Three Stats Pitfalls Facing the New Data Scientist with Sean Owen

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1) Data analysis can lead to misleading conclusions if analysts do not account for causation and simply observe correlations in data. Correlation does not necessarily imply causation. 2) When analyzing treatments or interventions, it is important to control for confounding variables but not mediating variables to accurately assess causal relationships. 3) Variables that are actually colliders (common effects of other variables) can introduce spurious correlations if those other common causes are not accounted for. 4) Techniques from causal inference and probabilistic graphical models, like do-calculus, can help data scientists properly reason about and interpret causal effects and the results of interventions based on observational data.

Données & analyses

Three Stats Pitfalls Facing  
the New Data Scientist
Sean Owen

2
Do I Know You?
• Apache Spark committer, PMC 
• “Advanced Analytics with Spark” 
• Recently: Director, Data Science @
Cloudera

3
Correlation is not causation.
But then, what is causation?

4
Which Best-Fit Line Is Best?
lm(speed ~ dist, cars) lm(dist ~ speed, cars)

5
Which Treatment is Better?
Treatment A Treatment B
Small Stones 93% (81/87) 87% (234/270)
Large Stones 73% (192/263) 69% (55/80)
78% (273/350) 83% (289/350)

6
Now, Which Treatment is Better?
Treatment A Treatment B
Low Blood pH 93% (81/87) 87% (234/270)
High Blood pH 73% (192/263) 69% (55/80)
78% (273/350) 83% (289/350)

7
Carburetors and Axle Ratio Uncorrelated
lm(drat ~ carb, mtcars)
r = -0.09

8
… Except in Both Halves of the Data?
lm(drat ~ carb, mtcars[ 
which(mtcars$cyl >= 6),])
lm(drat ~ carb, mtcars[ 
which(mtcars$cyl < 6),])
r = 0.52 r = 0.22

Resolution: Causation
• Humans reason causally
• Data doesn’t contain causal information
• Data correlations consistent with multiple causal models
• Correct inference requires adding causal model
10

11
One Consistent with Causal Knowledge
disti = β0 + β1speedi + ϵi

13
Controlling Confounders is Right
Treatment A Treatment B
Small Stones 93% (81/87) 87% (234/270)
Large Stones 73% (192/263) 69% (55/80)
78% (273/350) 83% (289/350)

15
Controlling Mediators is Wrong
Treatment A Treatment B
Low Blood pH 93% (81/87) 87% (234/270)
High Blood pH 73% (192/263) 69% (55/80)
78% (273/350) 83% (289/350)

17
Colliders Create Correlation
lm(drat ~ carb, mtcars)
r = -0.09

20
do-Calculus
P(Y|X) ≠ P(Y|do(X))
Just because it’s more often raining when you 
walk outside with an umbrella … 
… doesn’t mean that you carrying an umbrella  
makes it more likely to be raining.

22
P(C|do(S)) =
∑
t
P(C|do(S), t)P(t|do(S))
=
∑
t
P(C|do(S), do(t))P(t|do(S))
=
∑
t
P(C|do(S), do(t))P(t|S)
=
∑
t
P(C|do(t))P(t|S)
=
∑
s′
∑
t
P(C|do(t), s′)P(s′|do(t))P(t|S)
=
∑
s′
∑
t
P(C|t, s′)P(s′|do(t))P(t|S)
=
∑
s′
∑
t
P(C|t, s′)P(s′)P(t|S)

Conclusion
• Must bring causal info to data for proper interpretation
• Know common causal pitfalls!
• PGMs help reason about causal effects
• Do-calculus can clarify reasoning about intervention
23

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1. Three Stats Pitfalls Facing   the New Data Scientist Sean Owen

2. 2 Do I Know You? • Apache Spark committer, PMC  • “Advanced Analytics with Spark”  • Recently: Director, Data Science @ Cloudera

3. 3 Correlation is not causation. But then, what is causation?

4. 4 Which Best-Fit Line Is Best? lm(speed ~ dist, cars) lm(dist ~ speed, cars)

5. 5 Which Treatment is Better? Treatment A Treatment B Small Stones 93% (81/87) 87% (234/270) Large Stones 73% (192/263) 69% (55/80) 78% (273/350) 83% (289/350)

6. 6 Now, Which Treatment is Better? Treatment A Treatment B Low Blood pH 93% (81/87) 87% (234/270) High Blood pH 73% (192/263) 69% (55/80) 78% (273/350) 83% (289/350)

7. 7 Carburetors and Axle Ratio Uncorrelated lm(drat ~ carb, mtcars) r = -0.09

8. 8 … Except in Both Halves of the Data? lm(drat ~ carb, mtcars[  which(mtcars$cyl >= 6),]) lm(drat ~ carb, mtcars[  which(mtcars$cyl < 6),]) r = 0.52 r = 0.22

9. 9 3 Answers

10. Resolution: Causation • Humans reason causally • Data doesn’t contain causal information • Data correlations consistent with multiple causal models • Correct inference requires adding causal model 10

11. 11 One Consistent with Causal Knowledge disti = β0 + β1speedi + ϵi

12. 12 DistanceSpeed

13. 13 Controlling Confounders is Right Treatment A Treatment B Small Stones 93% (81/87) 87% (234/270) Large Stones 73% (192/263) 69% (55/80) 78% (273/350) 83% (289/350)

14. 14 OutcomeTreatment Size

15. 15 Controlling Mediators is Wrong Treatment A Treatment B Low Blood pH 93% (81/87) 87% (234/270) High Blood pH 73% (192/263) 69% (55/80) 78% (273/350) 83% (289/350)

16. 16 OutcomeTreatment pH

17. 17 Colliders Create Correlation lm(drat ~ carb, mtcars) r = -0.09

18. 18 CarburetorsAxle Ratio Cylinders

19. 19 Causation and do-Calculus

20. 20 do-Calculus P(Y|X) ≠ P(Y|do(X)) Just because it’s more often raining when you  walk outside with an umbrella …  … doesn’t mean that you carrying an umbrella   makes it more likely to be raining.

21. 21 CancerSmoking Genes? Tar

23. Conclusion • Must bring causal info to data for proper interpretation • Know common causal pitfalls! • PGMs help reason about causal effects • Do-calculus can clarify reasoning about intervention 23

24. Thank You @sean_r_owen

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