Measuring the Precision ofMulti-perspective Process Models

Felix Mannhardt joint work withMassimiliano de Leoni, Hajo A. Reijers,Wil M.P. van der Aalst

Department of Mathematics and Computer Science

Precision

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“Flower Model” lacking any precision

B

C

A

Department of Mathematics and Computer Science

Precision of Multi-perspective Process Models

SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

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A 𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛𝐴

SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

Loan < 2,000

Loan > 1,000

B𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛𝐵

𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛𝐵>𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛𝐴

Existing work ignores added precision by multi-perspective rules / constraints

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Approach: Multi-perspective Precision

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Multi-perspective Process Model (P)

Fitting EventLog (L)

Precision[0..1]

INPUT OUTPUT

APPROACH

∑𝒆∈𝑳

𝒐𝒃𝒔 𝒆𝒓𝒗𝒆𝒅𝑷 (𝒆)𝒑𝒓𝒆𝒄𝒊𝒔𝒊𝒐𝒏 (𝑷 ,𝑳)=¿ ∑

𝒆∈𝑳𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆𝑷 (𝒆)

Department of Mathematics and Computer Science

SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

Loan < 2,000

Loan > 1,000

SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

Loan < 2,000

Loan > 1,000

Precision: Observed / Possible Behavior

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SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

Loan < 2,000

Loan > 1,000C Id Event Loan obs pos1 Handle Request 800

1 Simple Check -

1 Decide -

2 Handle Request 1800

2 Ext. Check -

2 Decide -

SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

Loan < 2,000

Loan > 1,000

𝒐𝒃𝒔 𝑷 (𝒆𝟏 )=|{Handle Request }|=𝟏𝒑𝒐𝒔 𝑷 (𝒆𝟏 )=|{Handle Request }|=𝟏

𝒔𝒕𝒂𝒕𝒆 (𝒆𝟏 )=(¿>, {})

C Id Event Loan obs pos1 Handle Request 800 1 11 Simple Check -

1 Decide -

2 Handle Request 1800

2 Ext. Check -

2 Decide -

C Id Event Loan obs pos1 Handle Request 800 1 1

1 Simple Check - 1 11 Decide -

2 Handle Request 1800

2 Ext. Check -

2 Decide -𝒐𝒃𝒔 𝑷 (𝒆𝟐 )=|{Simple }̌|=𝟏𝒑𝒐𝒔 𝑷 (𝒆𝟐 )=¿

𝒔𝒕𝒂𝒕𝒆 (𝒆𝟐 )=(¿𝐻>, {𝐿=800 })

SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

Loan < 2,000

Loan > 1,000C Id Event Loan obs pos1 Handle Request 800 1 1

1 Simple Check - 1 1

1 Decide - 1 12 Handle Request 1800

2 Ext. Check -

2 Decide -𝒐𝒃𝒔 𝑷 (𝒆𝟑 )=|{Decide }|=𝟏𝒑𝒐𝒔 𝑷 (𝒆𝟑 )=|{Decide }|=𝟏

𝒔𝒕𝒂𝒕𝒆 (𝒆𝟑 )=(¿𝐻 ,𝑆>, {𝐿=800 })

SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

Loan < 2,000

Loan > 1,000C Id Event Loan obs pos1 Handle Request 800 1 1

1 Simple Check - 1 1

1 Decide - 1 1

2 Handle Request 1800 1 12 Ext. Check -

2 Decide -𝒐𝒃𝒔 𝑷 (𝒆𝟒 )=|{Handle Request }|=𝟏𝒑𝒐𝒔 𝑷 (𝒆𝟒 )=|{Handle Request }|=𝟏

𝒔𝒕𝒂𝒕𝒆 (𝒆𝟒 )=(¿ , {})

SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

Loan < 2,000

Loan > 1,000C Id Event Loan obs pos1 Handle Request 800 1 1

1 Simple Check - 1 1

1 Decide - 1 1

2 Handle Request 1800 1 1

2 Ext. Check - 1 22 Decide -𝒐𝒃𝒔 𝑷 (𝒆𝟓 )=|{Ext . }̌|=𝟏

𝒑𝒐𝒔 𝑷 (𝒆𝟓 )=|{Ext .Ce𝑐𝑘 ,𝑆𝑖𝑚𝑝𝑙𝑒 h𝐶 𝑒𝑐𝑘}|=𝟐

𝒔𝒕𝒂𝒕𝒆 (𝒆𝟓 )=(¿𝐻>, {𝐿=1800 })

C Id Event Loan1 Handle Request 800 1 1

1 Simple Check - 1 1

1 Decide - 1 1

2 Handle Request 1800 1 1

2 Ext. Check - 1 2

2 Decide - 1 1 𝒑𝒐𝒔 𝑷 (𝒆𝟔 )=|{𝐷𝑒𝑐𝑖𝑑𝑒 }|=𝟏

𝒔𝒕𝒂𝒕𝒆 (𝒆𝟔 )=(¿𝐻 ,𝐸>, {𝐿=1800 })

SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

Loan < 2,000

Loan > 1,000C Id Event Loan1 Handle Request 800 1 1

1 Simple Check - 1 1

1 Decide - 1 1

2 Handle Request 1800 1 1

2 Ext. Check - 1 2

2 Decide - 1 1

6 7

𝒐𝒃𝒔 𝑷 (𝒆 )=|{observed activities at state }|𝒑𝒐𝒔 𝑷 (𝒆 )=¿ {𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑖𝑒𝑠 𝑎𝑡 𝑠𝑡𝑎𝑡𝑒 }∨¿

𝒔𝒕𝒂𝒕𝒆 (𝒆 )=𝑠𝑡𝑎𝑡𝑒𝑜𝑓 h𝑡 𝑒𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑚𝑜𝑑𝑒𝑙

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Full Example for Model A & Model B

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SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

AC Id Event Loan1 Handle Request 800 1 1

1 Simple Check - 1 2

1 Decide - 1 1

2 Handle Request 1800 1 1

2 Extensive Check - 2 2

2 Decide - 1 1

3 Handle Request 1800 1 1

3 Simple Check - 2 2

3 Decide - 1 1

4 Handle Request 2500 1 1

4 Extensive Check - 1 2

4 Decide - 1 1

14 16

Model A

𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 (𝑃 ,𝐿 )=∑𝑒∈ 𝐿

𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑𝑃(𝑒)=14  

∑𝑒∈𝐿

𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒𝑃 (𝑒)=16  ≈𝟎 .𝟖𝟕𝟓

SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

Loan < 2,000

Loan > 1,000B

C Id Event Loan1 Handle Request 800 1 1

1 Simple Check - 1 11 Decide - 1 1

2 Handle Request 1800 1 1

2 Extensive Check - 2 2

2 Decide - 1 1

3 Handle Request 1800 1 1

3 Simple Check - 2 2

3 Decide - 1 1

4 Handle Request 2500 1 1

4 Extensive Check - 1 14 Decide - 1 1

14 14

Model B

𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 (𝑃 ,𝐿 )=∑𝑒∈ 𝐿

𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑𝑃(𝑒)=14  

∑𝑒∈ 𝐿

𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒𝑃(𝑒)=14  ≈𝟏

Evaluation on Road Fines Log

Inductive Miner Inductive Miner & Rules

Normative Model Normative Model & Rules

0.00.10.20.30.40.50.60.70.80.91.0

0.300.36

0.64

0.83

ETC Precision Precision Fitness

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Summary

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• 1st precision measure for multi-perspective process models− Fast to calculate− Flexible framework− Implemented in ProM

• Preliminary Evaluation− Illustrative examples− Real-life dataset with > 500,000 events

Handle750 Simple Decide

Handle1250 Ext. Decide

Handle5000 Simple Decide

Handle

750Simple Decide

Handle

1500Simpl

eDecid

e

SimpleCheck

ExtensiveCheck

Handle Request Decide

Loan

Loan < 2,000

Loan > 1,000

precision [0..1]

Department of Mathematics and Computer ScienceImage source: http://commons.wikimedia.org/wiki/File:Pictofigo_-_Idea.png

Questions? Remarks? Ideas?