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DeepI DeepIV: A : A F Flexibl ble A Appr pproa oach for for Co Counte terf rfac actu tual al Pr Predicti tion Greg Lewis * and Matt Taddy Jason Hartford and Kevin Leyton-Brown University of British Columbia Microsoft Research


  1. DeepI DeepIV: A : A F Flexibl ble A Appr pproa oach for for Co Counte terf rfac actu tual al Pr Predicti tion Greg Lewis * and Matt Taddy † Jason Hartford and Kevin Leyton-Brown University of British Columbia Microsoft Research & * NBER / † University of Chicago

  2. I need a model that predicts the effect of price on ticket sales SkyHighAir Jason

  3. Prediction with confounding effects We can raise prices and get more sales! Jason

  4. Prediction with confounding effects " = $ ! Sales Price !

  5. Prediction with confounding effects " = $ !, & Sales Price !

  6. Prediction with confounding effects " = $ !, & Sales Automated pricing engine Price increases prices as the plane fills ! = '(&)

  7. The observational distribution “response” “features / observed confounders” " = $(!, *) * Holidays Sales Price ! = '(*) “policy / treatment”

  8. The interventional distribution “response” “features / observed confounders” -("|do !̂ , *) * Holidays Sales Price Set ! = !̂ “policy / treatment”

  9. Identification of causal effects “response” “features / observed confounders” " = $(!, *) * Holidays Sales If *, ! & " observed, Price -("|do ! , *) is identified. See e.g. [Athey et al. ! = '(*) 2016], [ Shalit et al. 2017 ] “policy / treatment”

  10. Identification of causal effects “response” “features / observed confounders” " = $ !, *, & * Holidays Sales & Conference Not identified without further assumptions Price “latent / unobserved confounders” ! = '(*, &) “policy / treatment”

  11. Identification of causal effects “response” “features / observed confounders” " = $ !, * + & * Additive latent effects Holidays Sales & Conference “instrument” 3 Fuel Price “latent / unobserved confounders” Cost Variable that ! = '(*, 3, &) only affects the response indirectly via its effect on price “policy / treatment”

  12. Simulate a world without latent effects on price Holidays Sales Conference Estimated Fuel Cost Price

  13. Simulate a world without latent effects on price Holidays Sales Conference Estimated Fuel Cost Price

  14. The learning problem These assumptions imply the following identity 1 , 4 " *, 3 = 4 $ !, * *, 3 = ∫ $ !, * 67(!|*, 3) So we can recover $(!, *) solve the implied inversion problem ... B A min ;∈= > " ? − ∫ $ !, * ? 67 ! *, 3 ?CD 1. This holds if 4 & *] = 0 . In general we recover $(!, *) up to a constant wrt ! – see paper for details.

  15. � � ̇ A two-stage solution U T min M∈P > Q R − ∫ M J, K R SG J K, L RCV Stage 2: train network M N O using I J K, L using the Stage 1 : fit G H stochastic gradient descent model of your choice. with monte-carlo integration . We use mixture density 1 networks [Bishop 94] XY Z = −2 Q R − > M ] J ̇ V , K R × J V * ` J K, L ̇ ~G J V … " I J K, L G H 1 At each SGD > b N M ] J T ̇ , K R iteration |J T ̇ | ` J K, L !̇ Sample ̇ ~G J T M N O(J, K)

  16. Causal Validation • In general, out-of-sample validation causal models is challenging / impossible … • But… both our losses depend only on observable quantities and reflect causal loss, so we can simply use standard validation sets .

  17. Evaluation Simulation & Bing Ads Experiments

  18. Simulation Experiments Price Sensitivity Customer features c~d{0, 1, . . , 6} i lets us smoothly vary the correlation Customer between sales and Holidays Conference type price Ticket Ticket Fuel Cost Price Sales

  19. Simulation – low dimensional feature space

  20. Simulation – low dimensional feature space

  21. Simulation – low dimensional feature space

  22. Simulation – low dimensional feature space

  23. Simulation – low dimensional feature space

  24. Simulation – low dimensional feature space

  25. Simulation – low dimensional feature space [Darolles et al. 2011]

  26. Simulation – low dimensional feature space [Darolles et al. 2011]

  27. Implications and future directions • We recover heterogeneous treatment effects in settings with unobserved confounding effects for both discrete and continuous variables… and SGD scales naturally to very large datasets. • Can leverage the flexibility of deep nets for rich data types. E.g. raw text in our Bing ads application experiments / images in simulation. Future work: • Methods for uncertainty estimates over predictions. Code and paper available at http://bit.ly/DeepIV Poster #127

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