[DL輪読会]Theoretical Impediments to Machine Learning With Seven Sparks from the Causal Revolution

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1) The document discusses Judea Pearl's work on theoretical impediments to machine learning and the causal revolution in artificial intelligence. It outlines Pearl's three-level causal hierarchy of association, intervention, and counterfactuals. 2) It explains structural causal models (SCMs) which combine graphical models, structural equations, and counterfactual/interventional logic. SCMs allow specifying assumptions about causal relationships and answering queries about interventions and counterfactuals. 3) SCMs provide a framework for causal inference that addresses limitations of traditional machine learning like dependence on representative data samples and inability to answer interventional queries.

Theoretical Impediments to Machine Learning With
Seven Sparks from the Causal Revolution
Judea Pearl
1

¤ Pearl AI
¤ 2018/1/11 arXiv
¤ Judea Pearl
¤ ”One of the giants in the field of artificial intelligence" by Prof. Richard Korf
¤
¤
¤
¤
¤ DL
¤ +DL
¤
2

3
¤
¤
8
The Three Layer Causal Hierarchy
Level Typical Typical Questions Examples
(Symbol) Activity
1. Association
P(y|x)
Seeing What is?
How would seeing X
change my belief inY ?
What does a symptom tell me
about a disease?
What does a survey tell us
about the election results?
2. Intervention
P(y|do(x), z)
Doing
Intervening
What if?
What if I do X?
What if I take aspirin, will my
headache be cured?
What if we ban cigarettes?
3. Counterfactuals
P(yx|x′
, y′
)
Imagining,
Retrospection
Why?
Was it X that caused Y ?
What if I had acted
diﬀerently?
Was it the aspirin that
stopped my headache?
Would Kennedy be alive had
Oswald not shot him?
What if I had not been smok-
ing the past 2 years?
Figure 1: The Causal Hierarchy. Questions at level i can only be answered if information from level i or
higher is available.
An extremely useful insight unveiled by the logic of causal reasoning is the existence of a sharp

association
¤ 3 1
¤
¤
¤
¤ X Y
¤
¤ 2
9
!(#|%)
x y

intervention
¤
¤
¤
¤
¤
¤
¤
¤
10
!(#|%& ' , ))
X=x Z=z y
do

Counterfactuals
¤ 3
¤
¤
¤
¤
¤
¤
11
!(#$|&'
, #'
)
* &'
+ #'
X x Y=y

¤
¤
¤
¤ Garry King [Morgan+ 15]
“More has been learned about causal inference in the last few decades than the sum
total of everything that had been learned about it in all prior recorded history”
¤ Pearl
The Causal Revolution [Pearl+ 18]
Structural Causal Models SCM
14

SCM
¤ Assumption Query
¤ Estimand Estimate Fit
¤ SCM 7
16
The SCM deploys three parts
1. Graphical models,
2. Structural equations, and
3. Counterfactual and interventional logic
Graphical models serve as a language for representing what we know about the world, counterfactuals help
us to articulate what we want to know, while structural equations serve to tie the two together in a solid
semantics.
ES
ES
F
Assumptions
(Graphical model)
Data Fit Indices
Estimate
(Answer to query)
Query
answering the query)
(Recipe for
Estimand
Inputs Outputs
Figure 2: How the SCM “inference engine” combines data with causal model (or assumptions) to produce
answers to queries of interest.

Assumptions
¤ Assumption
¤
¤
¤
¤
¤
¤ d-
¤
17

¤
¤
¤
¤
¤
¤ 1 Pearl
¤ Do
¤ non-representative samples
21

¤ AI
¤ =
¤ Friston
¤
¤
¤ VAE
¤ Deep Kalman Filter[Krishnan+ 15, 16]
¤
25

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[DL輪読会]Theoretical Impediments to Machine Learning With Seven Sparks from the Causal Revolution

1. Theoretical Impediments to Machine Learning With Seven Sparks from the Causal Revolution Judea Pearl 1

2. ¤ Pearl AI ¤ 2018/1/11 arXiv ¤ Judea Pearl ¤ ”One of the giants in the field of artificial intelligence" by Prof. Richard Korf ¤ ¤ ¤ ¤ ¤ DL ¤ +DL ¤ 2

3. ¤ ¤ AI Pearl 3

4. ≠ ⇒ 1 ¤ ¤ ⇒AI 4

5. AI ¤ ¤ ¤ ¤ 1000 ⇒ 5

6. ¤ ⇒ ¤ What if ? ¤ 6

7. Pearl ¤ ¤ 20 ¤ AI 7

8. 3 ¤ ¤ 8 The Three Layer Causal Hierarchy Level Typical Typical Questions Examples (Symbol) Activity 1. Association P(y|x) Seeing What is? How would seeing X change my belief inY ? What does a symptom tell me about a disease? What does a survey tell us about the election results? 2. Intervention P(y|do(x), z) Doing Intervening What if? What if I do X? What if I take aspirin, will my headache be cured? What if we ban cigarettes? 3. Counterfactuals P(yx|x′ , y′ ) Imagining, Retrospection Why? Was it X that caused Y ? What if I had acted diﬀerently? Was it the aspirin that stopped my headache? Would Kennedy be alive had Oswald not shot him? What if I had not been smok- ing the past 2 years? Figure 1: The Causal Hierarchy. Questions at level i can only be answered if information from level i or higher is available. An extremely useful insight unveiled by the logic of causal reasoning is the existence of a sharp

9. association ¤ 3 1 ¤ ¤ ¤ ¤ X Y ¤ ¤ 2 9 !(#|%) x y

10. intervention ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ 10 !(#|%& ' , )) X=x Z=z y do

11. Counterfactuals ¤ 3 ¤ ¤ ¤ ¤ ¤ ¤ 11 !(#$|&' , #' ) * &' + #' X x Y=y

12. ¤ ¤ 1 ¤ ¤ ⇒ 3 ¤ 1 12

13. ¤ 5 ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ Pearl 13

14. ¤ ¤ ¤ ¤ Garry King [Morgan+ 15] “More has been learned about causal inference in the last few decades than the sum total of everything that had been learned about it in all prior recorded history” ¤ Pearl The Causal Revolution [Pearl+ 18] Structural Causal Models SCM 14

15. ¤ SCM 1. 2. 3. 3 ¤ ¤ ¤ 2 15

16. SCM ¤ Assumption Query ¤ Estimand Estimate Fit ¤ SCM 7 16 The SCM deploys three parts 1. Graphical models, 2. Structural equations, and 3. Counterfactual and interventional logic Graphical models serve as a language for representing what we know about the world, counterfactuals help us to articulate what we want to know, while structural equations serve to tie the two together in a solid semantics. ES ES F Assumptions (Graphical model) Data Fit Indices Estimate (Answer to query) Query answering the query) (Recipe for Estimand Inputs Outputs Figure 2: How the SCM “inference engine” combines data with causal model (or assumptions) to produce answers to queries of interest.

17. Assumptions ¤ Assumption ¤ ¤ ¤ ¤ ¤ ¤ d- ¤ 17

18. Do ¤ 2 ¤ ¤ do 18 x z y

19. ¤ ¤ ¤ ¤ ¤ ¤ 19

20. ¤ ⇒ ¤ ¤ ¤ X Y Z 20 x z y

21. ¤ ¤ ¤ ¤ ¤ ¤ 1 Pearl ¤ Do ¤ non-representative samples 21

22. ¤ ¤ ¤ ¤ 22

23. ¤ D- ⇒ 23

24. ¤ ¤ SCM ¤ ⇒ AI ¤ ¤ ¤ 24

25. ¤ AI ¤ = ¤ Friston ¤ ¤ ¤ VAE ¤ Deep Kalman Filter[Krishnan+ 15, 16] ¤ 25