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amshar@microsoft.com
1http://www.github.com/amit-sharma/causal-inference-tutorial
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Use these correlations to make a predictive model.
Future Activity ->
f(number of friends, logins in past month)

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Old Algorithm (A) New Algorithm (B)
50/1000 (5%) 54/1000 (5.4%)
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Old Algorithm (A) New Algorithm (B)
10/400 (2.5%) 4/200 (2%)
Old Algorithm (A) New Algorithm (B)
40/600 (6.6%) 50/800 (6.2%)
0
2
4
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Low-activity High-activity
CTR
Is Algorithm A better?
Old algorithm (A) New Algorithm
(B)
CTR for Low-
Activity users
10/400 (2.5%) 4/200 (2%)
CTR for High-
Activity users
40/600 (6.6%) 50/800 (6.2%)
Total CTR 50/1000 (5%) 54/1000 (5.4%)
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Average comment length decreases over time.
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But for each yearly cohort of users, comment length
increases over time.
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27http://plato.stanford.edu/entries/causation-mani/
28http://plato.stanford.edu/entries/causation-counterfactual/
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41Dunning (2002), Rosenzweig-Wolpin (2000)
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Does new Algorithm B increase CTR for recommendations on
Windows Store, compared to old algorithm A?
Does new Algorithm B increase CTR for recommendations on
Windows Store, compared to old algorithm A?
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𝑷𝒓𝒐𝒑𝒆𝒏𝒔𝒊𝒕𝒚 𝑁𝑒𝑤𝐴𝑙𝑔𝑜 𝑈𝑠𝑒𝑟𝑖 = 𝑳𝒐𝒈𝒊𝒔𝒕𝒊𝒄(𝑎 𝑐𝑎𝑡1, 𝑎 𝑐𝑎𝑡2, … 𝑎 𝑐𝑎𝑡𝑛)
Compare CTR between users with the same propensity score.
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Non-FriendsEgo Network
f5
u
f1
f4
f3f2
n5
u
n1
n4
n3n2
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73http://tylervigen.com/spurious-correlations
74
http://www.github.com/amit-sharma/causal-inference-
tutorial
amshar@microsoft.com
75
https://www.github.com/amit-sharma/causal-inference-tutorial
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> nrow(user_app_visits_A)
[1] 1,000,000
> length(unique(user_app_visits_A$user_id))
[1] 10,000
> length(unique(user_app_visits_A$product_id))
[1] 990
> length(unique(user_app_visits_A$category))
[1] 10
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> user_app_visits_B = read.csv("user_app_visits_B.csv")
> naive_observational_estimate <- function(user_visits){
# Naive observational estimate
# Simply the fraction of visits that resulted in a recommendation click-
through.
est =
summarise(user_visits,
naive_estimate=sum(is_rec_visit)/length(is_rec_visit))
return(est)
}
> naive_observational_estimate(user_app_visits_A)
naive_estimate
[1] 0.200768
> naive_observational_estimate(user_app_visits_B)
naive_estimate
[1] 0.226467
85
86
> stratified_by_activity_estimate(user_app_visits_A)
Source: local data frame [4 x 2]
activity_level stratified_estimate
1 1 0.1248852
2 2 0.1750483
3 3 0.2266394
4 4 0.2763522
> stratified_by_activity_estimate(user_app_visits_B)
Source: local data frame [4 x 2]
activity_level stratified_estimate
1 1 0.1253469
2 2 0.1753933
3 3 0.2257211
4 4 0.2749867
87
> stratified_by_category_estimate(user_app_visits_A)
Source: local data frame [10 x 2]
category stratified_estimate
1 1 0.1758294
2 2 0.2276829
3 3 0.2763157
4 4 0.1239860
5 5 0.1767163
… … …
> stratified_by_category_estimate(user_app_visits_B)
Source: local data frame [10 x 2]
category stratified_estimate
1 1 0.2002127
2 2 0.2517528
3 3 0.3021371
4 4 0.1503150
5 5 0.1999519
… … …
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> naive_observational_estimate(user_app_visits_A)
naive_estimate
[1] 0.200768
> ranking_discontinuity_estimate(user_app_visits_A)
discontinuity_estimate
[1] 0.121362
40% of app visits coming from recommendation click-
throughs are not causal.
Could have happened even without the
recommendation system.
93
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95
amshar@microsoft.com

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