Strategies for the incremental inference of majority-rule sorting - PowerPoint PPT Presentation

Alexandru OLTEANU Lab-STICC, Université Bretagne Sud, France 23/11/2018 DA2PL 2018 Poznan, Poland Strategies for the incremental inference of majority-rule sorting models alexandru.olteanu@univ-ubs.fr

a) direct elicitation: DM gives model parameters ; b) indirect elicitation: parameters are inferred from holistic judgments given by the DM ( assignment examples ); • one-shot or incremental elicitation; • assignment examples are selected or constructed ; Model tuning 1/12 Strategies for the incremental inference of MR-Sort Alexandru OLTEANU Context MCDA guides the DM through a decision aiding process . ? Formulate Solve Select Situate Decision and tune a model

a) direct elicitation: DM gives model parameters ; b) indirect elicitation: parameters are inferred from holistic judgments given by the DM ( assignment examples ); • one-shot or incremental elicitation; • assignment examples are selected or constructed ; Model tuning 1/12 • criteria weights w j ; Strategies for the incremental inference of MR-Sort Alexandru OLTEANU Sb h 2 ; Context MCDA guides the DM through a decision aiding process . ? Formulate Solve Select Situate Decision and tune a model MR-Sort • ordinal classification, or sorting ; • majority threshold λ > 1 • k categories and k − 1 profiles; • a ∈ c h ifg a S b h − 1 and a /

• one-shot or incremental elicitation; • assignment examples are selected or constructed ; 1/12 Strategies for the incremental inference of MR-Sort Alexandru OLTEANU Context MCDA guides the DM through a decision aiding process . ? Formulate Solve Select Situate Decision and tune a model Model tuning a) direct elicitation: DM gives model parameters ; b) indirect elicitation: parameters are inferred from holistic judgments given by the DM ( assignment examples );

1/12 Alexandru OLTEANU Strategies for the incremental inference of MR-Sort Context MCDA guides the DM through a decision aiding process . ? Formulate Solve Select Situate Decision and tune a model Model tuning a) direct elicitation: DM gives model parameters ; b) indirect elicitation: parameters are inferred from holistic judgments given by the DM ( assignment examples ); • one-shot or incremental elicitation; • assignment examples are selected or constructed ;

Research question: Can we develop a strategy to reduce the amount of information required from the DM ? 2/12 Strategies for the incremental inference of MR-Sort Alexandru OLTEANU The protocol Decision maker Elicitation Generate Model Updated Assignment alternatives inference MR-Sort examples model

2/12 Alexandru OLTEANU Strategies for the incremental inference of MR-Sort The protocol Decision maker Elicitation Generate Model Updated Assignment alternatives inference MR-Sort examples model Research question: Can we develop a strategy to reduce the amount of information required from the DM ?

Proposed strategies for generating alternatives

Non-dominated same category random (NDR) c h s t g j x g j a g j y then a is rejected; • if x y Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 3/12 Strategies for generating assignment examples Random (RND) • a ∶ g j ( a ) ∼ U ( min j , max j ) , ∀ j ∈ J

Strategies for the incremental inference of MR-Sort Alexandru OLTEANU 3/12 Strategies for generating assignment examples Random (RND) • a ∶ g j ( a ) ∼ U ( min j , max j ) , ∀ j ∈ J Non-dominated same category random (NDR) • if ∃ x , y ∈ c h s . t . g j ( x ) ⩾ g j ( a ) ⩾ g j ( y ) then a is rejected;

4/12 J Strategies for the incremental inference of MR-Sort Alexandru OLTEANU (2) w j i j J J J i and w j j J J Maximal minority coalition of criteria: (1) w j i j J J i and w j j J J J Minimal majority coalition of criteria: Strategies for generating assignment examples Fixing limit profiles (FLP) • we use the model inferred from the previous iteration ; • we try to bound each profile from above and below ;

4/12 Maximal minority coalition of criteria: Strategies for the incremental inference of MR-Sort Alexandru OLTEANU (2) (1) Minimal majority coalition of criteria: Strategies for generating assignment examples Fixing limit profiles (FLP) • we use the model inferred from the previous iteration ; • we try to bound each profile from above and below ; J + = { J + ⊆ J ∣ ∑ w j ⩾ λ and ∀ i ∈ J + , ∑ w j < λ } j ∈ J + − { i } j ∈ J + J − = { J − ⊆ J ∣ ∑ ∑ w j < λ and ∀ i ∈ J − J − , w j ⩾ λ } j ∈ J − ∪ { i } j ∈ J −

Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 5/12 Strategies for generating assignment examples Fixing limit profiles (FLP)

Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 5/12 Strategies for generating assignment examples Fixing limit profiles (FLP)

Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 5/12 Strategies for generating assignment examples Fixing limit profiles (FLP)

Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 5/12 Strategies for generating assignment examples Fixing limit profiles (FLP)

Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 5/12 Strategies for generating assignment examples Fixing limit profiles (FLP)

Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 5/12 Strategies for generating assignment examples Fixing limit profiles (FLP)

Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 5/12 Strategies for generating assignment examples Fixing limit profiles (FLP)

Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 6/12 Strategies for generating assignment examples Fixing limit profiles using a central model (FLP + ) • identical to FLP except that the model inferred from the previous iteration is centered within the search space ;

Strategies for the incremental inference of MR-Sort Alexandru OLTEANU 6/12 Strategies for generating assignment examples Fixing limit profiles using a central model (FLP + ) • identical to FLP except that the model inferred from the previous iteration is centered within the search space ; x

Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 6/12 Strategies for generating assignment examples Fixing limit profiles using a central model (FLP + ) • identical to FLP except that the model inferred from the previous iteration is centered within the search space ; x x x x

Strategies for the incremental inference of MR-Sort Alexandru OLTEANU 6/12 Strategies for generating assignment examples Fixing limit profiles using a central model (FLP + ) • identical to FLP except that the model inferred from the previous iteration is centered within the search space ; x x x

7/12 d J Strategies for the incremental inference of MR-Sort Alexandru OLTEANU (5) 1 (4) , otherwise d J 1 0 (3) Proximity of two MR-Sort models Distance between criteria importance parameters ′ 2 m ⋅ ∑ ∑ d C = 1 C , where J ′ ∈ ( J i ) i ∈ 1 .. m ⎧ ⎪ , if ∑ ′ ′ and ∑ ′′ ′′ ⎪ j ⩾ λ j ⩾ λ ⎪ ⎪ ⎪ j ∈ J ′ w j ∈ J ′ w ⎪ ⎪ ⎪ ⎪ ′ ′ ′ and ∑ ′′ ′′ ⎨ or ∑ C = j < λ j < λ ⎪ ⎪ j ∈ J ′ w j ∈ J ′ w ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ Distance between category profiles importance parameters ′ ′′ ∑ ∑ ∣ g j ( b h ) − g j ( b h )∣ ( k − 1 ) ⋅ m ⋅ d P = h ∈ 1 .. k − 1 j ∈ J

Experimental validation

• 50 models for each config. of m , k , n st Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 8/12 Experimental framework • m ∈ { 3 , 4 } • k ∈ { 2 , 3 } • n in = 4 • n st ∈ { 1 , 4 } • n te = 10 , 000

9/12 3 criteria, 3 categories 78 85 53 140 FLP NDR 4 criteria, 2 categories Classification accuracy 10 71 100 Classification accuracy 10 RND NDR 36 45 62 46 80 FLP 28 60 Strategies for the incremental inference of MR-Sort Alexandru OLTEANU 4 criteria, 3 categories Classification accuracy 20 24 45 RND 107 NDR RND NDR Classification accuracy 3 criteria, 2 categories 10 90 FLP 41 Retrieving the original model 1 . 00 1 . 00 0 . 95 0 . 95 0 . 90 0 . 90 0 . 85 0 . 85 FLP + FLP FLP + RND ∣ A i ∣ ∣ A i ∣ 1 . 00 1 . 00 0 . 95 0 . 95 0 . 90 0 . 90 FLP + FLP + 0 . 85 0 . 85 NDR + FLP + FLP + RND + ∣ A i ∣ ∣ A i ∣

10/12 40 30 40 50 60 70 10 90 100 d B 4 criteria, 2 categories 10 20 30 50 10 60 70 80 90 100 110 120 130 140 d B 4 criteria, 3 categories Alexandru OLTEANU Strategies for the incremental inference of MR-Sort 20 80 3 criteria, 3 categories 70 20 30 40 50 60 d B d B 10 20 30 40 50 60 3 criteria, 2 categories 80 90 Distance measures 0 . 5 0 . 5 0 . 4 0 . 4 0 . 3 0 . 3 0 . 2 0 . 2 0 . 1 0 . 1 ∣ A i ∣ ∣ A i ∣ 0 . 5 0 . 5 FLP + FLP + 0 . 4 0 . 4 NDR + RND + 0 . 3 0 . 3 0 . 2 0 . 2 0 . 1 0 . 1 ∣ A i ∣ ∣ A i ∣

Conclusions and perspectives