Real Negatives Matter: Continuous Training with Real Negatives for Delayed Feedback Modeling

Asymptotically Unbiased Estimation for Delayed Feedback Modeling via Label Correction

“…Distinct from previous methods, current mainstream approaches employ the importance sampling method to estimate the real expectation 𝑤 .𝑟 .𝑡 another observed distribution [5,10,27,28]. Ktena et al [10] assumes that all samples are initially labeled as negative, then duplicate samples with a positive label and ingest them to the training pipeline upon their conversion.…”

“…To address this, ES-DFM [12] introduces an observation window to study the trade-off between waiting for more accurate labels in the window and exploiting fresher training data out of the window. Gu et al [5] Table 2: Main notations used in the paper.…”

“…Importance sampling has been widely studied and applied in many recent tasks, e.g., counterfactual learning [26] and unbiased estimation [5,27]. Typically, previous approaches use importance sampling to estimate the expectation of training loss from the observed distribution and rewrite the ideal CVR loss function as follows:…”

“…where 𝑓 𝜃 is the desired CVR model pursuing unbiased CVR prediction, 𝑝 (x, 𝑦) and 𝑞(x, 𝑦) respectively denote the joint density function of the ground truth and the observed and duplicated distribution, and 𝑤 (x, 𝑦) is the likelihood ratio of the ground truth distribution with respect to the observed and duplicated distribution introduced by importance sampling, chasing for an unbiased 𝑓 * 𝜃 (x). Currently, by assuming or ensuring 𝑝 (x) ≈ 𝑞(x) and carefully designing the sample duplicating mechanisms, all published methods [5,10,27] apply the same derivation of the formulation of 𝑤 (x, 𝑦) that firstly published at [10] as follows:…”

“…For instance, FNC/FNW [10] set 𝑤 𝑜 = 0 and re-sent all positive samples when conversion arrives. ES-DFM [27] only duplicate delay positive samples which previously have been incorrectly labeled as fake negatives; While DEFER [5] reuse all samples with actual label after completing the label attribution to maintain equal feature distribution and to utilize the real negative samples. Moreover, to bridge the distribution bias, importance sampling [1] is adopted to correct the disparity between the ground-truth and the observed but biased distribution.…”