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Large-scale Causal Approaches to Debiasing Post-click Conversion Rate Estimation with Multi-task Learning

Wenhao Zhang, Wentian Bao, Xiao-Yang Liu, Keping Yang, Quan Lin, Hong Wen, Ramin Ramezani

arXiv:1910.09337v2cs.IRcs.LG

TL;DR

Post-click CVR estimation faces selection bias because click-space training differs from exposure-space inference, alongside data sparsity from rare clicks. The paper proposes Multi-IPW and Multi-DR, causal estimators built in a multi-task learning framework. Experiments with billions of data samples show that the methods outperform state-of-the-art CVR predictive models.

  • Problem

    Click-space training data differ systematically from the exposure space used for inference, and rare clicks contribute to CVR data sparsity.

    Source: Problem formulation · p. 2

  • Method

    The paper develops Multi-IPW and Multi-DR as causal CVR estimators within a multi-task learning framework.

    Source: Problem formulation · p. 2

  • Results

    The authors report that their methods outperform state-of-the-art CVR predictive models in experiments with billions of data samples.

    Source: §6 · p. 12

  • Takeaways & Limitations

    The authors conclude that the estimators address industrial CVR estimation in a principled, effective, and efficient way.

    Source: §6 · p. 12

    An unbiased training or testing dataset for CVR is generally unobtainable in real practice, limiting direct unbiasedness evaluation.

    Source: §4.4 · p. 9

Abstract

from arXiv · show

Post-click conversion rate (CVR) estimation is a critical task in e-commerce recommender systems. This task is deemed quite challenging under the industrial setting with two major issues: 1) selection bias caused by user self-selection, and 2) data sparsity due to the rare click events. A successful conversion typically has the following sequential events: "exposure -> click -> conversion". Conventional CVR estimators are trained in the click space, but the inference is done in the entire exposure space. They fail to account for the causes of the missing data and treat them as missing at random. Hence, their estimations are highly likely to deviate from the real values by large. In addition, the data sparsity issue can also handicap many industrial CVR estimators which usually have large parameter spaces. In this paper, we propose two principled, efficient and highly effective CVR estimators for industrial CVR estimation, namely, Multi-IPW and Multi-DR. The proposed models approach the CVR estimation from a causal perspective and account for the causes of missing not at random. In addition, our methods are based on the multi-task learning framework and mitigate the data sparsity issue. Extensive experiments on industrial-level datasets show that our methods outperform the state-of-the-art CVR models.

1 Introduction

Post-click CVR estimation matters in e-commerce, but click-space training and exposure-space inference create selection bias, while rare clicks limit training data. The paper proposes causal multi-task estimators to address both challenges.

1 Introduction

  • The study addresses selection bias in post-click CVR estimation, a widely recognized issue in recommender systems.The introduction illustrates selective exposure with music services that favor genres receiving positive user feedback.Source: §1 · p. 1

Problem formulation

  • Selection bias arises because click-space training data are self-selected and systematically differ from the full exposure space used for inference.Non-clicking does not necessarily mean a user is uninterested in purchasing an item.Source: Problem formulation · p. 2
  • Rare clicks constrain training data: click-through rates are 5.2% in the production dataset and 4% in the public dataset.The paper reports 0.6 billion samples versus 5.3 billion parameters for production, and 4.3 million samples versus 2.6 billion parameters for the public dataset.Source: Problem formulation · p. 2
  • For tractability, the paper assumes the exposure space is the item space of interest, supported by the postulation that most items are exposed at least once.The dataset contains 81.5 million items and 11.5 billion exposures, averaging about 150 exposures per item.Source: Problem formulation · p. 2
  • Multi-IPW and Multi-DR combine causal approaches with multi-task learning to target selection bias and data sparsity together.The authors describe this as the first combination of IPW-based and DR-based methods with multi-task learning.Source: Problem formulation · p. 2
  • The authors report that ESMM is biased and that their methods outperform ESMM and other state-of-the-art causal models in industrial experiments.They also state that the proposed methods are theoretically unbiased.Source: Problem formulation · p. 2

2 Related works

The related-work discussion contrasts the proposed CVR estimators with approaches to selection bias and missing-not-at-random data in recommender systems. It distinguishes them by task, challenges addressed, and model-training strategy.

2 Related works

  • ESMM trains in the exposure space using auxiliary CTR and CTCVR tasks, but the authors argue it is biased.They direct readers to Section 3.2 for their argument.Source: §2 · p. 3
  • IPW methods can remain biased when propensities are inaccurate, while DR methods can retain unbiasedness when their imputation model is accurate.The cited DR approaches were not designed for CVR's data sparsity, and the described joint-learning approach is inefficient in industrial settings.Source: §2 · p. 3
  • Unlike prior methods focused on rating prediction, the paper targets e-commerce CVR and combines multi-task learning with causal approaches to address selection bias and data sparsity.Its deep networks co-train propensity, imputation, and prediction models, rather than training modules separately or alternatively.Source: §2 · p. 3

3 Causal CVR Estimators with multi-task learning

The section defines prediction inaccuracy and unbiasedness for CVR estimation, then uses a counterexample to show that ESMM cannot ensure unbiased estimates.

3.1 Preliminary

  • Prediction inaccuracy P is defined over all user-item pairs using cross-entropy between true conversion labels and predicted scores.The loss is e(r_u,i, r̂_u,i) = −r_u,i log(r̂_u,i) − (1 − r_u,i) log(1 − r̂_u,i).Source: §3.1 · p. 3
  • Naive CVR models train on clicked user-item pairs and average cross-entropy over observed labels; unbiasedness requires expected estimated inaccuracy over O to equal P.Clicks depend on unobserved factors, making the observed data missing not at random.Source: §3.1 · p. 3

3.2 Is ESMM an Unbiased CVR Estimator?

  • ESMM has positive estimation bias in a counterexample, so it cannot ensure unbiased CVR estimation for every exposure space.The counterexample is illustrated in Figure 2.Source: Figure 2 · p. 4, §3.2 · p. 4

3.3 A causal perspective to unbiased CVR estimation

The section frames selection bias as a mismatch between click-space training and exposure-space prediction. It explains that click intervention would remove this mismatch, but the hypothetical intervention data are unavailable in practice.

3.3 A causal perspective to unbiased CVR estimation

  • Training on a hypothetical “do dataset” would align training and inference spaces by forcing clicks on every exposed item, removing confounding by self-selection factors Z.Z can include purchase interest or price discount.Source: §3.3 · p. 4, Figure 3 · p. 5
  • The “do dataset” cannot be obtained in reality, so the challenge is to train on observed MNAR data as if using that intervention-generated dataset.The section points to two estimators for unbiased CVR prediction with MNAR data.Source: §3.3 · p. 4
  • ESMM trains over the exposure space without intervening on clicks, leaving conversion labels MNAR and preventing unbiased estimation when confounder Z remains.The example contrasts a last-entry observed zero without intervention with a true conversion label of one under intervention.Source: §3.3 · pp. 4–5

3.4 Multi-task Learning Module

The multi-task module uses the larger CTR task to share learned features with CVR, addressing data sparsity. Multi-IPW learns propensity scores jointly with CVR and is unbiased when those scores are accurate.

3.4 Multi-task Learning Module

  • CTR training data generally exceeds CVR training data by 1–2 orders of magnitude, and shared representations pass its learned features to CVR.This is the paper's stated mechanism for remedying data sparsity.Source: §3.4 · p. 5
  • Multi-task learning co-trains tasks and can reduce duplicate embedding storage and training time.The paper says Multi-IPW and Multi-DR inherit these potential training efficiencies.Source: §3.4 · p. 5

3.5 Multi-task Inverse Propensity Weighting CVR Estimator

  • Multi-IPW jointly learns propensity scores from the CTR task and CVR from the shared multi-task framework.It uses predicted CTR scores as propensities and defines its loss over exposure-space data.Source: §3.5 · pp. 5–6, Figure 4 · p. 6
  • Multi-IPW is unbiased when its estimated propensity scores accurately match the true propensities.The paper formally derives the estimator's bias under that condition.Source: §3.5 · p. 6
  • Multi-IPW gains better CVR prediction through parameter sharing and reduces training time and parameter storage relative to conventional IPW estimators.The estimator is unbiased when estimated propensity scores are accurate.Source: §3.5 · p. 6

3.6 Multi-task Doubly Robust CVR Estimator

IPW-based models depend on accurate propensity estimates for unbiasedness, a condition the paper describes as too restrictive in practice. Algorithm 1 trains CTR and CVR together on sampled observed user-item pairs.

3.6 Multi-task Doubly Robust CVR Estimator

  • IPW-based models are unbiased only when propensities are accurately estimated, a condition described as too restrictive in practice.The paper notes that prior work introduced doubly robust estimators to address this issue.Source: §3.6 · p. 6

Algorithm 1: Multi-Inverse Propensity Weighting

  • Algorithm 1 samples observed user-item pairs and co-trains CTR and CVR, updating both tasks alongside shared parameters.The algorithm's input includes observed conversion labels and user-item features.Source: Algorithm 1: Multi-Inverse Propensity… · p. 7

end

Multi-DR augments Multi-IPW with an imputation model for prediction error. Its estimator is unbiased when either propensity estimates or prediction-error estimates are accurate.

Multi-task Doubly Robust CVR Estimator

  • Multi-DR augments Multi-IPW with an imputation model that estimates prediction error.The shared embeddings connect the CTR, CVR, and imputation tasks; the CTR task supplies predicted propensity scores.Source: end · p. 7
  • Multi-DR is unbiased when either estimated propensity scores are accurate or estimated prediction errors are accurate.The theorem states these alternatives in terms of zero propensity error or zero prediction-error deviation.Source: end · p. 7

Algorithm 2: Multi-Doubly Robust

Algorithm 2 takes observed conversion labels and user-item features as input, then samples user-item pairs to co-train CTR, CVR, and imputation tasks.

Algorithm 2: Multi-Doubly Robust

4 Experimentation

The experiments compare the proposed estimators with non-causal and causal baselines on public and production data, using prediction metrics and a proxy assessment of unbiasedness. The setup also probes computational efficiency and sensitivity to implementation parameters.

4 Experimentation

  • The study asks whether the proposed methods outperform state-of-the-art CVR estimators, improve industrial efficiency, and remain robust to hyperparameter choices.Experiments use a public dataset and a large-scale Mobile Taobao production dataset.Source: §4 · p. 8

4.1 Datasets

  • Ali-CCP is drawn from Taobao recommender-system traffic logs, while the production dataset comprises three weeks of Mobile Taobao transactions.The production experiment divides data into four subsets and tests on each subset’s final day, as described in the supplied setup passage.Source: §4.1 · p. 8, §4 · p. 8

4.2.1 Non-causal estimators

  • Non-causal baselines include a click-space MLP, click-space oversampling, exposure-space ESMM, and exposure-space naive imputation.Oversampling duplicates positive conversion samples at rate k = 5.Source: §4.2.1 · p. 9

4.2.2 Causal estimators

  • Causal comparisons include Naive IPW, Joint Learning DR, and Heuristic DR, with the latter evaluated across five smoothing rates.The tested η values are 0.0005, 0.001, 0.002, 0.005, and 0.01.Source: §4.2.2 · p. 9

4.3 Metrics

  • AUC and weighted Group AUC (GAUC) measure prediction quality, while the public dataset is assessed with AUC only.The study uses CTCVR-AUC/GAUC to evaluate estimator unbiasedness.Source: §4.3 · p. 9, §4.4 · p. 9

4.4 Unbiased Evaluation

  • Because unbiased CVR evaluation data are generally unobtainable in practice, the study uses CTCVR-AUC/GAUC as its unbiasedness proxy.Random exposure can produce unbiased CTR evaluation data, but users cannot be forced to click randomly to create unbiased CVR evaluation data.Source: §4.4 · p. 9

4.5.1 Ali-CCP experiment

  • On Ali-CCP, embeddings have dimension 18 and multi-task MLPs use a 512 × 256 × 128 × 32 × 2 architecture.The setup uses Adam with learning rate 0.0002 and batch size 1024.Source: §4.5.1 · p. 9, Table 3 · p. 10

4.5.2 Production set experiment

  • Production comparisons use a shared batch size of 10000 and 1024 × 512 × 256 × 128 × 32 × 2 MLPs, with feature-specific embedding dimensions.The setup also applies L2 normalization to Multi-DR’s imputation model with coefficient 0.0001.Source: §4.5.2 · p. 10, Table 2 · p. 10

5 Results and Discussion

Multi-IPW and Multi-DR outperform the comparison models across the reported experiments, with Multi-DR usually ahead of Multi-IPW. The authors also report lower or equivalent training time, economical memory use, and parameter-sensitive performance.

5.1 Model Assessments (Q1)

  • Multi-IPW and Multi-DR are clear winners over other baselines across all reported experiments.In production, both consistently outperform Joint Learning DR; the authors attribute the improvement to multi-task learning’s remedy for data sparsity.Source: §5.1 · p. 10
  • Multi-DR mostly performs better than Multi-IPW, and the paper’s tail-bound result supports this expectation when its imputation model is well-trained.The stated bound condition is 0 ≤ ê ≤ 2e.Source: §5.1 · p. 11
  • Both IPW-based models outperform Base in all experiments, which the authors interpret as evidence that their propensity model is accurate enough in practice.The passage notes that unbiasedness requires accurately estimated propensities.Source: §5.1 · p. 11

5.2 Computational efficiency (Q2)

  • Multi-IPW and Multi-DR require less or equivalent training time than baselines and use memory economically through parameter sharing.Figure 5 compares epoch training hours, embedding-parameter size, and hidden-layer-parameter size.Source: §5.2 · p. 11, Figure 5 · p. 11

5.3 Hyper-parameters in model implementation

  • IPW bound τ clamps propensity values above a threshold to handle high propensity variance; its plausible range is between the minimum and mean propensity.Multi-DR also under-samples unclicked examples at rate λ rather than adding all of them, addressing worsening class imbalance.Source: §5.3 · pp. 11–12

5.4 Empirical study on hyper-Parameter sensitivity (Q3)

  • For Multi-IPW, performance improves as τ% rises within 50%–90%, but CVR AUC drops when the threshold exceeds 95%.The authors reason that a larger bound allows undesired propensity variability.Source: §5.4 · p. 12, Figure 6 · p. 12
  • For Multi-DR, λ = 1.5 gives the best prediction, performance declines when λ > 5, and a small number of unclicked examples can boost prediction.The reported boost occurs for λ ∈ [1.0, 1.5]; the authors link larger sampling rates to worse class imbalance.Source: §5.4 · p. 12, Figure 6 · p. 12

6 Conclusion and future works

The paper concludes that Multi-IPW and Multi-DR address selection bias and data sparsity in industrial CVR estimation. It reports strong, efficient performance on experiments with billions of samples and identifies sequential-pattern debiasing of CTR as a possible extension.

6 Conclusion and future works

  • Experiments with billions of samples show that Multi-IPW and Multi-DR outperform state-of-the-art CVR predictive models while addressing selection bias and data sparsity.The paper describes the approach as principled, highly effective, and efficient.Source: §6 · p. 12
  • The authors suggest generalizing the approach to CTR debiasing by exploiting the sequence item pool → exposure → click.Source: §6 · p. 12
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