current MLN Theory Ht: 1.345 initiatedAt(move(X , Y ), T) ← happensAt(walking(X ), T), happensAt(walking(Y ), T), distLessThan(X , Y , 34, T) 0.865 terminatedAt(move(X , Y ), T) ← happensAt(inactive(X ), T), not distLessThan(X , Y , 34, T) Training Interpretation It holdsAt(move(id1 , id2 ), 10) happensAt(walking(id1 ), 9) happensAt(walking(id2 ), 9) coords(id1 , 23, 104, 9) coords(id2 , 42, 84, 9) direction(id1 , 212, 9) direction(id2 , 78, 9) Training Stream

. . . . . .

Training Interpretation It′ not holdsAt(move(id1 , id2 ), 100) happensAt(walking(id1 ), 99) happensAt(walking(id2 ), 99) coords(id1 , 205, 23, 99) coords(id2 , 462, 24, 99) direction(id1 , 23, 99) direction(id2 , 798, 99)

. . .

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WoLED Evaluation on the CAVIAR Dataset

Method Precision Recall F1-score Theory size Time (sec) (a) Moving ECcrisp 0.909 0.634 0.751 28 – OLED 0.867 0.724 0.789 34 28 WoLED 0.882 0.835 0.857 30 59 OSLα 0.837 0.590 0.692 3316 1300 OSL

  • > 25 hrs

MaxMargin 0.844 0.941 0.890 28 1692 XHAIL 0.779 0.914 0.841 14 7836 Meeting ECcrisp 0.687 0.855 0.762 23 – OLED 0.947 0.760 0.843 31 22 WoLED 0.892 0.888 0.889 29 52 OSLα 0.902 0.863 0.882 1231 180 OSL

  • > 25 hrs

MaxMargin 0.919 0.813 0.863 23 1133 XHAIL 0.804 0.927 0.861 15 7248 (b) Moving OLED 0.682 0.787 0.730 38 63 WoLED 0.783 0.821 0.801 51 108 ECcrisp 0.721 0.639 0.677 28 – Meeting OLED 0.701 0.886 0.782 41 43 WoLED 0.808 0.877 0.841 56 98 ECcrisp 0.644 0.855 0.735 23 –

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WoLED Evaluation on the CAVIAR Dataset

0.751 0.789 0.857 0.692 0.89 0.841

Manual rules OLED WoLED OSLa MaxMargin XHAIL

F1-Score (Move Together Activity)

0.762 0.843 0.889 0.882 0.863 0.861 Manual rules OLED WoLED OSLa MaxMargin XHAIL

F1-Score (Meet Each Other Activity)

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WoLED Evaluation on the CAVIAR Dataset

28 59 1300 1692 7836 Manual rules OLED WoLED OSLa MaxMargin XHAIL

Training Time (Sec) (Move Together Activity)

0.857 0.89

F1-Score (Move Together Activity)

22 52 180 1133 7248 Manual rules OLED WoLED OSLa MaxMargin XHAIL

Training Time (Sec) (Meet Each Other Activity)

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WoLED Evaluation on the CAVIAR Dataset

28 34 30 3316 28 14

Manual rules OLED WoLED OSLa MaxMargin XHAIL

Theory Size (Move Together Activity)

23 31 29 1231 23 15

Manual rules OLED WoLED OSLa MaxMargin XHAIL

Theory Size (Meet Each Other Activity)

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WoLED Holdout Evaluation

2 4 6 8 10 12 14 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Number of Time Points(x1000) F1-score OSLa WoLED OLED

2 4 6 8 10 12 14 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Number of Time Points (x1000) F1-Score OSLa WoOLED OLED

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Summary

◮ An efficient, online MLN learner (structure+weights). ◮ Built on top of the LoMRF1 platform. ◮ https://github.com/nkatzz/OLED Future work: ◮ Further evaluation. ◮ Concept drift. ◮ Different Weight learning schemes. ◮ Distributed learning.

1https://github.com/anskarl/LoMRF