機械学習と機械発見：自然科学融合が誘起するデータ科学の新展開

⾒
https://itakigawa.github.io/
2023.2.18 @
(WPI-ICReDD)
⾒

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JST (3.5 )
AIP iPS G (4 )
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(Bioinformatics)
Materials Informatics
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稿

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(g) (cm)

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(g) (cm)
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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(g) (cm)
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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(g) (cm)
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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(g) (cm)
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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(g) (cm)
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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(g) (cm)
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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(g) (cm)
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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(g) (cm)
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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(g)
(cm)
む
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View Slide

(g) (cm)
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
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(g)
(cm)
む
む
(cm)
(g)
む
む

View Slide

む
む
or
5 6.25 7.5 8.75 10
90 112.5 135 157.5 180
●
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●
(g)
(cm)
(cm)
(g)
む
む

View Slide

( )
J aime la
musique
I love music

View Slide

Deep Fake
"MQIB(P "MQIB'PME "MQIB5FOTPS
ChatGPT

View Slide

GPT n 稿 (Lossy )

View Slide

Decision
Tree
Random
Forest
GBDT
Nearest
Neighbor
Logistic
Regression
SVM
Gaussian
Process
Neural
Network

View Slide

View Slide

0 1
P( =red)

View Slide

Random Forest
Gaussian Process
Logistic Regression
0 1
P( =red)

View Slide

Random Forest Neural Network SVR Kernel Ridge
p1 p2 p3 p4

View Slide

(Bioinformatics)
Materials Informatics
( )
稿

View Slide

3
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( )
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View Slide

( )
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View Slide

( )

View Slide

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
EI =
Z 1
y⇤
y · p(y)dy
Expected Improvement (EI)
Machine Learning Prediction
Prediction Interval
:
UQ ( )

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=

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ダ
ダ (data leakage)
=

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ダ
ダ (data leakage)
テ Training ( )
=

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ダ
ダ (data leakage)
テ Training ( ) デ Validation ( )
=

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ダ
ダ (data leakage)
テ Training ( ) デ Validation ( ) ト Test ( )
=

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( )
AAAChnichVHLTsJAFD3UF+ID1I2JGyLBuCJTg2JcEd245CGPBAlp64gNpW3aQkTiD5i4lYUrTVwYP8APcOMPuOATjEtM3LjwUpoYJeJtpnPmzD13zsyVTU21Hca6PmFsfGJyyj8dmJmdmw+GFhbzttGwFJ5TDM2wirJkc03Vec5RHY0XTYtLdVnjBbm2198vNLllq4Z+4LRMXq5LVV09VhXJISp7WhEroQiLMTfCw0D0QARepIzQIw5xBAMKGqiDQ4dDWIMEm74SRDCYxJXRJs4ipLr7HOcIkLZBWZwyJGJr9K/SquSxOq37NW1XrdApGg2LlGFE2Qu7Zz32zB7YK/v8s1bbrdH30qJZHmi5WQleLGc//lXVaXZw8q0a6dnBMbZdryp5N12mfwtloG+edXrZnUy0vcZu2Rv5v2Fd9kQ30Jvvyl2aZ65H+JHJC70YNUj83Y5hkN+IiVuxeDoeSe56rfJjBatYp34kkMQ+UshR/SoucYWO4BdiwqaQGKQKPk+zhB8hJL8AVLKQnA==
x1
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
x2
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
y
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
f
f
y
x1 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
x2
x2
y

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( )
x1
x2
y
f
f
y
x2
x2
y
‣
(= )
(x , x ) y
( )

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( )
x1
x2
y
f
f
y
x2
x2
y
‣
(= )
(x , x ) y
( )
‣ (x , x ) ( )
y (x , x )

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x1
x2
y
f
f
y
x2
⾒ ( )
N = = N = = N = =

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Fisher
( )
. (Replication)
⾒ ( )
. (Local Control)
. (Randomization) (Fisher )
Data Leakage

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:

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:
( ) ⾒
༗઒અ෉
Herbert Simon
Simon HA, Machine Discovery. ( )
Langley PW, Simon HA, Bradshaw G, Zytkow JM, Scienti c Discovery:
Computational Explorations of the Creative Process ( ).
, . (1996)
, . (2001)

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3
.
.
( )
.

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x
y

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x
y
A.

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Two Cultures:
Leo Breiman, Statistical Modeling: The Two Cultures. (with comments and a rejoinder by
the author), Statistical Science, 16(3): 199-231 (August 2001)
https://doi.org/10.1214/ss/1009213726

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Two Cultures:
Data Modeling Algorithmic Modeling 2
https://doi.org/10.1214/ss/1009213726

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Two Cultures:
( )
https://doi.org/10.1214/ss/1009213726

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Two Cultures:
( )
CP
https://doi.org/10.1214/ss/1009213726

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Two Cultures:
( )
CP
2001 20
https://doi.org/10.1214/ss/1009213726

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Two Cultures:
( )
CP
2001 20
Cox Efron ( )
https://doi.org/10.1214/ss/1009213726

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Two Cultures:
( )
CP
2001 20
Cox Efron ( )
20話 2021 Observational Studies
https://doi.org/10.1214/ss/1009213726

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Two Cultures:
Breiman's main point is: If you want prediction, do prediction for its own sake
and forget about the illusion of representing nature. (Judea Pearl)
https://doi.org/10.1353/obs.2021.0008

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Two Cultures:
Breiman's main point is: If you want prediction, do prediction for its own sake
and forget about the illusion of representing nature. (Judea Pearl)
https://doi.org/10.1353/obs.2021.0008
Three Lessons
There have been particularly exciting developments in the last ﬁve years.  
What has been learned? The three lessons that seem most important to one:
Rashomon: the multiplicity of good models;
Occam: the conﬂict between simplicity and accuracy;
Bellman: dimensionality—curse or blessing.

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Rashomon: the multiplicity of good models
΍Ϳʲᤵʳͷதʢͳ͔ʣ
ᶄ (և઒ཾ೭հͷ࡞඼ʮᤵͷதʯ͔Β) ؔ܎ऀͷ͍͏͜ͱ͕৯͍ҧͬͯɺਅ૬͕Θ͔Βͳ͍
͜ͱΛ͍͏ɻʮਅ૬͸ᤵͷதͩʯ(ਫ਼બ൛ ೔ຊࠃޠେࣙయΑΓ)ʢ
Rashomon 1950

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Rashomon 1950
Rashomon E ect ( ):

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Rashomon 1950
Rashomon E ect ( ):
⾒ ( )

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Rashomon 1950
Rashomon E ect ( ):
⾒ ( )
( )

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Underspeci cation
(specify )
( )

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Underspeci cation
(specify )
( )
Underspeci cation
Google

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Occam: the conflict between simplicity and accuracy
ResNet : 2600
ResNet : 4500
E cientNet-B : 6600
VGG : 1 4400
⾒
20×20 1200
1000×1000 300
-layer, -heads BERT: 1 1000
GPT- XL: 15 5800
GPT- : 1750
ダ
( )
ダ

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Occam: the conflict between simplicity and accuracy
ResNet : 2600
ResNet : 4500
E cientNet-B : 6600
VGG : 1 4400
⾒
20×20 1200
1000×1000 300
GPT- XL: 15 5800
GPT- : 1750
ダ
( )
ダ
( )

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Bellman: dimensionality curse or blessing
( ⾒ )

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( ⾒ )
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
1
1
) 1 1 ( d )

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( ⾒ )
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
0.5
p
d
1
1
) 1 1 ( d )

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( ⾒ )
0.5
p
d
1
1
) 1 1 ( d )
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
d = 2
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
0.5
p
2

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( ⾒ )
0.5
p
d
1
1
) 1 1 ( d )
d = 2
0.5
p
2
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
d = 4
1

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( ⾒ )
0.5
p
d
1
1
) 1 1 ( d )
d = 2
0.5
p
2
d = 4
1
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
d > 4
0.5
p
d

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( ⾒ )
0.5
p
d
1
1
) 1 1 ( d )
d = 2
0.5
p
2
d = 4
1
d > 4
0.5
p
d
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
> 1
!?

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( ⾒ )
0.5
p
d
1
1
) 1 1 ( d )
d = 2
0.5
p
2
d = 4
1
d > 4
0.5
p
d
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
> 1
!?
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
V (d) =
⇡ d
2
d
2
· d
2
! 0 (d ! 1)
=
=
d
AAAB/XicbVDLSgNBEOz1GeMr6tHLYBA8hV3xdRGCXjxGMA9I1jA7O5sMmZldZmaFsAS/wauevYlXv8Wjf+Ik2YNJLGgoqrrp7goSzrRx3W9naXlldW29sFHc3Nre2S3t7Td0nCpC6yTmsWoFWFPOJK0bZjhtJYpiEXDaDAa3Y7/5RJVmsXwww4T6AvckixjBxkpN7zFE18jrlspuxZ0ALRIvJ2XIUeuWfjphTFJBpSEca9323MT4GVaGEU5HxU6qaYLJAPdo21KJBdV+Njl3hI6tEqIoVrakQRP170SGhdZDEdhOgU1fz3tj8T+vnZroys+YTFJDJZkuilKOTIzGv6OQKUoMH1qCiWL2VkT6WGFibEIzWwIxspl48wksksZpxbuonN+flas3eToFOIQjOAEPLqEKd1CDOhAYwAu8wpvz7Lw7H87ntHXJyWcOYAbO1y9Fl5UB
1d = 1

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⾒ ( )

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⾒ ( )
. (Lipschitz )
⾒ ( ) d
d= 100 (10 )
d= 10 =100

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⾒ ( )
. (Lipschitz )
⾒ ( ) d
d= 100 (10 )
d= 10 =100
( )
. (d> )

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3
.
.
( )
.

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Informatics
( )
⾒

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Informatics
( )
⾒
⾒ (Herbert Simon!)
⾒ ( )

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Informatics
( )
⾒
⾒ (Herbert Simon!)
⾒ ( )
⾒

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( )

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( )
X Y
Y

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vs

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vs
(= )

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vs
(= )
• “Theory-driven models can be wrong. But data-driven models cannot be wrong or
right. Data-driven are not trying to describe an underlying reality.”
David Hand, KDD2018 (Keynote Talk)
http://videolectures.net/kdd2018_hand_data_science/

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vs
(= )
• “Theory-driven models can be wrong. But data-driven models cannot be wrong or
right. Data-driven are not trying to describe an underlying reality.”
David Hand, KDD2018 (Keynote Talk)
http://videolectures.net/kdd2018_hand_data_science/
⾒
( )

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⾒
Universal Approximation Theorem
⾒
( )
Blackbox vs

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⾒
⾒
Universal Approximation Theorem
⾒
( )
Blackbox vs

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Physics-informed ML, Geometric ML, Causal ML
https://doi.org/10.1038/s42254-021-00314-5
×
×
×

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⾒ (NP-hard )
Schrittweiser et al. Mastering Atari, Go, chess and shogi by planning with a learned model.
(“MuZero”, Nature, 2020)
Davies et al. Advancing mathematics by guiding human intuition with AI. (Nature, 2021)
Fawzi et al. Discovering faster matrix multiplication algorithms with reinforcement learning.
(“AlphaTensor”, Nature, 2022)
×
closed /

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3
⾒
.
.
( )
.
( )

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機械学習と機械発見：自然科学融合が誘起するデータ科学の新展開

機械学習と機械発見：自然科学融合が誘起するデータ科学の新展開

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