Learning preferences with multiple-criteria models Olivier Sobrie Université Paris-Saclay - CentraleSupélec Université de Mons - Faculté polytechnique June 21, 2016 Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 1 / 54
1. Introduction Preferences Preferences problems - some examples Sorting of hotels Choice of a pair of shoes Preference learning - some examples Google Amazon Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 2 / 54
1. Introduction Learning the preferences ◮ Hot topic in last years ◮ Several research communities study the learning of preferences Learning of preferences Multiple-criteria Preference . . . decision analysis (MCDA) learning (PL) ◮ Examples of sorting problems (ordered classification) treated in MCDA and PL Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 3 / 54
1. Introduction Example of MCDA sorting problem I ◮ Maria (DM) has to choose for an accommodation for her next holidays in Barcelona ◮ She sorts a small subset of accommodations A ∗ in two ordered sets : “Bad” and “Good” A ∗ Good Bad Front Maritim Travelhodge Majestic Plaza Rambla Hotel W ≻ Hilton Miramar ◮ She wants to obtain a full sorting of all the hotels in Barcelona ◮ She asks for the support of a decision analyst Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 4 / 54
1. Introduction Example of MCDA sorting problem II Decision maker (DM) Decision analyst (DA) asks questions provides preference information ◮ The DA helps Maria identifying the criteria that amount for her . . . distance to the beach 600m 300m 50m 200m . . . distance to the center 500m 100m 600m 300m . . . price 150 e 130 e 90 e 80 e . . . 45m 2 35m 2 30m 2 25m 2 size . . . rating . . . Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 5 / 54
1. Introduction Example of MCDA sorting problem III Decision maker (DM) Decision analyst (DA) asks questions Decision process Start provides preference information A ∗ Choice of a Good Bad Front Maritim Travelhodge Majestic Plaza Rambla Hotel W ≻ learning set A ∗ Hilton Miramar yes Add Fix some parameters info? no Learning of a model Restart the process Model no (globally or partially) accepted? OK for this model yes Decision maker (DM) Decision analyst (DA) asks questions End provides preference information Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 6 / 54
1. Introduction Example of PL sorting problem I ◮ From a large database, we would like to have a model predicting the health status of a patient before anesthesia ◮ Database built from different data sources ◮ Data generated by a ground truth ◮ The database contains ± 1000 patients ◮ Patients are evaluated on attributes and assigned to a category reflecting their health status ◮ Categories are ordered (ASA score) Sever Incapaciting Mild systemic Healthy ≻ ≻ systemic ≻ systemic ≻ Moribound disease disease disease Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 7 / 54
1. Introduction Example of PL sorting problem II ◮ The database is given as input to a learning algorithm Learning Model algorithm ◮ The model learned is then used as a blackbox for predicting the assignments of other patients Learned model Assignment Patient Learned (ASA score) evaluation model ◮ The performance of the model and learning algorithm are assessed using indicators such as classification accuracy , area under the curve , etc. Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 8 / 54
1. Introduction MCDA versus PL Multiple criteria decision analysis Preference learning ◮ Small datasets ◮ Large datasets A ∗ Good Bad Front Maritim Travelhodge Majestic Plaza Rambla Hotel W ≻ Hilton Miramar Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 9 / 54
1. Introduction MCDA versus PL Multiple criteria decision analysis Preference learning ◮ Small datasets ◮ Large datasets A ∗ Good Bad Front Maritim Travelhodge Majestic Plaza Rambla Hotel W ≻ Hilton Miramar ◮ Strong interactions ◮ No/little interactions Decision maker (DM) Decision analyst (DA) asks questions Ground Truth provides preference information Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 9 / 54
1. Introduction MCDA versus PL Multiple criteria decision analysis Preference learning ◮ Small datasets ◮ Large datasets A ∗ Good Bad Front Maritim Travelhodge Majestic Plaza Rambla Hotel W ≻ Hilton Miramar ◮ Strong interactions ◮ No/little interactions Decision maker (DM) Decision analyst (DA) asks questions Ground Truth provides preference information ◮ Interpretable models ◮ Blackbox models Interpretable Interpretable Input Output Input Output model model Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 9 / 54
1. Introduction Aim of this thesis Make some links between MCDA and PL Use MCDA models to deal with PL problems (outranking models and additive value function models) Validation of the learning algorithms as done in PL Test the algorithms and models on a real application Study the expressivity of the MCDA models Bring new techniques in MCDA and PL Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 10 / 54
1. Introduction Outline of the presentation Background Contributions 3 4 Application Metaheuristic 2 5 MR-Sort NCS 6 New veto rule 1 Introduction 8 7 UTA-poly AVF UTA-splines Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 11 / 54
1. Introduction Outline of the presentation Background Contributions 3 4 Application Metaheuristic 2 5 MR-Sort NCS 6 New veto rule 1 Introduction 8 7 UTA-poly AVF UTA-splines Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 11 / 54
2. Majority rule sorting model Outline of the presentation Background Contributions 3 4 Application Metaheuristic 2 5 MR-Sort NCS 6 New veto rule 1 Introduction 8 7 UTA-poly AVF UTA-splines Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 11 / 54
2. Majority rule sorting model Majority rule sorting model ◮ Sorting model ( p ordered categories , i.e. C p ≻ C p − 1 ≻ . . . ≻ C 1 ) ◮ Axiomatized by Bouyssou and Marchant (2007a,b) ◮ n weights ( w 1 , . . . , w n ) ◮ 1 majority threshold ( λ ) C 3 ◮ p − 1 profiles ( b 1 , . . . , b p − 1 ) b 2 C 2 Assignment rule b 1 a ∈ C h C 1 ⇔ � � w j ≥ λ and w j < λ j : a j ≥ b h − 1 j : a j ≥ b h j j crit. 1 crit. 2 crit. 3 crit. 4 crit. 5 w 1 w 2 w 3 w 4 w 5 Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 12 / 54
2. Majority rule sorting model MR-Sort applied to Maria’s decision problem ◮ Sorting accommodations in two categories : Good and Bad 45m 2 Assignment rule 0m 0m 0 e 5 � hotel ∈ Good ⇔ w j ≥ λ j : a j ≥ b 1 Good j 25m 2 200m 400m 100 e 3 b 1 Bad 5m 2 600m 800m 200 e 1 crit. beach center price size rating 0 . 2 w j 0 . 2 0 . 2 0 . 2 0 . 2 λ = 0 . 8 Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 13 / 54
2. Majority rule sorting model MR-Sort applied to Maria’s decision problem ◮ Sorting accommodations in two categories : Good and Bad 45m 2 Assignment rule 0m 0m 0 e 5 � hotel ∈ Good ⇔ w j ≥ λ 50m j : a j ≥ b 1 Good j 30m 2 90 e 25m 2 300m 400m 100 e 3 b 1 Hilton Bad 600m ∈ Good 5m 2 600m 800m 200 e 1 � w j = 0 . 8 crit. beach center price size rating 0 . 2 w j 0 . 2 0 . 2 0 . 2 0 . 2 j : a j ≥ b 1 j λ = 0 . 8 Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 13 / 54
2. Majority rule sorting model MR-Sort applied to Maria’s decision problem ◮ Sorting accommodations in two categories : Good and Bad 45m 2 Assignment rule 0m 0m 0 e 5 � hotel ∈ Good ⇔ w j ≥ λ 100m 35m 2 j : a j ≥ b 1 Good 4 j 25m 2 300m 400m 100 e 3 b 1 Plaza 300m 130 e Bad ∈ Bad 5m 2 600m 800m 200 e 1 � w j = 0 . 6 crit. beach center price size rating 0 . 2 w j 0 . 2 0 . 2 0 . 2 0 . 2 j : a j ≥ b 1 j λ = 0 . 8 Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 13 / 54
2. Majority rule sorting model Outline of the presentation Background Contributions 3 4 Application Metaheuristic 2 5 MR-Sort NCS 6 New veto rule 1 Introduction 8 7 UTA-poly AVF UTA-splines Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 14 / 54
3. Metaheuristic for learning a MR-Sort model Outline of the presentation Background Contributions 3 4 Application Metaheuristic 2 5 MR-Sort NCS 6 New veto rule 1 Introduction 8 7 UTA-poly AVF UTA-splines Learning preferences with multiple-criteria models O. Sobrie - June 21, 2016 14 / 54
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