stage de recherche master 2 mva de l’ens cachan nouvelles … · 2018-06-29 · introduction...
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Stage de Recherche Master 2 MVA de l’ENS Cachan
Nouvelles techniques de ML pour la medecine :
FACTEURS PREDICTIFS DE LAREHOSPITALISATION PRECOCE DE
DREPANOCYTAIRES ADULTES POUR CRISEVASO-OCCLUSIVE
Simon Bussy
encadre par
Anne-Sophie Jannot, Stephane Gaiffas, Agathe Guilloux
Presentation INSERM
5 octobre 2015
MVA | Presentation INSERM | Simon BUSSY 1/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Introduction
Contexte : CMAP et equipe INSERM no 22 del’HEGP ; finance par l’Institut Europlace de Finance.
HEGP : centre de reference pour le traitement desCVOTaux de rehospitalisation eleve (∼ 20%)But : construire un modele predictif des rechutes
MVA | Presentation INSERM | Simon BUSSY 2/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Introduction
Contexte : CMAP et equipe INSERM no 22 del’HEGP ; finance par l’Institut Europlace de Finance.HEGP : centre de reference pour le traitement desCVO
Taux de rehospitalisation eleve (∼ 20%)But : construire un modele predictif des rechutes
MVA | Presentation INSERM | Simon BUSSY 2/42
![Page 4: Stage de Recherche Master 2 MVA de l’ENS Cachan Nouvelles … · 2018-06-29 · Introduction Modeles` Algorithmes Simulations Organisation Presentation´ Preprocessing R´esultats](https://reader034.vdocuments.mx/reader034/viewer/2022042419/5f361ddc3b75ac66665dea80/html5/thumbnails/4.jpg)
Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Introduction
Contexte : CMAP et equipe INSERM no 22 del’HEGP ; finance par l’Institut Europlace de Finance.HEGP : centre de reference pour le traitement desCVOTaux de rehospitalisation eleve (∼ 20%)
But : construire un modele predictif des rechutes
MVA | Presentation INSERM | Simon BUSSY 2/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Introduction
Contexte : CMAP et equipe INSERM no 22 del’HEGP ; finance par l’Institut Europlace de Finance.HEGP : centre de reference pour le traitement desCVOTaux de rehospitalisation eleve (∼ 20%)But : construire un modele predictif des rechutes
MVA | Presentation INSERM | Simon BUSSY 2/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
1 Modeles
2 Algorithmes
3 Simulations
4 Organisation
5 Presentation
6 Preprocessing
7 Resultats
8 Conclusion
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modelisation
MVA | Presentation INSERM | Simon BUSSY 4/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modelisation
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele de melange
Echantillon (X1,T1) , . . ., (Xn,Tn) ∈ Rd × N∗ i.i.d . ∼ P
Zi ∈ {0, 1} v .a. latente t.q. ∀i ∈ J1, nK, ∀k ∈ {0, 1}, Ti |Zi = k ∼ `k
π0(Xi ) = P(Zi = 0|Xi ) = 1
1+e−X>i β
∀i ∈ J1, nK,Zi ∼ B(1− π0(Xi ))
∀i ∈ J1, nK, ∀t ∈ N∗, fTi |Xi(t) = π0(Xi )fTi |Xi ,0(t) + (1− π0(Xi ))fTi |Xi ,1(t)
`k ∼ G(pk ) de densite ∀t ∈ N∗, fk (t) = pk (1− pk )t−1
MVA | Presentation INSERM | Simon BUSSY 5/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele de melange
Echantillon (X1,T1) , . . ., (Xn,Tn) ∈ Rd × N∗ i.i.d . ∼ P
Zi ∈ {0, 1} v .a. latente t.q. ∀i ∈ J1, nK, ∀k ∈ {0, 1}, Ti |Zi = k ∼ `k
π0(Xi ) = P(Zi = 0|Xi ) = 1
1+e−X>i β
∀i ∈ J1, nK,Zi ∼ B(1− π0(Xi ))
∀i ∈ J1, nK, ∀t ∈ N∗, fTi |Xi(t) = π0(Xi )fTi |Xi ,0(t) + (1− π0(Xi ))fTi |Xi ,1(t)
`k ∼ G(pk ) de densite ∀t ∈ N∗, fk (t) = pk (1− pk )t−1
MVA | Presentation INSERM | Simon BUSSY 5/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele de melange
Echantillon (X1,T1) , . . ., (Xn,Tn) ∈ Rd × N∗ i.i.d . ∼ P
Zi ∈ {0, 1} v .a. latente t.q. ∀i ∈ J1, nK, ∀k ∈ {0, 1}, Ti |Zi = k ∼ `k
π0(Xi ) = P(Zi = 0|Xi ) = 1
1+e−X>i β
∀i ∈ J1, nK,Zi ∼ B(1− π0(Xi ))
∀i ∈ J1, nK, ∀t ∈ N∗, fTi |Xi(t) = π0(Xi )fTi |Xi ,0(t) + (1− π0(Xi ))fTi |Xi ,1(t)
`k ∼ G(pk ) de densite ∀t ∈ N∗, fk (t) = pk (1− pk )t−1
MVA | Presentation INSERM | Simon BUSSY 5/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele de melange
Echantillon (X1,T1) , . . ., (Xn,Tn) ∈ Rd × N∗ i.i.d . ∼ P
Zi ∈ {0, 1} v .a. latente t.q. ∀i ∈ J1, nK, ∀k ∈ {0, 1}, Ti |Zi = k ∼ `k
π0(Xi ) = P(Zi = 0|Xi ) = 1
1+e−X>i β
∀i ∈ J1, nK,Zi ∼ B(1− π0(Xi ))
∀i ∈ J1, nK, ∀t ∈ N∗, fTi |Xi(t) = π0(Xi )fTi |Xi ,0(t) + (1− π0(Xi ))fTi |Xi ,1(t)
`k ∼ G(pk ) de densite ∀t ∈ N∗, fk (t) = pk (1− pk )t−1
MVA | Presentation INSERM | Simon BUSSY 5/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele de melange
Echantillon (X1,T1) , . . ., (Xn,Tn) ∈ Rd × N∗ i.i.d . ∼ P
Zi ∈ {0, 1} v .a. latente t.q. ∀i ∈ J1, nK, ∀k ∈ {0, 1}, Ti |Zi = k ∼ `k
π0(Xi ) = P(Zi = 0|Xi ) = 1
1+e−X>i β
∀i ∈ J1, nK,Zi ∼ B(1− π0(Xi ))
∀i ∈ J1, nK, ∀t ∈ N∗, fTi |Xi(t) = π0(Xi )fTi |Xi ,0(t) + (1− π0(Xi ))fTi |Xi ,1(t)
`k ∼ G(pk ) de densite ∀t ∈ N∗, fk (t) = pk (1− pk )t−1
MVA | Presentation INSERM | Simon BUSSY 5/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele de melange
Echantillon (X1,T1) , . . ., (Xn,Tn) ∈ Rd × N∗ i.i.d . ∼ P
Zi ∈ {0, 1} v .a. latente t.q. ∀i ∈ J1, nK, ∀k ∈ {0, 1}, Ti |Zi = k ∼ `k
π0(Xi ) = P(Zi = 0|Xi ) = 1
1+e−X>i β
∀i ∈ J1, nK,Zi ∼ B(1− π0(Xi ))
∀i ∈ J1, nK, ∀t ∈ N∗, fTi |Xi(t) = π0(Xi )fTi |Xi ,0(t) + (1− π0(Xi ))fTi |Xi ,1(t)
`k ∼ G(pk ) de densite ∀t ∈ N∗, fk (t) = pk (1− pk )t−1
MVA | Presentation INSERM | Simon BUSSY 5/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Inference du modele
θ = {p0,p1, β} ∈ Rd+3
`n(θ) = 1n log
∏ni=1 Pθ(Ti |Xi ) = 1
n∑n
i=1 log[
p0(1−p0)Ti−1
1+e−X>i β0+ p1(1−p1)Ti−1
1+eX>i β0
]
θ ∈ argmin(p0,p1,β)∈]0,1[2×Rd+1
{− 1
n∑n
i=1 log[ p0(1−p0)Ti−1
1+e−X>i β0
+p1(1−p1)Ti−1
1+eX>i β0
]+λ1‖β‖1 +
λ22 ‖β‖
22
}
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Inference du modele
θ = {p0,p1, β} ∈ Rd+3
`n(θ) = 1n log
∏ni=1 Pθ(Ti |Xi ) = 1
n∑n
i=1 log[
p0(1−p0)Ti−1
1+e−X>i β0+ p1(1−p1)Ti−1
1+eX>i β0
]
θ ∈ argmin(p0,p1,β)∈]0,1[2×Rd+1
{− 1
n∑n
i=1 log[ p0(1−p0)Ti−1
1+e−X>i β0
+p1(1−p1)Ti−1
1+eX>i β0
]+λ1‖β‖1 +
λ22 ‖β‖
22
}
MVA | Presentation INSERM | Simon BUSSY 6/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Inference du modele
θ = {p0,p1, β} ∈ Rd+3
`n(θ) = 1n log
∏ni=1 Pθ(Ti |Xi ) = 1
n∑n
i=1 log[
p0(1−p0)Ti−1
1+e−X>i β0+ p1(1−p1)Ti−1
1+eX>i β0
]
θ ∈ argmin(p0,p1,β)∈]0,1[2×Rd+1
{− 1
n∑n
i=1 log[ p0(1−p0)Ti−1
1+e−X>i β0
+p1(1−p1)Ti−1
1+eX>i β0
]+λ1‖β‖1 +
λ22 ‖β‖
22
}
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Regression logistique
Yi = 1{Ti≤s} ; seuil s de 15 jours
`n(β) =∑n
i=1 Yi log(g(X>i β)) + (1− Yi ) log(1− g(X>i β))
βElasticNet ∈ argminβ∈Rd
{−∑n
i=1 Yi log(g(X>i β)) + (1− Yi ) log(1− g(X>i β)) + λ2‖β‖22 + λ1‖β‖1
}
Score : AUC
ROC : R→ [0, 1]2
t 7→(P(s(X) ≥ t |Y = 0),P(s(X) ≥ t |Y = 1)
)
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Regression logistique
Yi = 1{Ti≤s} ; seuil s de 15 jours
`n(β) =∑n
i=1 Yi log(g(X>i β)) + (1− Yi ) log(1− g(X>i β))
βElasticNet ∈ argminβ∈Rd
{−∑n
i=1 Yi log(g(X>i β)) + (1− Yi ) log(1− g(X>i β)) + λ2‖β‖22 + λ1‖β‖1
}
Score : AUC
ROC : R→ [0, 1]2
t 7→(P(s(X) ≥ t |Y = 0),P(s(X) ≥ t |Y = 1)
)
MVA | Presentation INSERM | Simon BUSSY 7/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Regression logistique
Yi = 1{Ti≤s} ; seuil s de 15 jours
`n(β) =∑n
i=1 Yi log(g(X>i β)) + (1− Yi ) log(1− g(X>i β))
βElasticNet ∈ argminβ∈Rd
{−∑n
i=1 Yi log(g(X>i β)) + (1− Yi ) log(1− g(X>i β)) + λ2‖β‖22 + λ1‖β‖1
}
Score : AUC
ROC : R→ [0, 1]2
t 7→(P(s(X) ≥ t |Y = 0),P(s(X) ≥ t |Y = 1)
)
MVA | Presentation INSERM | Simon BUSSY 7/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Regression logistique
Yi = 1{Ti≤s} ; seuil s de 15 jours
`n(β) =∑n
i=1 Yi log(g(X>i β)) + (1− Yi ) log(1− g(X>i β))
βElasticNet ∈ argminβ∈Rd
{−∑n
i=1 Yi log(g(X>i β)) + (1− Yi ) log(1− g(X>i β)) + λ2‖β‖22 + λ1‖β‖1
}
Score : AUC
ROC : R→ [0, 1]2
t 7→(P(s(X) ≥ t |Y = 0),P(s(X) ≥ t |Y = 1)
)
MVA | Presentation INSERM | Simon BUSSY 7/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Esperance-Maximisation
`cn(θ, T ,Z) = 1n∑n
i=1 log[Zi
(log(1− π0(Xi )) + log p1 + (Ti − 1) log(1− p1)
)+(1− Zi )
(log(π0(Xi )) + log p0 + (Ti − 1) log(1− p0)
)]
Etape E :
Qn(θ, θ(l)) = Eθ(l) [`cn(θ, T ,Z)|T ]
Remplacer Zi par q(l)i = E
θ(l) [Zi |Ti ] =p(l)
1 (1−p(l)1 )Ti−1(1−π0(Xi ))
p(l)0 (1−p(l)
0 )Ti−1π0(Xi )+p(l)1 (1−p(l)
1 )Ti−1(1−π0(Xi ))
Etape M :
θ(l+1) ∈ arg maxθQn(θ, θ
(l))
p(l+1)0 =
n−∑n
i=1 q(l)i∑n
i=1 Ti (1−q(l)i )
; p(l+1)1 =
∑ni=1 q(l)
i∑ni=1 Ti q
(l)i
β(l+1) ∈ arg minβ
{−Qn(θ, θ(l)) + λ1‖β‖1 +
λ22 ‖β‖
22
}avec L-BGFS-B
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Esperance-Maximisation
`cn(θ, T ,Z) = 1n∑n
i=1 log[Zi
(log(1− π0(Xi )) + log p1 + (Ti − 1) log(1− p1)
)+(1− Zi )
(log(π0(Xi )) + log p0 + (Ti − 1) log(1− p0)
)]Etape E :
Qn(θ, θ(l)) = Eθ(l) [`cn(θ, T ,Z)|T ]
Remplacer Zi par q(l)i = E
θ(l) [Zi |Ti ] =p(l)
1 (1−p(l)1 )Ti−1(1−π0(Xi ))
p(l)0 (1−p(l)
0 )Ti−1π0(Xi )+p(l)1 (1−p(l)
1 )Ti−1(1−π0(Xi ))
Etape M :
θ(l+1) ∈ arg maxθQn(θ, θ
(l))
p(l+1)0 =
n−∑n
i=1 q(l)i∑n
i=1 Ti (1−q(l)i )
; p(l+1)1 =
∑ni=1 q(l)
i∑ni=1 Ti q
(l)i
β(l+1) ∈ arg minβ
{−Qn(θ, θ(l)) + λ1‖β‖1 +
λ22 ‖β‖
22
}avec L-BGFS-B
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Esperance-Maximisation
`cn(θ, T ,Z) = 1n∑n
i=1 log[Zi
(log(1− π0(Xi )) + log p1 + (Ti − 1) log(1− p1)
)+(1− Zi )
(log(π0(Xi )) + log p0 + (Ti − 1) log(1− p0)
)]Etape E :
Qn(θ, θ(l)) = Eθ(l) [`cn(θ, T ,Z)|T ]
Remplacer Zi par q(l)i = E
θ(l) [Zi |Ti ] =p(l)
1 (1−p(l)1 )Ti−1(1−π0(Xi ))
p(l)0 (1−p(l)
0 )Ti−1π0(Xi )+p(l)1 (1−p(l)
1 )Ti−1(1−π0(Xi ))
Etape M :
θ(l+1) ∈ arg maxθQn(θ, θ
(l))
p(l+1)0 =
n−∑n
i=1 q(l)i∑n
i=1 Ti (1−q(l)i )
; p(l+1)1 =
∑ni=1 q(l)
i∑ni=1 Ti q
(l)i
β(l+1) ∈ arg minβ
{−Qn(θ, θ(l)) + λ1‖β‖1 +
λ22 ‖β‖
22
}avec L-BGFS-B
MVA | Presentation INSERM | Simon BUSSY 8/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Simulations
Idee : tester le schema de prediction suivant :
Pour la regression logistique : Zi ∼ Yi = 1{Ti≤s} , AUC surles Yi
Pour l’EM : AUC sur les Zi
MVA | Presentation INSERM | Simon BUSSY 9/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Simulations
Idee : tester le schema de prediction suivant :
Pour la regression logistique : Zi ∼ Yi = 1{Ti≤s} , AUC surles Yi
Pour l’EM : AUC sur les Zi
MVA | Presentation INSERM | Simon BUSSY 9/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Simulations
Idee : tester le schema de prediction suivant :
Pour la regression logistique : Zi ∼ Yi = 1{Ti≤s} , AUC surles Yi
Pour l’EM : AUC sur les Zi
MVA | Presentation INSERM | Simon BUSSY 9/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Estimation des vrais parametres
Comparaison des histogrammes de temps de retour reels et simules apres estimation
Parametres p0 p1 π
θ 0,005 0,511 0,872
Resultats de prediction sur les vraies donnees
MVA | Presentation INSERM | Simon BUSSY 10/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Generation des donnees
On genere Zi ∼ B(1− π0) pour n = 1000 sejoursavec π0 = 0,8721
Puis Ti ∼ G(pZi ) avec p0 = 0,005 et p1 = 0,511
Et enfin les donnees d’apprentisssage :
∀i ∈ J1,nK,
∀j ∈ J1,aK,{
X ji |Zi = 0 ∼ N (0,1)
X ji |Zi = 1 ∼ N (0.5,1)
∀j ∈ Ja + 1,dK,X ji ∼ N (0,1)
MVA | Presentation INSERM | Simon BUSSY 11/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Generation des donnees
On genere Zi ∼ B(1− π0) pour n = 1000 sejoursavec π0 = 0,8721
Puis Ti ∼ G(pZi ) avec p0 = 0,005 et p1 = 0,511
Et enfin les donnees d’apprentisssage :
∀i ∈ J1,nK,
∀j ∈ J1,aK,{
X ji |Zi = 0 ∼ N (0,1)
X ji |Zi = 1 ∼ N (0.5,1)
∀j ∈ Ja + 1,dK,X ji ∼ N (0,1)
MVA | Presentation INSERM | Simon BUSSY 11/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Generation des donnees
On genere Zi ∼ B(1− π0) pour n = 1000 sejoursavec π0 = 0,8721
Puis Ti ∼ G(pZi ) avec p0 = 0,005 et p1 = 0,511
Et enfin les donnees d’apprentisssage :
∀i ∈ J1,nK,
∀j ∈ J1,aK,{
X ji |Zi = 0 ∼ N (0,1)
X ji |Zi = 1 ∼ N (0.5,1)
∀j ∈ Ja + 1,dK,X ji ∼ N (0,1)
MVA | Presentation INSERM | Simon BUSSY 11/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Resultats : regression logistique
Courbe ROC pour la prediction de la regression logistique
MVA | Presentation INSERM | Simon BUSSY 12/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Resultats : regression logistique
β appris par la regression logistique
MVA | Presentation INSERM | Simon BUSSY 13/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Resultats : EM
Courbe ROC pour la prediction de l’EM
MVA | Presentation INSERM | Simon BUSSY 14/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Resultats : EM
β appris par l’EM
MVA | Presentation INSERM | Simon BUSSY 15/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Comparaison des deux methodes
Comparaison des AUC des 2 methodes pour 100 tests
MVA | Presentation INSERM | Simon BUSSY 16/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Organisation des donnees
Donnees heterogenes, differentes sources
1 sejour / patient : ”choix aleatoire par classe”, tauxde rechute de 12,84%
MVA | Presentation INSERM | Simon BUSSY 17/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Organisation des donnees
Donnees heterogenes, differentes sources1 sejour / patient : ”choix aleatoire par classe”, tauxde rechute de 12,84%
MVA | Presentation INSERM | Simon BUSSY 17/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Organisation des donnees
Reorganisation des donnees
MVA | Presentation INSERM | Simon BUSSY 18/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Organisation des donnees
Creation d’un fichier JSON
MVA | Presentation INSERM | Simon BUSSY 19/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Presentation des donnees
218 patients, 479 visites
Nombre de visites par patient Temps inter-visites
MVA | Presentation INSERM | Simon BUSSY 20/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Les parametres vitaux
Les parametres vitaux
9 variables gardeesProbleme : durees 6= et alignement
Nombre de pointspar parametre vital
Variables biologiques en communa tous les sejours
MVA | Presentation INSERM | Simon BUSSY 21/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Les parametres vitaux
Les parametres vitaux9 variables gardees
Probleme : durees 6= et alignement
Pression arterielle systolique [mmHg], notee PA max ;pression arterielle diastolique [mmHg], notee PA min ;
saturation en oxygene [%] ; Douleur EVA [U] ; frequencerespiratoire [mvt/min] ; temperature [◦C] ; poids [kg] ;
oxygene [L/min] ; frequence cardiaque [bpm]
MVA | Presentation INSERM | Simon BUSSY 21/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Les parametres vitaux
Les parametres vitaux9 variables gardeesProbleme : durees 6= et alignement
Evolution de la temperature au cours de 10 sejours
MVA | Presentation INSERM | Simon BUSSY 21/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Les parametres vitaux
Rescaling entre [0,1]
Interpolation : p valeursPuis filtre de Savitzky–Golay : p′ valeurs de gradient
∀j ∈ J1,NK, xj =xj−mink (xk )
maxk (xk )−mink (xk )
MVA | Presentation INSERM | Simon BUSSY 22/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Les parametres vitaux
Rescaling entre [0,1]Interpolation : p valeursPuis filtre de Savitzky–Golay : p′ valeurs de gradient
Frequence respiratoire pourun patient positif
Frequence respiratoire pourun patient negatif
MVA | Presentation INSERM | Simon BUSSY 22/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Les parametres vitaux
Comportements differents en moyenne
Test de Mann-Whitney-Wilcoxon
Pression arterielle diastolique et moyennes par classe
MVA | Presentation INSERM | Simon BUSSY 23/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Les parametres vitaux
Comportements differents en moyenneTest de Mann-Whitney-Wilcoxon
Test de Mann-Whitney-Wilcoxon pour la temperature
MVA | Presentation INSERM | Simon BUSSY 23/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Preprocessing
MVA | Presentation INSERM | Simon BUSSY 24/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Selection de p et p′
Procedure suivie :
MVA | Presentation INSERM | Simon BUSSY 25/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Selection de p et p′
Procedure suivie :
MVA | Presentation INSERM | Simon BUSSY 25/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Selection de p et p′
Procedure suivie :
MVA | Presentation INSERM | Simon BUSSY 25/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Selection de p et p′
Resultats apres 50 iterations
Dimension de l’espace : 446Donnees manquantes remplacees par les moyennes
Concept Nombre de points Ecart typeFq cardiaque 28 0,3∇ Fq cardiaque 26 0
PA max 28 0∇ PA max 26 0
Temperature 30 8,4∇ Temperature 18 0Saturation O2 34 4,8∇ Saturation O2 26 0
Douleur EVA 21 0,7∇ Douleur EVA 26 0
Debit O2 16 4,6∇ Debit O2 26 0
Fq respiratoire 21 5,3∇ Fq respiratoire 26 0
PA min 28 0∇ PA min 26 0
MVA | Presentation INSERM | Simon BUSSY 26/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Selection de p et p′
Resultats apres 50 iterationsDimension de l’espace : 446
Donnees manquantes remplacees par les moyennes
MVA | Presentation INSERM | Simon BUSSY 26/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Selection de p et p′
Resultats apres 50 iterationsDimension de l’espace : 446Donnees manquantes remplacees par les moyennes
MVA | Presentation INSERM | Simon BUSSY 26/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Benjamini-Hochberg
Tests de Mann-Whitney-Wilcoxon : 446 p-values
Procedure de Benjamini-Hochbergα = 0,9 ; 50 iterations
MVA | Presentation INSERM | Simon BUSSY 27/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Benjamini-Hochberg
Tests de Mann-Whitney-Wilcoxon : 446 p-valuesProcedure de Benjamini-Hochberg
α = 0,9 ; 50 iterations
On conserve k features avec
k = argmax{
j : p(j) ≤ αjK
}
MVA | Presentation INSERM | Simon BUSSY 27/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Benjamini-Hochberg
Tests de Mann-Whitney-Wilcoxon : 446 p-valuesProcedure de Benjamini-Hochbergα = 0,9 ; 50 iterations
MVA | Presentation INSERM | Simon BUSSY 27/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Benjamini-Hochberg
45 features selectionnees (> 13 des cas)
MVA | Presentation INSERM | Simon BUSSY 28/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Binarisation
Binarisation par quartiles ; dim = 156 ∼ 4× 45
MVA | Presentation INSERM | Simon BUSSY 29/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Binarisation
Binarisation par quartiles ; dim = 156 ∼ 4× 45
MVA | Presentation INSERM | Simon BUSSY 29/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Binarisation
Binarisation par quartiles ; dim = 156 ∼ 4× 45
MVA | Presentation INSERM | Simon BUSSY 29/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Binarisation
Binarisation par quartiles ; dim = 156 ∼ 4× 45
MVA | Presentation INSERM | Simon BUSSY 29/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Binarisation
Alternative : screening TV
βkTV ∈ argmin
β∈R10
{−
n∑i=1
Yi log(g((Dki )>β))+(1−Yi ) log(1−g((Dk
i )>β))+λ10∑
j=2
|βj−βj−1|}
MVA | Presentation INSERM | Simon BUSSY 30/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Association + decorrelation
Ajout des produits cartesiens
dim = 11978 ∼(156
2
)Decorrelation |ρ| < 0,95Finalement, dim = 10574
MVA | Presentation INSERM | Simon BUSSY 31/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Association + decorrelation
Ajout des produits cartesiensdim = 11978 ∼
(1562
)
Decorrelation |ρ| < 0,95Finalement, dim = 10574
MVA | Presentation INSERM | Simon BUSSY 31/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Association + decorrelation
Ajout des produits cartesiensdim = 11978 ∼
(1562
)Decorrelation |ρ| < 0,95
Finalement, dim = 10574
MVA | Presentation INSERM | Simon BUSSY 31/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Association + decorrelation
Ajout des produits cartesiensdim = 11978 ∼
(1562
)Decorrelation |ρ| < 0,95Finalement, dim = 10574
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Association + decorrelation
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Schema recapitulatif
MVA | Presentation INSERM | Simon BUSSY 33/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Resultats : regression ridge (dim = 10546)
Courbe ROC pour la regression `2 dans l’espace de dimension 10546
Classe Precision Recall Support0 0,96 0,77 561 0,38 0,80 10
Moyenne/Total 0,87 0,77 66
MVA | Presentation INSERM | Simon BUSSY 34/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Resultats : regression ridge (dim = 10546)
Probabilites predites sur le jeu de test
MVA | Presentation INSERM | Simon BUSSY 35/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Resultats : regression ridge (dim = 10546)
Coefficients de |βridge| tries
MVA | Presentation INSERM | Simon BUSSY 36/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Resultats : regression lasso (dim = 10546)
Courbe ROC pour la regression `1 dans l’espace de dimension 10546
Classe Precision Recall Support0 0,98 0,82 561 0,47 0,90 10
Moyenne/Total 0,90 0,83 66
MVA | Presentation INSERM | Simon BUSSY 37/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Resultats : Support du lasso
Coefficients de |βlasso| non nuls tries
MVA | Presentation INSERM | Simon BUSSY 38/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Resultats : regression ridge (dim = 30)
Courbe ROC pour la regression `2 dans l’espace de dimension 30
Classe Precision Recall Support0 0,96 0,89 561 0,57 0,80 10
Moyenne/Total 0,90 0,88 66
MVA | Presentation INSERM | Simon BUSSY 39/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Resultats : regression ridge (dim = 30)
Probabilites predites sur le jeu de test
MVA | Presentation INSERM | Simon BUSSY 40/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele censure pour l’EM
Echantillon(
X1, (T1, δ1)), . . . ,
(Xn, (Tn, δn)
)∈ Rd × (N∗ × {0, 1})
Ti = Ri ∧ Ci et δi = 1{Ri≤Ci}
Hyp 1 : ∀i ∈ J1, nK,Ri ⊥⊥ Ci |Zi ,Xi
Hyp 2 : ∀i ∈ J1, nK,Ci ⊥⊥ Zi ,Xi
`cn(θ, T ,∆,Z) = 1n∑n
i=1 δi
{Zi [log(1− π0(Xi )) + log(p1(Ti ))] + (1−
Zi )[log(π0(Xi )) + log(p0(Ti ))] + log(G(T−i ))}
+ (1− δi ){
Zi [log(1− π0(Xi )) +
log(F1(T−i ))] + (1− Zi )[log(π0(Xi )) + log(F0(T−i ))] + log(g(Ti ))}
Implementation a terminer et a tester !
MVA | Presentation INSERM | Simon BUSSY 41/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele censure pour l’EM
Echantillon(
X1, (T1, δ1)), . . . ,
(Xn, (Tn, δn)
)∈ Rd × (N∗ × {0, 1})
Ti = Ri ∧ Ci et δi = 1{Ri≤Ci}
Hyp 1 : ∀i ∈ J1, nK,Ri ⊥⊥ Ci |Zi ,Xi
Hyp 2 : ∀i ∈ J1, nK,Ci ⊥⊥ Zi ,Xi
`cn(θ, T ,∆,Z) = 1n∑n
i=1 δi
{Zi [log(1− π0(Xi )) + log(p1(Ti ))] + (1−
Zi )[log(π0(Xi )) + log(p0(Ti ))] + log(G(T−i ))}
+ (1− δi ){
Zi [log(1− π0(Xi )) +
log(F1(T−i ))] + (1− Zi )[log(π0(Xi )) + log(F0(T−i ))] + log(g(Ti ))}
Implementation a terminer et a tester !
MVA | Presentation INSERM | Simon BUSSY 41/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele censure pour l’EM
Echantillon(
X1, (T1, δ1)), . . . ,
(Xn, (Tn, δn)
)∈ Rd × (N∗ × {0, 1})
Ti = Ri ∧ Ci et δi = 1{Ri≤Ci}
Hyp 1 : ∀i ∈ J1, nK,Ri ⊥⊥ Ci |Zi ,Xi
Hyp 2 : ∀i ∈ J1, nK,Ci ⊥⊥ Zi ,Xi
`cn(θ, T ,∆,Z) = 1n∑n
i=1 δi
{Zi [log(1− π0(Xi )) + log(p1(Ti ))] + (1−
Zi )[log(π0(Xi )) + log(p0(Ti ))] + log(G(T−i ))}
+ (1− δi ){
Zi [log(1− π0(Xi )) +
log(F1(T−i ))] + (1− Zi )[log(π0(Xi )) + log(F0(T−i ))] + log(g(Ti ))}
Implementation a terminer et a tester !
MVA | Presentation INSERM | Simon BUSSY 41/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele censure pour l’EM
Echantillon(
X1, (T1, δ1)), . . . ,
(Xn, (Tn, δn)
)∈ Rd × (N∗ × {0, 1})
Ti = Ri ∧ Ci et δi = 1{Ri≤Ci}
Hyp 1 : ∀i ∈ J1, nK,Ri ⊥⊥ Ci |Zi ,Xi
Hyp 2 : ∀i ∈ J1, nK,Ci ⊥⊥ Zi ,Xi
`cn(θ, T ,∆,Z) = 1n∑n
i=1 δi
{Zi [log(1− π0(Xi )) + log(p1(Ti ))] + (1−
Zi )[log(π0(Xi )) + log(p0(Ti ))] + log(G(T−i ))}
+ (1− δi ){
Zi [log(1− π0(Xi )) +
log(F1(T−i ))] + (1− Zi )[log(π0(Xi )) + log(F0(T−i ))] + log(g(Ti ))}
Implementation a terminer et a tester !
MVA | Presentation INSERM | Simon BUSSY 41/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele censure pour l’EM
Echantillon(
X1, (T1, δ1)), . . . ,
(Xn, (Tn, δn)
)∈ Rd × (N∗ × {0, 1})
Ti = Ri ∧ Ci et δi = 1{Ri≤Ci}
Hyp 1 : ∀i ∈ J1, nK,Ri ⊥⊥ Ci |Zi ,Xi
Hyp 2 : ∀i ∈ J1, nK,Ci ⊥⊥ Zi ,Xi
`cn(θ, T ,∆,Z) = 1n∑n
i=1 δi
{Zi [log(1− π0(Xi )) + log(p1(Ti ))] + (1−
Zi )[log(π0(Xi )) + log(p0(Ti ))] + log(G(T−i ))}
+ (1− δi ){
Zi [log(1− π0(Xi )) +
log(F1(T−i ))] + (1− Zi )[log(π0(Xi )) + log(F0(T−i ))] + log(g(Ti ))}
Implementation a terminer et a tester !
MVA | Presentation INSERM | Simon BUSSY 41/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Modele censure pour l’EM
Echantillon(
X1, (T1, δ1)), . . . ,
(Xn, (Tn, δn)
)∈ Rd × (N∗ × {0, 1})
Ti = Ri ∧ Ci et δi = 1{Ri≤Ci}
Hyp 1 : ∀i ∈ J1, nK,Ri ⊥⊥ Ci |Zi ,Xi
Hyp 2 : ∀i ∈ J1, nK,Ci ⊥⊥ Zi ,Xi
`cn(θ, T ,∆,Z) = 1n∑n
i=1 δi
{Zi [log(1− π0(Xi )) + log(p1(Ti ))] + (1−
Zi )[log(π0(Xi )) + log(p0(Ti ))] + log(G(T−i ))}
+ (1− δi ){
Zi [log(1− π0(Xi )) +
log(F1(T−i ))] + (1− Zi )[log(π0(Xi )) + log(F0(T−i ))] + log(g(Ti ))}
Implementation a terminer et a tester !
MVA | Presentation INSERM | Simon BUSSY 41/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Conclusion
De nombreuses pistes restent a explorer maispremiers resultats encourageants !
Tester sur une cohorte exterieureProgres techniques et culturels (ICML, SMILE)These a venir orientee sur les questions posees lorsde ce stage : modelisation de variable longitudinales,adaptation des algorithmes d’apprentissageclassiques a ces donnees, problemes d’alignements,etc.
MVA | Presentation INSERM | Simon BUSSY 42/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Conclusion
De nombreuses pistes restent a explorer maispremiers resultats encourageants !Tester sur une cohorte exterieure
Progres techniques et culturels (ICML, SMILE)These a venir orientee sur les questions posees lorsde ce stage : modelisation de variable longitudinales,adaptation des algorithmes d’apprentissageclassiques a ces donnees, problemes d’alignements,etc.
MVA | Presentation INSERM | Simon BUSSY 42/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Conclusion
De nombreuses pistes restent a explorer maispremiers resultats encourageants !Tester sur une cohorte exterieureProgres techniques et culturels (ICML, SMILE)
These a venir orientee sur les questions posees lorsde ce stage : modelisation de variable longitudinales,adaptation des algorithmes d’apprentissageclassiques a ces donnees, problemes d’alignements,etc.
MVA | Presentation INSERM | Simon BUSSY 42/42
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Introduction Modeles Algorithmes Simulations Organisation Presentation Preprocessing Resultats Conclusion
Conclusion
De nombreuses pistes restent a explorer maispremiers resultats encourageants !Tester sur une cohorte exterieureProgres techniques et culturels (ICML, SMILE)These a venir orientee sur les questions posees lorsde ce stage : modelisation de variable longitudinales,adaptation des algorithmes d’apprentissageclassiques a ces donnees, problemes d’alignements,etc.
MVA | Presentation INSERM | Simon BUSSY 42/42