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Predicting winning price in real time bidding

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Introduction of the online advertising, the real time bidding and the winning price.

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Predicting winning price in real time bidding

  1. 1. Predicting Winning Price in Real Time Bidding Wush 2019/5/10
  2. 2. Outlines Introduction Problem Definition Related Works Winning Price Models · · · · 2/61
  3. 3. Introduction
  4. 4. Online Advertising 4/61
  5. 5. Ad Exchange 5/61
  6. 6. Trading the Impressions Impression: the opportunity of displaying ad The sellers provide: The buyers provide: · · Information of the publisher Identity of the audience - - · The bidding price which is hopefully based on the estimation of the value - 6/61
  7. 7. Why Exchanging Ads? Higher profit for publishers. ## Wider reach for advertisers. ## 7/61
  8. 8. Common Rule of the Bidding 8/61
  9. 9. Problem Definition
  10. 10. Winning Price (a.k.a. Market Price, Bid Landscaping in the literature) The winning price is the lowest price to win. The winning price of a buyer is the highest bidding price from its competitors. · · 10/61
  11. 11. Winning Price The winning price of the purple gentleman is 200$. The winning price of others is 250$. · · 11/61
  12. 12. Problem Definition We are one specific buyer. Predicting the winning price of future auctions given the historical winning/losing bid information the buyer observed · · 12/61
  13. 13. The Importance of the Winning Price The winning price represents: The winning price helps the bidding strategy, for example it is the input of the proposed bidding strategy by Zhang et al. [2]. In our experiments, the winning price improves the estimation of the Click- Through-Rate(CTR) and the Conversion Rate(CVR). · The cost of the impression after winning. The value of the impression to the competitor if they follow the truthful bidding rule. [1] - - · · 13/61
  14. 14. Challenge of Predicting the Winning Price The winning price is not always available as a buyer. It is observed after winning. · 14/61
  15. 15. Example In practice, the ad exchange server only notice the winner. The purple gentleman knows his winning price is 200$ because he is asked to pay. The winning price of others is unknown. · · · 15/61
  16. 16. Related Works
  17. 17. Ghosh et al. WWW 2009 [3] Proposed adaptive bidding algorithms under a fixed budget with user- specified constraints. Assume the winning price was drawn i.i.d. from a pdf specific . · · 17/61
  18. 18. Cue et al. KDD 2011 [4] Study the prediction of the winning price on the seller side. Model the winning price with the mixture-of-log-normal distribution on various targeting attributes. · · 18/61
  19. 19. Zhang et al. 2014 [2] Propose a framework to optimize the bidding strategy for DSPs. The cost, usually the same as the winning price, is a required input. Assume the cost is the bidding price. · · · 19/61
  20. 20. Wu et al. 2015 [5] Study the predicting winning price on the buyer side. Propose the technique of offline simulation to study the winning price problem. Study the linear regression model, censored regression model and mixture model. · · · 20/61
  21. 21. Wang et al. PKDD 2016 [6] Use K-L distance and tree based clustering algorithm to split the data into clusters For each clusters, the Kaplan–Meier estimator [7] is used to construct the winning price model. · · 21/61
  22. 22. Zhu et al. ICBD 2017 [8] Use gamma based regression model.· 22/61
  23. 23. Wu et al. KDD 2018 [9] Propose generalized winning price model to combine the censored learning with deep learning structures and distributions. · 23/61
  24. 24. Lee et al. AAAI 2018 [10] Deep neural network model which predicts the probability of each bidding price from minimum price to the maximum price. · 24/61
  25. 25. Models Parametric Models Non-parametric Models · · Continuous Model Discrete Model - - 25/61
  26. 26. Parametric Models where the CDF is and the PDF is . The loss of observed data is The loss of censored data is: · ∼y w Px Fx fx · log ( ( ))fx y w · if if - log( (b))Fx b > y w - log(1 − (b))Fx b < y w 26/61
  27. 27. Non-parametric Continuous Model Kaplan-Meier Estimator· P( > b) = ( 1 − ) yw ∏ i<b di ni : number of observed instances whose winning price equal to : number of instances whose winning price is greater than or equal to The above formula only involves and assumes i.i.d. is used to do clustering to make the i.i.d. assumption more realistic. · di i · ni i · y w · x 27/61
  28. 28. Non-parametric Discrete Model Suppose is the label space. Directly model the winning price as problem of multiclass classification. Censored data is reduced to binary classification problem. · ∈ {0, 1, 2, . . . , L}y w · · 28/61
  29. 29. Experiments
  30. 30. Dataset iPinYou YOYI · · 30/61
  31. 31. Parametric Models Structure Distribution Structure v.s. Distribution· linear wide, the wide part of the wide_and_deep. cross, the cross part of the cross_and_deep. deep, thedeeppart of bothwide_and_deepandcross_and_deep`. wide_and_deep, the Wide & Deep model proposed by Cheng et al. [11]. cross_and_deep, the Deep & Cross model proposed by Wang et al. [12]. · · · · · · normal lognormal gumbel · · · 31/61
  32. 32. Wide The model is the same as linear. The features are cross product transformed before training. · · 32/61
  33. 33. Example of Cross Product Transform If the feature is a:1, b:2, c:3, and d:4 New features are generated as: ab:2, ac:3, ad:4, bc:6, bd:8, cd:12 · · 33/61
  34. 34. Cross Generalize the wide structure. A -layers network The first layer is the input, denoted as . The following layers are defined recursively: · · k · u0 · = + +ul+1 u0 u T l wl cl ul 34/61
  35. 35. Deep A embedding layer followed by dense neuron network.· 35/61
  36. 36. Embedding Layer A -th dimensional embedding layer of input is a matrix . If the -th entry of is denoted as and non-zero, then the -th column of the matrix , denoted as , is extracted and multiplied by . Concatenate all extracted vectors and feed it into the following deep neuron network. · k ∈xi ℝ p W ∈ ℝ k×p · j xi xi,j j W Wj xi,j · 36/61
  37. 37. Wide and Deep Suppose the last layer of the deep is . Suppose the input layer of the wide is . Concatenate and as the last layer of the wide_and_deep. · Ldeep · Lwide · Ldeep Lwide 37/61
  38. 38. Cross and Deep cross_and_deep combines deep and cross similarly as wide_and_deep did.· 38/61
  39. 39. Results 39/61
  40. 40. Comparing Link Structures on Won Data iPinYou Season 2 structure won_lll won_mse won_mae cross -4.458 435.889 13.590 cross_and_deep -4.433 414.747 13.215 deep -4.431 412.864 13.134 linear -4.539 512.625 15.928 wide -4.472 448.596 14.219 wide_and_deep -4.431 413.334 13.062 40/61
  41. 41. Comparing Link Structures on Won Data iPinYou Season 3 structure won_lll won_mse won_mae cross -4.772 816.968 21.250 cross_and_deep -4.754 787.671 20.569 deep -4.756 790.303 20.388 linear -4.834 924.407 23.641 wide -4.782 833.122 21.757 wide_and_deep -4.753 786.513 20.448 41/61
  42. 42. Remarks The wide and wide_and_deep outperforms on won data. The difference between the linear and deep learning structures is significant. · · 42/61
  43. 43. Comparing Link Structures on Lost Data iPinYou Season 2 structure lost_lll lost_mse lost_mae cross -19.850 14058.296 105.764 cross_and_deep -20.588 13989.828 105.309 deep -20.561 13696.278 103.350 linear -15.974 18460.761 127.935 wide -17.814 17260.354 122.508 wide_and_deep -20.652 13907.566 104.641 43/61
  44. 44. Comparing Link Structures on Lost Data iPinYou Season 3 structure lost_lll lost_mse lost_mae cross -15.143 17969.929 125.961 cross_and_deep -15.372 17282.075 122.987 deep -13.534 23347.424 146.844 linear -13.918 22594.970 144.408 wide -14.680 21592.311 140.879 wide_and_deep -15.300 16898.019 121.129 44/61
  45. 45. Remarks The wide_and_deep is generally better. The peroformance is worse compared to the result on won data. The log likelihood and the MSE are not consistent. · · · 45/61
  46. 46. Distributions We study normal, log normal and gumbel distribution.· Cue et al. [4] modeled the winning price with log normal distribution. The definition of the gumbel distribution is closed to the true winning price model. - - 46/61
  47. 47. Gumbel Distribution Let be a sequence of i.i.d. distributed random variable, and let . will converges to gumbel distribution as and the tails of are exponentially decay. is similar to the definition of the winning price. · , , . . . ,X1 X2 Xn = max ( , , . . . , )Mn X1 X2 Xn · Mn n → ∞ Xi · Mn 47/61
  48. 48. Gumbel Distribution The gumbel distribution has two parameters: the location parameter and the shape parameter . If , then · μ σ · X ∼ (x|μ, σ)FGumbel where is the Euler-Mascheroni constant. . - E(X) = μ + γσ γ ≈ 0.5772 - Var(X) = π 2 6 σ 2 48/61
  49. 49. Gumbel Distribution 49/61
  50. 50. Comparing Distributions on Won Data iPinYou Season 2 loss won_lll won_mse won_mae gumbel -4.322 468.823 14.601 lognormal -4.538 458.067 12.918 normal -4.431 412.864 13.134 50/61
  51. 51. Comparing Distributions on Won Data iPinYou Season 3 loss won_lll won_mse won_mae gumbel -4.654 843.855 21.561 lognormal -4.648 848.830 19.996 normal -4.756 790.303 20.388 51/61
  52. 52. Comparing Distributions on Lost Data iPinYou Season 2 loss lost_lll lost_mse lost_mae gumbel -9.581 14231.215 108.672 lognormal -7.909 13824.231 111.678 normal -20.561 13696.278 103.350 52/61
  53. 53. Comparing Distributions on Lost Data iPinYou Season 3 loss lost_lll lost_mse lost_mae gumbel -9.262 23474.736 153.059 lognormal -7.742 21750.399 160.935 normal -13.534 23347.424 146.844 53/61
  54. 54. Remarks Normal and log Normal are better than gumbel distribution.· 54/61
  55. 55. Overall Comparison on Won Data (iPinYou Season 2) structure loss won_lll won_mse won_mae cross gumbel -4.343 491.622 15.011 cross lognormal -4.563 479.010 13.708 cross normal -4.458 435.889 13.590 cross_and_deep gumbel -4.327 463.923 14.462 cross_and_deep lognormal -4.539 469.396 12.966 cross_and_deep normal -4.433 414.747 13.215 deep gumbel -4.322 468.823 14.601 deep lognormal -4.538 458.067 12.918 deep normal -4.431 412.864 13.134 linear gumbel -4.435 545.822 16.597 linear lognormal -4.637 550.276 15.943 linear normal -4.539 512.625 15.928 wide gumbel -4.365 492.236 15.346 wide lognormal -4.575 490.376 14.194 wide normal -4.472 448.596 14.219 wide_and_deep gumbel -4.322 464.398 14.392 wide_and_deep lognormal -4.543 474.609 13.161 wide_and_deep normal -4.431 413.334 13.062 55/61
  56. 56. Overall Comparison on Won Data (iPinYou Season 3) structure loss won_lll won_mse won_mae cross gumbel -4.666 867.277 21.883 cross lognormal -4.669 893.975 20.816 cross normal -4.772 816.968 21.250 cross_and_deep gumbel -4.653 846.974 21.540 cross_and_deep lognormal -4.650 892.055 20.067 cross_and_deep normal -4.754 787.671 20.569 deep gumbel -4.654 843.855 21.561 deep lognormal -4.648 848.830 19.996 deep normal -4.756 790.303 20.388 linear gumbel -4.724 960.077 23.964 linear lognormal -4.720 950.949 22.628 linear normal -4.834 924.407 23.641 wide gumbel -4.676 880.143 22.557 wide lognormal -4.668 919.953 21.048 wide normal -4.782 833.122 21.757 wide_and_deep gumbel -4.657 842.247 21.719 wide_and_deep lognormal -4.654 918.087 20.500 wide_and_deep normal -4.753 786.513 20.448 56/61
  57. 57. Overall Comparison on Lost Data (iPinYou Season 2) structure loss lost_lll lost_mse lost_mae cross gumbel -7.290 18704.716 113.935 cross lognormal -7.708 13114.019 108.035 cross normal -19.850 14058.296 105.764 cross_and_deep gumbel -6.129 7866.812 87.542 cross_and_deep lognormal -7.792 13813.948 111.713 cross_and_deep normal -20.588 13989.828 105.309 deep gumbel -9.581 14231.215 108.672 deep lognormal -7.909 13824.231 111.678 deep normal -20.561 13696.278 103.350 linear gumbel -9.461 19114.244 135.220 linear lognormal -7.840 17860.179 136.949 linear normal -15.974 18460.761 127.935 wide gumbel -9.926 17912.905 129.369 wide lognormal -7.894 14205.306 114.369 wide normal -17.814 17260.354 122.508 wide_and_deep gumbel -9.541 14311.347 108.995 wide_and_deep lognormal -7.863 13458.078 109.584 wide_and_deep normal -20.652 13907.566 104.641 57/61
  58. 58. Overall Comparison on Lost Data (iPinYou Season 3) structure loss lost_lll lost_mse lost_mae cross gumbel -9.420 18821.443 134.273 cross lognormal -7.658 16598.557 134.770 cross normal -15.143 17969.929 125.961 cross_and_deep gumbel -9.441 18570.968 133.435 cross_and_deep lognormal -7.575 16075.654 133.584 cross_and_deep normal -15.372 17282.075 122.987 deep gumbel -9.262 23474.736 153.059 deep lognormal -7.742 21750.399 160.935 deep normal -13.534 23347.424 146.844 linear gumbel -9.424 22536.705 149.660 linear lognormal -7.753 18996.485 146.948 linear normal -13.918 22594.970 144.408 wide gumbel -9.594 21302.872 144.834 wide lognormal -7.711 19227.174 149.027 wide normal -14.680 21592.311 140.879 wide_and_deep gumbel -9.518 18694.377 133.615 wide_and_deep lognormal -7.612 16108.994 133.714 wide_and_deep normal -15.300 16898.019 121.129 58/61
  59. 59. Remarks The performance on the lost data is still much worse than the performance on the won data. The non-linear link structure improves the performance. We do not know the best distributions and the best combination of the distribution and link structure. · · · 59/61
  60. 60. Insights Overfitting is always an important problem No known distribution performs well. Our work will base on non-parametric discrete models. Censored part decreases “bias” but increases “variance”. · · · 60/61
  61. 61. Reference [1] L. M. Ausubel and P. Milgrom, “The lovely but lonely vickrey auction,” in Combinatorial auctions, chapter 1, 2006. [2] W. Zhang, S. Yuan, and J. Wang, “Optimal real-time bidding for display advertising,” in Proceedings of the 20th acm sigkdd international conference on knowledge discovery and data mining, 2014, pp. 1077–1086. [3] A. Ghosh, B. I. P. Rubinstein, S. Vassilvitskii, and M. Zinkevich, “Adaptive bidding for display advertising,” in Proceedings of the 18th international conference on world wide web, 2009, pp. 251–260. [4] Y. Cui, R. Zhang, W. Li, and J. Mao, “Bid landscape forecasting in online ad exchange marketplace,” in Proceedings of the 17th acm sigkdd international conference on knowledge discovery and data mining, 2011, pp. 265–273. [5] W. C.-H. Wu, M.-Y. Yeh, and M.-S. Chen, “Predicting winning price in real time bidding with censored data,” in Proceedings of the 21st acm sigkdd international conference on knowledge discovery and data mining, 2015, pp. 1305–1314. [6] Y. Wang, K. Ren, W. Zhang, J. Wang, and Y. Yu, “Functional bid landscape forecasting for display advertising.” in ECML/pkdd (1), 2016, vol. 9851, pp. 115–131. [7] E. L. Kaplan and P. Meier, “Nonparametric estimation from incomplete observations,” Journal of the American Statistical Association, vol. 53, no. 282, pp. 457– 481, 1958. [8] W. Y. Zhu, W. Y. Shih, Y. H. Lee, W. C. Peng, and J. L. Huang, “A gamma-based regression for winning price estimation in real-time bidding advertising,” in 2017 ieee international conference on big data (big data), 2017, pp. 1610–1619. [9] W. Wu, M.-Y. Yeh, and M.-S. Chen, “Deep censored learning of the winning price in the real time bidding,” in Proceedings of the 24th acm sigkdd international conference on knowledge discovery & data mining, 2018, pp. 2526–2535. [10] C. Lee, W. R. Zame, J. Yoon, and M. van der Schaar, “DeepHit: A deep learning approach to survival analysis with competing risks,” in Proceedings of the thirty- second AAAI conference on artificial intelligence, (aaai-18), the 30th innovative applications of artificial intelligence (iaai-18), and the 8th AAAI symposium on educational advances in artificial intelligence (eaai-18), new orleans, louisiana, usa, february 2-7, 2018, 2018, pp. 2314–2321. [11] H.-T. Cheng et al., “Wide & deep learning for recommender systems,” in Proceedings of the 1st workshop on deep learning for recommender systems, 2016, pp. 7–10. [12] R. Wang, B. Fu, G. Fu, and M. Wang, “Deep & cross network for ad click predictions,” in Proceedings of the adkdd’17, 2017, pp. 12:1–12:7. 61/61

Introduction of the online advertising, the real time bidding and the winning price.

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