=Paper=
{{Paper
|id=Vol-2926/paper2
|storemode=property
|title=AnyNets: Adaptive Deep Neural Networks for Medical Data with Missing Values
|pdfUrl=https://ceur-ws.org/Vol-2926/paper2.pdf
|volume=Vol-2926
|authors=Maria Kalweit,Gabriel Kalweit,Joschka Boedecker
|dblpUrl=https://dblp.org/rec/conf/ijcai/KalweitKB21
}}
==AnyNets: Adaptive Deep Neural Networks for Medical Data with Missing Values==
https://ceur-ws.org/Vol-2926/paper2.pdf
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b?QrM BM h #H2 R 7`QK i?2 l*A `2TQbBiQ`vR (RR),
Ç EB/M2v .Bb2 b2, *H bbB7v T iB2Mib bmz2`BM; M/ MQi bmz2`BM; 7`QK +?`QMB+ FB/M2v
/Bb2 b2 # b2/ QM #HQQ/ i2bib HQM; rBi? Qi?2` K2 bm`2bX
Ç .B #2i2b, *H bbB7v T iB2Mib rBi? M/ rBi?Qmi /B #2i2b #v /B ;MQbiB+ K2 bm`2K2MibX
Ç J KKQ;` T?B+b, S`2/B+i i?2 b2p2`Biv Q7 K KKQ;` T?B+ K bb H2bBQM U#2MB;M Q`
K HB;M MiV 7`QK "A@_.a ii`B#mi2b HQM; rBi? i?2 ;2 Q7 i?2 T iB2MiX
Ç "`2 bi * M+2`, *Hmbi2` ++Q`/BM; iQ i?2 b2p2`Biv Q7 i?2 + M+2` U#2MB;M Q` K HB;M MiVX
h?2 / i b2i +QMi BMb 72 im`2b +? ` +i2`BxBM; i?2 +2HH Mm+H2BX
Ç h?v`QB/, *QKT`Bb2b /2KQ;` T?B+ 72 im`2b- bvKTiQKb M/ H #Q` iQ`v i2bib- BM Q`/2`
iQ +Hmbi2` BM MQ`K H- bm#+HBMB+ H ?vTQi?v`QB/BbK M/ ?vTQi?v`QB/BbKX
h?2 / i b2ib +QMi BM 7`QK 8 iQ k9 72 im`2b M/ mT iQ RkW KBbbBM; p Hm2bX q2 2p Hm i2
i?2 +H bbB}+ iBQM T2`7Q`K M+2 QM EB/M2v .Bb2 b2- .B #2i2b M/ J KKQ;` T?B+b M/
2p Hm i2 i?2 +Hmbi2`BM; T2`7Q`K M+2 QM "`2 bi * M+2` M/ h?v`QB/- r?2`2 r2 BMb2`i 7`QK
Ry@dyW KBbbBM; p Hm2b `iB}+B HHvX
. i b2i Oa KTH2b O62 im`2b OJBbbBM;
EB/M2v .Bb2 b2 9yy k9
.B #2i2b de3 3
J KKQ;` T?B+b NeR 8
"`2 bi * M+2` eNN N ࠍ
h?v`QB/ kR9 8 ࠍ
h #H2 R
. i b2ib 7Q` +H bbB}+ iBQM M/ +Hmbi2`BM; i bFbX
8X 1tT2`BK2Mi H _2bmHib
q2 2p Hm i2 i?2 T2`7Q`K M+2 Q7 MvL2ib QM i?`22 +H bbB}+ iBQM M/ irQ +Hmbi2`BM; i bFb
mbBM; i?2 / i b2ib /2b+`B#2/ #Qp2X 6Q` HH / i b2ib- r2 TTHv 8@7QH/ +`Qbb@p HB/ iBQM
iQ Q#i BM K2 M ++m` +B2b M/ bi M/ `/ /2pB iBQMb Qp2` HH 7QH/bX >vT2`T ` K2i2`b `2
imM2/ mbBM; _ M/QK a2 `+? Qp2` R8 `mMb 7Q` HH `+?Bi2+im`2b- BM+Hm/BM; i?2 # b2HBM2b-
mbBM; i?2 +QM};m` iBQM bT +2b b?QrM BM h #H2 kX 6Q` T`2T`Q+2bbBM;- HH 72 im`2b `2 b+ H2/
BM i?2 ` M;2 < >X b +iBp iBQM 7mM+iBQM- r2 mb2 `2+iB}2/ HBM2 ` mMBib U_2GlV 7Q` HH
?B//2M H v2`bX 6Q` QTiBKBx iBQM r2 mb2 / K (Rk)X
R
?iiTb,ff `+?Bp2XB+bXm+BX2/mfKHf/ i b2ibXT?T
17
JQ/2H S ` K2i2` *QM};X aT +2
HH Bi2` iBQMb < >
# i+? bBx2 < >
H2 `MBM; ` i2 <ࠍ ࠍ >
?B//2M /BKࠒ ࠒࠒ < >
6*@* MmK H v2`b < >
6*@1 MmK H v2`bࠒ < >
H i2Mi /BKX < >
ള, ?B//2M /BKXࠒࠒ < >
MvL2i@* ͐, ?B//2M /BKX < >
͐ ള, MmK H v2`bࠒ < >
MvL2i@1 /BKX Q7 < >
, ?B//2M /BKࠒࠒ < >
h #H2 k
*QM};m` iBQM bT +2b Q7 i?2 /Bz2`2Mi TT`Q +?2bX U V h?2 ?B//2M /BK2MbBQM 7Q` HH 7mHHv@+QMM2+i2/
H v2`b Q7 HH `+?Bi2+im`2bX U V A7 MQi /2MQi2/ /Bz2`2MiHv- 7Q` miQ2M+Q/2` M2irQ`Fb- i?2 ?B//2M
/BK2MbBQM M/ MmK#2` Q7 H v2`b Bb mb2/ 7Q` #Qi? 2M+Q/2` M/ /2+Q/2` KQ/mH2bX 6Q` .1*-
യ ࠃ < > r b mb2/X
8XRX *H bbB}+ iBQM h bFb
h?2 +H bbB}+ iBQM `2bmHib `2 b?QrM BM h #H2 jX h?2 MvL2ib@*H bbB}2` Bb QmiT2`7Q`KBM;
i?2 7mHHv@+QMM2+i2/ M2m` H M2irQ`Fb BM +QK#BM iBQM rBi? K2 M- x2`Q M/ F@LL BKTmi iBQM
7Q` HH / i b2ibX h?2 #2bi ++m` +v Q7 RXy Bb +?B2p2/ 7Q` i?2 EB/M2v .Bb2 b2 / i b2i-
r?2`2 MvL2i Bb #H2 iQ ;2M2` HBx2 T2`72+iHv iQ i?2 i2bi b2iX AM 6B;m`2 j- r2 M Hvx2 i?2
BM~m2M+2 Q7 KBbbBM; 72 im`2 p Hm2b QM i?2 +QK#BM2/ H i2Mi `2T`2b2Mi iBQM ͒ ഽ Yઠ 7Q`
b KTH2b Yઠ BM EB/M2v .Bb2 b2 rBi? +Q``2bTQM/BM; H #2Hb રઠ UMQ +?`QMB+ FB/M2v /Bb2 b2V
M/ રઠ U+?`QMB+ FB/M2v /Bb2 b2VX aBM;H2 KBbbBM; p Hm2b 7Q` KQbi Q7 i?2 72 im`2b /Q MQi
? p2 H `;2 BKT +i QM i?2 H i2Mi `2T`2b2Mi iBQM- r?B+? K2 Mb i? i i?2v T`Q# #Hv `2
KBbbBM; i ` M/QK M/ + M #2 BKTmi2/ BKTHB+BiHv #v i?2 M2m` H M2irQ`FX aQK2 72 im`2b
? p2 ?B;?2` BM~m2M+2 M/ +? M;2 i?2 K2 MBM; Q7 i?2 H i2Mi `2T`2b2Mi iBQM bB;MB}+ MiHvX
. i b2i J2 M w2`Q F@LL MvL2ib@*H bbB}2`
EB/M2v .Bb2 b2 q q q q
.B #2i2b q q q q
J KKQ;` T?B+b q q q q
h #H2 j
J2 M ++m` +v M/ bi M/ `/ /2pB iBQMb 7Q` 8@7QH/ +`Qbb p HB/ iBQM Qp2` i?2 K2/B+ H / i b2ib mbBM;
bmT2`pBb2/ H2 `MBM;X
18
, ,
all features
observable
feature 5 is na
#features
feature 16 is na
feature 20 is na
latent dimension
6B;m`2 j, oBbm HBx iBQM Q7 i?2 +QK#BM2/ H i2Mi `2T`2b2Mi iBQMb ͒ ഽ ࢳ 7Q` irQ b KTH2b Yઠ Yડ rBi?
H #2Hb રઠ U+?`QMB+ FB/M2v /Bb2 b2V M/ રડ UMQ +?`QMB+ FB/M2v /Bb2 b2V BM EB/M2v .Bb2 b2X
h?2 }`bi `Qr `2T`2b2Mib +iBp iBQMb Q7 i?2 H i2Mi p2+iQ` Q7 bBx2 e9 7Q` i?2 b KTH2 યઠ UH27iV M/ યડ
U`B;?iV rBi?Qmi Mv KBbbBM; p Hm2b Ui?2 #`B;?i2`- i?2 ?B;?2` i?2 +iBp iBQMbV- i?2 ઢ@i? `Qr i?2
+iBp iBQMb Q7 i?2 H i2Mi p2+iQ` r?2M b2iiBM; i?2 ઢ@i? 72 im`2 b OBX q?BH2 KBbbBM; p Hm2 7Q`
72 im`2 8 /Q2b MQi ? p2 M BKT +i Ui?2 H i2Mi p2+iQ` HQQFb bBKBH ` iQ i?2 p2+iQ` BM i?2 }`bi `QrV-
KBbbBM; p Hm2b 7Q` 72 im`2 Re M/ ky +? M;2 i?2 72 im`2 `2T`2b2Mi iBQM bB;MB}+ MiHvX
8XkX *Hmbi2`BM; h bFb
hQ 2p Hm i2 i?2 +Hmbi2`BM;@T2`7Q`K M+2 Q7 HH TT`Q +?2b- r2 +QMbB/2` /Bz2`2Mi T2`+2Mi ;2b
Q7 BMb2`i2/ KBbbBM; p Hm2b 7Q` "`2 bi * M+2` M/ h?v`QB/X 6Q` +Hmbi2`BM;- r2 +QKTmi2
++m` +B2b # b2/ QM i?2 T`2/B+i2/ +H bb2b રઠʽ Ur?2`2 HH TQbbB#H2 T2`Kmi iBQMb Q7 +Hmbi2`
A.b `2 +QMbB/2`2/V M/ i?2 ;Bp2M ;`QmM/ i`mi? +H bb2b રઠ #v,
થࠍ
++m` +v રઠ રઠʽ NBY ๑ T2`K રઠʽ રઠ
T2`Kࠃ થ ઠ
r?2`2 Bb i?2 b2i Q7 HH T2`Kmi iBQMb M/ રઠʽ રઠ B7 રઠʽ રઠ M/ y 2Hb2X h?2 `2bmHib
7Q` i?2 "`2 bi * M+2` / i b2i `2 b?QrM BM h #H2 9X MvL2ib@miQ2M+Q/2` QmiT2`7Q`Kb
HH # b2HBM2b- 2bT2+B HHv x2`Q BKTmi iBQM #v Q`/2`b Q7 K ;MBim/2 7Q` ?B;? KQmMi Q7
KBbbBM; p Hm2bX
JBbbBM; o Hm2b (W) J2 M w2`Q F@LL MvL2ib@miQ2M+Q/2`
RyW q q q q
jyW q q q q
8yW q q q q
dyW q q q q
h #H2 9
J2 M ++m` +v M/ bi M/ `/ /2pB iBQMb 7Q` 8@7QH/ +`Qbb p HB/ iBQM Qp2` i?2 "`2 bi * M+2` / i b2i
rBi? ઢ4k +H bb2b mbBM; .1*X
6Q` h?v`QB/- b?QrM BM h #H2 8- i?2 MvL2ib@miQ2M+Q/2` T2`7Q`Kb QMHv bHB;?iHv #2ii2`
i? M i?2 F@LL BKTmi iBQM # b2HBM2- r?B+? KB;?i #2 /m2 iQ i?2 p2`v bK HH b2i Q7 kR9
b KTH2bX
19
JBbbBM; o Hm2b (W) J2 M w2`Q F@LL MvL2ib@miQ2M+Q/2`
RyW q q q q
jyW q q q q
8yW q q q q
dyW q q q q
h #H2 8
J2 M ++m` +v M/ bi M/ `/ /2pB iBQMb 7Q` 8@7QH/ +`Qbb p HB/ iBQM Qp2` i?2 h?v`QB/ / i b2i rBi?
ઢ4j +H bb2b mbBM; .1*X
eX .Bb+mbbBQM
h?2 +QK#BM2/ `2T`2b2Mi iBQM ͒ ഽ Yઠ Q7 HH Q#b2`p2/ 72 im`2b H2 `M2/ BM MvL2ib +QMi BMb
BM7Q`K iBQM Q7 HH i?2 p BH #H2 72 im`2b M/ BKTHB+BiHv Bb #H2 iQ H2 `M i? i +2`i BM 72 im`2b
`2 KBbbBM;X h?Bb bi M/b BM +QMi` bi iQ /22T M2m` H M2irQ`Fb BM +QK#BM iBQM rBi? K2 M
BKTmi iBQM Q` F@LL BKTmi iBQM M/ Bb Q7 /p Mi ;2 B7 i?2 #b2Mi p Hm2b `2 `2H i2/
iQ i?2 `2bTQMb2 / i M/ MQi KBbbBM; i ` M/QKX 6Q` x2`Q BKTmi iBQM- KBbbBM; p Hm2b
+ M #2 `2T`2b2Mi2/ b x2`Qb- r?B+? Bb 2[mBp H2Mi iQ b2iiBM; i?2 r2B;?ib Q7 i?2 `2bT2+iBp2
BMTmi M2m`QMb iQ x2`Qc i?2 #B b- ?Qr2p2`- `2K BMbX h?2 72 im`2 rBHH i?mb biBHH ? p2 M
BM~m2M+2 QM i?2 Qmi+QK2- #mi TQbbB#Hv rBi? M BM+`2 b2/ BKTQ`i M+2 Q7 i?2 MQM@KBbbBM;
72 im`2bX h?Bb 2z2+i + M 2bT2+B HHv #2 b22M BM i?2 `2bmHib Q7 mMbmT2`pBb2/ +Hmbi2`BM;X h?2
`2K BMBM; BM~m2M+2 Q7 i?2 x2`Q@BKTmi2/ p Hm2b +? M;2b i?2 bi`m+im`2 Q7 i?2 b KTH2b U HbQ
7Q` J*_ M/ J_ p `B #H2bV r?B+? H2 /b iQ T2`7Q`K M+2 /2+`2 b2 BM i?2 mMbmT2`pBb2/
+ b2 7Q` BM+`2 bBM; KQmMib Q7 KBbbBM; p Hm2bX h?2 T`2b2M+2 Q7 H #2Hb BM i?2 bmT2`pBb2/
+ b2 HH2pB i2b i?Bb Bbbm2- ?2M+2 i?2 T2`7Q`K M+2 /2+`2 b2 Bb bK HH2`X
dX *QM+HmbBQM
AM i?Bb T T2`- r2 BMi`Q/m+2/ MQp2H +H bb Q7 / TiBp2 M2m` H M2irQ`Fb + HH2/ MvL2ib
r?B+? Bb + T #H2 Q7 T`Q+2bbBM; b2i Q7 p `B #H2 BMTmi 72 im`2bX q2 b?Qr2/ i?2 2{+ +v
Q7 MvL2ib BM i?2 bmT2`pBb2/ M/ mMbmT2`pBb2/ + b2 7Q` p `BQmb K2/B+ H / i b2ib M/
?B;?HB;?i2/ i?2B` /p Mi ;2b BM i?2B` TTHB+ iBQM iQ 2H2+i`QMB+ K2/B+ H `2+Q`/b Q` `2;Bbi`B2b
r?B+? + M +QMi BM K Mv / i ivT2b- ` M;BM; 7`QK +QMiBMmQmb M/ + i2;Q`B+ H p Hm2b iQ
BK ;2b- M/ +QKKQMHv bmz2` 7`QK bB;MB}+ Mi KQmMi Q7 KBbbBM; 2Mi`B2bX
_272`2M+2b
(R) AX :QQ/72HHQr- uX "2M;BQ- X *Qm`pBHH2- .22T G2 `MBM;- JAh S`2bb- kyReX ?iiT,
ffrrrX/22TH2 `MBM;#QQFXQ`;X
(k) CX uQQM- qX _X w K2- X " M2`D22- JX * /2B` b- X JX H - JX p M /2` a+? `-
S2`bQM HBx2/ bm`pBp H T`2/B+iBQMb pB i`22b Q7 T`2/B+iQ`b, M TTHB+ iBQM iQ + `/B +
i` MbTH Mi iBQM- SGPa PL1 Rj UkyR3V RĜRNX l_G, ?iiTb,ff/QBXQ`;fRyXRjdRfDQm`M HX
TQM2XyRN9N38X /QB,RyXRjdRfDQm`M HXTQM2XyRN9N38X
20
(j) _X CX X GBiiH2- .X "X _m#BM- ai iBbiB+ H M HvbBb rBi? JBbbBM; . i - CQ?M qBH2v
aQMb- AM+X- la- RN3eX
(9) SX 1X J+EMB;?i- EX JX J+EMB;?i- aX aB/ MB- X CX 6B;m2`2/Q- JBbbBM; . i ,
:2MiH2 AMi`Q/m+iBQM- S2`bQMM2H Sbv+?QHQ;v- kyy3X
(8) :X 1X X SX X " iBbi - JX *X JQM `/- bim/v Q7 F@M2 `2bi M2B;?#Qm` b M
BKTmi iBQM K2i?Q/- BM, >Aa- kyykX
(e) aX >Q+?`2Bi2`- CX a+?KB/?m#2`- GQM; b?Q`i@i2`K K2KQ`v- L2m` H *QKTmiX N URNNdV
Rdj8ĜRd3yX l_G, ?iiT,ff/tX/QBXQ`;fRyXRRekfM2+QXRNNdXNX3XRdj8X /QB,RyXRRekfM2+QX
RNNdXNX3XRdj8X
(d) JX >m2;H2- :X E Hr2Bi- hX >m2;H2- CX "Q2/2+F2`- 1tTH BM #H2 B BM ?2 Hi?+ `2 M/
K2/B+BM2, /vM KB+ /22T M2m` H M2irQ`F 7Q` KmHiBKQ/ H +HBMB+ H / i M HvbBb-
aim/B2b BM *QKTmi iBQM H AMi2HHB;2M+2 UkykRVX l_G, ?iiT,ff/tX/QBXQ`;fRyXRyydf
Nd3@j@yjy@8jj8k@eX /QB,RyXRyydfNd3@j@yjy@8jj8k@eX
(3) JX w ?22`- aX EQiim`- aX _ p M# F?b?- "X SQ+xQb- _X _X a H F?mi/BMQp- X CX
aKQH - .22T b2ib- BM, AX :mvQM- lX oX Gmt#m`;- aX "2M;BQ- >X q HH +?- _X 62`;mb-
aX oBb?r M i? M- _X : `M2ii U1/bXV- /p M+2b BM L2m` H AM7Q`K iBQM S`Q+2bbBM;
avbi2Kb jy- *m`` M bbQ+B i2b- AM+X- kyRd- TTX jjNRĜj9yRX l_G, ?iiT,ffT T2`bXMBTbX
++fT T2`feNjR@/22T@b2ibXT/7X
(N) sX :mQ- GX : Q- sX GBm- CX uBM- AKT`Qp2/ /22T 2K#2//2/ +Hmbi2`BM; rBi? HQ+ H
bi`m+im`2 T`2b2`p iBQM- BM, S`Q+22/BM;b Q7 i?2 hr2Miv@aBti? AMi2`M iBQM H CQBMi
*QM72`2M+2 QM `iB}+B H AMi2HHB;2M+2- AC*A@Rd- kyRd- TTX Rd8jĜRd8NX l_G, ?iiTb,
ff/QBXQ`;fRyXk9NejfBD+ BXkyRdfk9jX /QB,RyXk9NejfBD+ BXkyRdfk9jX
(Ry) CX J +[m22M- aQK2 K2i?Q/b 7Q` +H bbB}+ iBQM M/ M HvbBb Q7 KmHiBp `B i2 Q#b2`p @
iBQMb- BM, AM 8@i? "2`F2H2v avKTQbBmK QM J i?2K iB+ H ai iBbiB+b M/ S`Q# #BHBiv-
RNed- TTX k3RĜkNdX
(RR) X bmM+BƦM- .X L2rK M- l*A J +?BM2 G2 `MBM; _2TQbBiQ`vX ?iiT,ffrrrX
B+bXm+BX2/mf KH2 `MfJG_2TQbBiQ`vX?iKH- kyydX l_G, ?iiT,ffrrrXB+bXm+BX2/mf0$
bBK0KH2 `Mf&JG_'2TQbBiQ`vX?iKHX
(Rk) .X EBM;K - CX " - / K, K2i?Q/ 7Q` biQ+? biB+ QTiBKBx iBQM- AMi2`M iBQM H
*QM72`2M+2 QM G2 `MBM; _2T`2b2Mi iBQMb UkyR9VX
21