TranSUN: A Preemptive Paradigm to Eradicate Retransformation Bias Intrinsically from Regression Models in Recommender Systems
Authors: Jiahao Yu
Haozhuang Liu
Yeqiu Yang
Lu Chen
Wu Jian
Yuning Jiang
Bo Zheng
Venue: NeurIPS 2025 poster ()
Keywords: Recommender Systems
Regression Models in Recommender Systems
Primary area: applications
TL;DR: Novel paradigm and model family to address retransformation bias  in regression models in recommender systems

Abstract: Regression models are crucial in recommender systems. However, retransformation bias problem has been conspicuously neglected within the community. While many works in other fields have devised effective bias correction methods, all of them are post-hoc cures externally to the model, facing practical challenges when applied to real-world recommender systems. Hence, we propose a preemptive paradigm to eradicate the bias intrinsically from the models via minor model refinement. Specifically, a novel TranSUN method is proposed with a joint bias learning manner to offer theoretically guaranteed unbiasedness under empirical superior convergence. It is further generalized into a novel generic regression model family, termed Generalized TranSUN (GTS), which not only offers more theoretical insights but also serves as a generic framework for flexibly developing various bias-free models. Comprehensive experimental results demonstrate the superiority of our methods across data from various domains, which have been successfully deployed in two real-world industrial recommendation scenarios, i.e. product and short video recommendation scenarios in Guess What You Like business domain in the homepage of Taobao App (a leading e-commerce platform with DAU > 300M), to serve the major online traffic.

TranSUN: A Preemptive Paradigm to Eradicate Retransformation Bias Intrinsically from Regression Models in Recommender Systems
Jiahao Yu'!, Haozhuang Liu', Yeqiu Yang", Lu Chen, Jian Wu, Yuning Jiang, Bo Zheng Taobao & Tmall Group of Alibaba, Beijing, China
www.gyeiiuyyy.ccnyyooo (yujiahao sitiiaaaoyyh..iuhhaooe jihhoouuaa....
joshuawu,
@alibaba-inc.com
Abstract
Regression models crucial in recommender systems. However, retransformation bias problem has been conspicuously neglected within the community. While many works in other fields have devised effective bias correction methods, all of them are post-hoc cures externally to the model, facing practical challenges when applied real-world recommender systems. Hence, we propose preemptive paradigm to eradicate the bias intrinsically from the models via minor model refinement. Specifically, a novel TranSUN method is proposed with joint bias learning manner to offer theoretically guaranteed unbiasedness under empirical superior convergence. It is further generalized into novel generic regression model family, termed Generalized TranSUN (GTS), which not only offers more theoretical insights but also serves as generic framework for flexibly developing various bias-free models. Comprehensive experimental results demonstrate the superiority of our methods across data from various domains, which have been successfully deployed in two real-world industrial recommendation scenarios, i.e. product and short video recommendation scenarios in Guess What You Like business domain in the homepage of Taobao App (a leading e-commerce platform with DAU > 300M), to serve the major online traffic.
Introduction
Regression models play pivotal role in recommender systems, which have been widely applied to prediction tasks for targets including user engagement duration [38, 9, 23, 22], transaction amount [15, 42, 44], lifetime value [26, 41, 40, 21, 24], etc. Mean squared error (MSE) loss a predominant choice for loss functions of regression models, which adopts for target and features x an apriori assumption y|ı ~ (x; 0), o²), where (s(xx; 0), o²) is a Gaussian distribution with f( 0) as mean and o² as variance and (x; 0) is o-paaraeterrzed predictor aiming to learn Ey-P((()s) [y]- However, the real target distribution frequently violates the Gaussian assumption in recommendation scenarios due to the high skewed characteristics of the target data [7, 41, 40], which critically impedes the model convergence. This problem motivates prevalent adoption various transformations T for target y in the MSE-based regression models, abbr. transformed MSE, which facilitates the conformity between the transformed distribution P(T(Y) (z)) and the hypothetical distribution (x; f), o²), thereby improving the performance of model convergence [32, 31].
Though effective, leads to the retransformation bias problem [2. 31, 37], i.e. the estimate for [y))(( [y] is biased when the prediction f(x; 0) of the transformed MSE model is back-
'These authors contributed equally to this research. Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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transformed to the original space, as
(f(;;))) & Ey-P(Y)))
(I)
where T-1 is the inverse function of T. This critical issue has been conspicuously neglected within the community of recommender systems. Fortunately, there are still many effective works in other fields specifically studying the bias problem, all of which resort the statistics of the model residuals to design post-processing bias correction mechanisms exactly after the model has been trained [12, 13, 33, 31,
Oue
14]. Despite the progress, all the prior works are post- hoc approaches designed and applied externally to the model, which face practical challenges when applied to the real-world recommender systems (detailed Ap- pendix C). Therefore, we challenge the prior paradigm by asking: Can we eradicate the retransformation bias intrinsically from the model in preemptive manner?
000
Figure 1: Illustration of biasedness and con- vergence of MSE, LogMSE, and our Tran- SUN (T is logarithmic) during the train- ing on the Indus dataset, where PGR de- notes the ratio of the prediction mean to the ground truth mean in batch and the loss value is normalized by the maximum value. As illustrated, MSE model has diffi- culty converging, while LogMSE model is significantly biased (i.e. PGR < 1.0). Differ- ently, our method simultaneously maintains prediction unbiasedness (i.e. PGR is near 1 1.0) and superior convergence.
To answer this, this paper proposes novel preemp- tive paradigm to eradicate bias from the model exactly during the training phase via minor model refinement. Specifically, we propose the novel TranSUN method to empower the transformed MSE model with intrinsic unbiasedness via introducing jointly-learned auxiliary model branch for explicit bias modeling. Our method not only achieves theoretically guaranteed unbiased- ness but also exhibits superior empirical convergence, as shown in Fig. 1. Interestingly, we point out that not all explicit bias modeling schemes bring theoretically guaranteed unbiasedness, and we further generalize TranSUN into a novel generic regression model family, termed Generalized TranSUN (GTS), shed light
the underlying mechanism to intrinsically maintain model's unbiasedness. Essentially, GTS estab- lishes the intrinsic unbiasedness through exploiting target transformation with conditional linearity based on particular point estimates [20] of T(y) [z. exhibiting a more general model assumption com- pared to the vanilla MSE model. With this generic framework, not only various fras-free regression models can be directly devised to cope with varying data scenarios, but also any given regression model can be flexibly debiased in plug-and-play manner even if the given model does not utilize any target transformation.
The major contributions can be summarized as follows.
We propose a novel preemptive paradigm to eradicate retransformation bias intrinsically from regression models to challenge the conventional ones, which is also the first work in the recommender system community to address the long-neglected bias problem.
We propose the novel TranSUN, theoretically grounded, empirical convergence- frienddl. and transformation-agnosti methodology, to endow the transformed MSE model with intrinsic unbiasedness exactly during the training phase.
We further propose a novel regression model family, termed Generalized TranSUN (GTS), offer more theoretical insights, which also provides a generic framework for flexibly developing various bias-free regression models. Notably, our TranSUN and GTS have been validated to be directly applicable other fields beyond the recommender system domain.
Extensive experiments on synthetic and real-world data validate the superiority and broad applicability of our methods. Now, TranSUN has been deployed in two core recommendation scenarios, i.e. product and short video recommendation, in Guess What You Like domain in the homepage of Taobao App (a leading e-commerce platform with DAU > 300M) to serve the major online traffic.
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2 Related works
Regression models recommender systems mainly fall into two categories, i.e. value regression and classification-bent based regression, and our method belongs to the former. Value regression defines target as a continuous random variable and directly predicts target value using the expectation of the hypothetical distribution [22, 7, 48, 41, 42, 44], e.g. Gaussian distribution adopted by the MSE-based model family [42, 44, 43], ZILN distribution [40, 41J. By contrast, classification-base regression defines target as a discrete random variable via dividing it into multiple bins [45, 46, 9, 47], which mainly introduces either hierarchical routing [23, 21, 24, 39] ordinal dependencies [23, 38] to boost models. Despite the progress, all the prior works neglect the study of model biasedness problems (e.g. retransformation bias problem), which probably lead to the systematic errors in the model predictions (as shown in Eq. (3)), e.g. systematic underestimation of duration models in vidco recommender systems. Differently, our paper specifically addresses this critical biasedness problem.
Retransformation bias was initially identified in [2], with several works deriving theoretical correction terms by assuming the transformed distribution [13, 3, 8, 31J. Subsequent studies advanced correction frameworks free from distributional assumptions [12, 35, 5, 37, 27], achieving notable success across various fields [11, 19, 18, 30, 25, 1, 14, 34, 36, 33, 37J. Nonetheless, these approaches are still post-hoe remedies out of the model, bringing practical challenges when applied to industrial recommender systems. Differently, we preemptively address the bias via intrinsic model refinement.
Conditional transformation models (CTM) learns a parametric transformation introducing interaction between target and input to transform them into variables of assumed distribu- tions [16, 28, 4]. CLTM is further restricted to using affine transformation for enhanced interpretabil- ity [29]. whose model assumption is a(z) + hY())) 2) [(x) ~ NN0, 1) with Y, denoting y/æ and h-(-) being parameter-free. Though CLTM and our GTS are superficially similar, they have one key differences, i.e. different dependencies in model assumptions, where the slope 3(x) in CLTM's only related to x, while ours (Eq. (11)) is related to both x and y. In addition, regarding model classes and motivations, CLTM belongs transformation models [17] for interval estimation, while GTS is a value regression model for unbiased point estimation.
3 Method
3.1
Preliminary
Given a training set D (Zr,))((<,)) ~ P(X, Y)}, where x denotes the input features and y denotes the continuous target label, the goal of the regression task is to make the model prediction fz; 0) and the ground truth y as close as possible, where is the parameter of the model f. In the recommender system community, transformed MSE model is commonly adopted to boost the model convergence performance on high-skewed data, which is formulated as
C MSE
B(EN))D [s(z; ((w)))
where T is a customized bijective mapping. However, since minimizing Eq. (2) makes fa; 0) be an estimate of Ey-P(Y\=) [[y)] (derived Appendix B. directly back-transforming f(x; 0) leads to the retransformation bias problem, as shown in Eq. (1). Taking a common example in the industrial community, assuming the inverse transformation T is convex, e.g. T(y) is log(y + 1) or vy. then the retransformation bias will result in the systematic underestimation of model prediction xr as
ū| = (J = TT [T())) S Eey-P(Yl))
T (T())) PP PY()))
where < obtained by Jensen's inequality and it reversed when T-1 concave.
3.2 TranSUN: joint bias learning
To intrinsically eradicate the retransformation bias, we propose TranSUN, which introduces an auxiliary branch 2(2; 0z) to the transformed MSE model to explicitly learn the bias. Specifically,
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we employ a multiplicative bias modeling scheme. i.e. supervising 2(2; to learn the ratio of the ground truth y to the biased prediction (f 0)): hence the bias learning loss is formulated as
T sun
[ (2 stop_ grad [T- 0))
(4)
where stop_grad is applied to prevent the gradients of C from passing 0, |æ]| denotes the absolute value of z, and c is a positive hyperparameter for avoiding division by zero. The reason for adopting this scheme is that the target ratio has intuitively small variance, empirically making the loss much smoother (as shown in Fig. 3a and discussed in Appendix A.2). During training, our model jointly learns the bias modeling task and the main regression task achieve preemptive debiasing, thus the total loss is formulated as
TranSUN = MIE + 4
(5)
In the testing phase, the model prediction 8|22 is formulated as
أ| 2(;; 02) (IT- (f(=;)))++))
(6)
Theoretical analysis of unbiasedness. To illustrate the inherent unbiasedness of our method, we prove the prediction a| to be an estimate of ((yp(()>)) [y] as follows (see Appendix B.2 for details). Owing to the stop_grad operation, the optimization of the total loss LT TranSUN can be decomposed into two independent parts,
min CT TransUN + min MISE + min 22 8.0,
0,
In the second part, the prediction ÿ is derived as the estimate of (Y) (x) [y] via
min CT + Yx P(X): E (2(1;02) + +) Eyy-P(Y 9 (Y) 19]-
0.
T (f(z; 0)) +
(8)
#=;00) (IT
Key discussion. According to Eq. (8), propose an interesting argument: not all bias learning schemes provide theoretically guaranteed unbiasedness. As an example, supposing we turn the learn- ing target of 2(2; 0z) in Eq. (4) to the ratio of biased prediction to ground truth, i.e. T- (z; 0))/u. then the model prediction is derived as an estimate of 1/Ey>P(YYs>) [ (derived in Appendix B.3), which is a biased estimate bringing model underestimation according to Eq. (3). More empirical results are shown in Table 5. Therefore, in the next section, we point out that it is conditional linearity as the essential mechanism for the unbiasedness of TranSUN, rather than the explicit bias learning.
3.3 Generalized TranSUN (GTS)
In this section, we generalize TranSUN to a novel generic regression model family, termed Gener- alized TranSUN (GTS). to provide more insights into the intrinsic unbiasedness mechanism of our method. The total loss function of GTS is formulated as
[ (2(2: 0.) y. stop_ (f ())1))
Lers CH, x. T(y): 0g)
E ((
(9)
where H. is a known apriori distribution parameterized by x and 0g. f(r; 0g) is the expectation of the hypothesized distribution H. (x, 02), and is parameter-frre function with x(-) > 0.
Specifically, the first loss term Cx,, is termed conditional point loss, which supervises f(x; 0g) to specifically learn a conditional point estimate Qy-P(Y (x) [T(y)] (e.g. arithmetic mean, median, mode) via customizing the apriori conditional probability assumption of T ja Hz(,, 0g), with
fzz fg)) = ET())~H,(a,,) [T()] = (TG)))(((M))))) [T())] [T())
Qy-P(r)a) [T()]]- (10)
The second loss term in Eq. (9) is termed linear transformation loss which much resembles linear- transformed MSE, whereas the key difference that our slope x (f((x;; 0,)) is dynamically generated by the learned conditional point fz; Additionally, due to the stop_grat operation, the slope xs (f(1;; 02)) is actually completely determined by LH,, In the testing phase, the prediction of GTS is o/e = [x;; 0z)/k: 1//a(a (a;; (.)), which can also proved unbiased by following the derivation process in Eq. (7, 8) (also derived in Appendix B.4).

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642
60
60
340 901-0
G
RS- BC
18)--B (e)
(0
( 5M5M-M
8M)
Figure 2: Density and statistics of the sampled (Y from the eight pre-defined H(Y).
Model assumption. Given any sample x, GTS essentially exploits customized z-conditioned point (abbr: Q) to generate Q-conditioned slope k for linear transformation of target y. Hence, the model assumption of GTS is formulated
(ar; + Yz Btw.n//xx///PPAA K(Qg~P(Y)e) (TV)) o/(,,
(11)
where Y, (w/rr and N denotes Gaussian distribution. As shown in Eq. (11), the slope is conditioned on P(Y(z), making GTS akin to a intervals are determined by the condition Accordingly, GTS can be viewed as a conditional linear- transformed MSE, the unbiasedness of which is naturally maintained since Amear-transforme MSE is unbiased itself. Notably the violation of model assumptions will not invalidate the model's theoretical unbiasedness, which only affects the model performance (e.g. convergence). Furthermore, according Eq. (II), the variance of the hypothetical distribution of y lar is modeled as a² (xx()), where one can explicitly model the heteroscedasticity by specifying Q and with the domain knowledge, exhibiting a more general model assumption than the traditional MSE model.
MSE where the
Application. There are two main application scenarios for the proposed GTS. The first is to directly devise various bias-free regression models by customizing the assumption T(y) ~ (2, fg) and k's function type to cope with different data scenarios. Some design guidelines are shown in Appendix A.6, with reference results provided in Table 15, 10. The second to serve as a plug- and-play debiasing module to directly eradicate bias from any given regression model, even if the given model does not use any transformation Specifically, for any given regression model M, one can easily establish the debiased model M' by setting T to identity transformation, Lx, to the loss function of M, and f(x; 0q) to the prediction of M. More empirical results are shown in Table 6.
4 Experiments on synthetic data
In this section, we conduct experiments on synthetic data to evaluate model performance. Specifically, we sample abundant instances {y J.V from the pre-defined distribution H(Y) to form the conditional distribution P. (Yz),, and then models are trained on { for learning regression task, after which the error between model prediction and the theoretical-calculate expectation Ey~H((y) [v] are computed for evaluation.
4.1 Experiment settings
Data and metric. We adopt 8 distributions H((Y) from three categories: right-skewed, left-skewed, and symmetric. Details are shown in Appendix 1.1.1. Fig. 2 illustrates the density and some statistics of the sampled P. (Y((z)). We adopt SRE (Signed Relative Error) as the metric, i.e. (ÿ u)/y where & and y are prediction and ground truth, respectively.
Implementation details.
See Appendix D.1.2 for the detailed introduction.
4.2 Results on synthetic data
Effectiveness on eradicating retransformation bias. Three transformations, i.e. linear, square, and logarithmic transformations, are employed to compare the performance between transformed MSE and our TranSUN. As demonstrated in Table the retransformation bias problem arises in transformed MSE when the transformation is not linear, i.e. model becoming underestimated with T(y) = Iy + 1) and overestimated with T(y) = y² which is consistent with Eq. (3). contrast, TranSUN maintains unbiasedness (|SRE) < 0.7 %) regardless of the transformation applied. Notably
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Table 1: Comparison results of transformed MSE (T-MSE) and TranSUN under different transfor- mations T on synthetic data. Red boldface indicates that ISRE! >1% The difference to T-MSE is statistically significant at 0.02 level.
Methods
T()
RS-G
RS-BU
RS-ZIG
LS-B
LS-BU
SM-U
SM-TN
SM-BU
MSB
0.0010
0.0023
0,0015
-0.0013
-0.0022
-0.0655
0.0005
-0.0043
T-MSE
-0.0012
0.0023
-0.0013
-0.0017
-0.0024
-0.0065
-0.0003
-0.0042
T(y) 0.5g
TranSUN
-0.0011
0.0022
-0.0014
-0.0015
-0.0020
-0.0066
-0.0006
-0.0045
T-MSE
T(y) In(y 1)
-0.1401
-0,3108
-0.4481
-0,0179
-0.1877
-0.2447
-0.0217
-0,5341
TranSUN
0.0014
0.0013
-0.0010
0.0014
0.0033
-0.0038
-0.0017
-0.0088
T-MSE
T(y) y²
0.2122
1.1015
1.7534
0.0479
0.0506
0.1442
0.0193
0.3264
TranSUN
-0.0045
0.0038
0.0019
0,0016
0.0063
-0.0069
-0.0035
0,0025
Table 2: Comparison results of advanced regression models synthetic data. The best results are in
boldface and the second best are underlined. Gray background indicates that ISREI <1% %
Methods
RS-G
RS-BU
RS-ZIG
LS-B
LS-BU
SM-U
SM-TN
SM-BU
MAE
-0.1508
-0.5624
798.7456
0.0351
0.0967
0.0050
0.0006
0.0040
WI.R [9]
0.2483
ZILN [40]
-0,0032
-0.2077
-0,0022
0.0030
0,1866
0.1326
0.0024
0.2829
MDME [21]
-0.1132
-0.5876
-0.1758
0.2730
0.1004
0,5500
-0.1146
-0.7511
TPM [23]
0.8303
0.1670
3,4244
-0,0411
-0.0303
0.0055
0.0080
0.0060
CREAD [38]
0.6511
0.1127
2.3508
-0.0361
-0.0291
0.0054
0.0060
0.0053
OptDist [41]
-0.0024
-0.2068
-0.0021
0.0019
0.1869
0.1328
0.0022
0.2826
LogSUN
0.0014
0.0013
-0.0010
0.0014
0,0033
-0.0038
-0.0017
-0.0058
MSE both exhibit unbiasedness in Table 1, that is because they converge well due to the extreme simplicity of input features and model architectures. Differently, MSE exhibits significantly poor convergence real-world data, as detailed in the next section (Table 8).
MSE and
Comparison with state-of-the-arts. Our TranSUN is further compared with state-of-the-arr re- gression models in the recommender system field. As shown in Table 2, our TranSUN achieves the best performance
is the only method that maintains unbiasedness across all distributions. Subse- quently, we provide an analysis of the biasedness of the baselines. The MAE model overestimates the mean on left-skewed and underestimates on right-skewed data due to its median modeling approach. WLR exhibits an error of 0.2483 on RS-ZIG, roughly equivalent to p+/(1 p+) = 0.25 (p+ is the positive rate of RS-ZIG), consistent with the derivations in [9]. ZILN and OptDist both show significant biasedness on certain distributions, owing to these severely violating the LogNormal or ZILN distribution assumptions. MDME overestimates the mean on left-skew and underestimates on right-skew data, likely because it estimates the mean of mode buckets under mode sub-distribution, which also explains its biasedness on SM-BU and SM-U as sampling error may result in severe mode estimation error these data. TPM underestimates the mean on left-skew and overestimates it on right-skew data, likely because it learns the average of quantiles. Note that increasing bin number can reduce its bias, as shown in See E. CREAD presents similar bias problem to TPM, whereas slightly alleviated due to its EAD binning method [38].
Comparison of GTS instance models. Some common Lu, and i are selected to devise different instances of GTS, providing reference results for its application. As exhibited in Table 15, in terms of Lu, MSE loss is empirically the most versatile loss as it fastly converges to the unbiased solution in all distributions, whose Q corresponds to the arithmetic mean point. Among other losses, MAE loss presents better convergence right-skewed data, while MSPE and MAPE loss both converge more effectively on left-skewed and symmetric data. Regarding function K, all candidates exhibit unbiasedness consistent with TranSUN. The performance of real-world data is shown in Table 10.

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Table Comparison of transformed MSE (T-MSE) and TranSUN under different transformations T on CIKMI6 train and DTMart train. Bold indicates that gain <-70%. The differences are statistically significant at 0.05 level.
CIKM16 train
DTMart train
Methods
TO
TRE
MRE.
TRE +
MRE. 4
T-MSE
T(y) Iufy +1)
0,3468
0,3352
0,2894
0,1432
TranSUN
0.0133 (-962%)
0.0171 (9455)
0.0803 (-7239)
0.0725 (449.48)
T-MSE
0.1386
0.1243
0,4388
0,3421
T(y)= vV
TranSUN
0.0388 6.7200%
0.0283 (77.2%)
0.0907 (-79.36)
0.066 (-90.%%)
T-MSE
T(y) = =artan(y))
3,6266
10,9861
0.6936
0.3678
TranSUN
0.3528 (J0039%)
1.2674 (-88.5%)
0.1554 (-77.88)
0.0678 (4166)
5 Experiments on real-world data
5.1 Experiment settings
Datasets and metrics. We adopt two public datasets (CIKM16' DTMart?) from different fields and one exclusive industrial dataset (abbr. Indus) collected from an e-commerce platform. Details are shown in Appendix 1.2.1. Indus aims to predict the Gross Merchandise Value (GMV) of each order paid on the platform, where the Pareto phenomenon occurs, i.e. 80% of the GMV being contributed by the top 30% high-priced samples. Hence, we further conduct evaluation solely on the top high-priced samples, abbr. Indus Top test. Two metrics akin to SRE in Sec. 4.1 are specifically proposed for assessing unbiasedness (see Appendix D.2.2 for detailed discussion), i.e. Total Ratio Error (TRE) M and Mean Ratio Error (MRE). Specifically, TRE and MRE are defined as E (U/ - ////E // Mi
and / Li=1 (w: //i/i respectively, where is prediction, y/ is ground truth, and M is sample number. We further adopt some metrics commonly used the literature [43, 21, 23, 38), iee. NRMSE, NMAE, XAUC, and NDCG (NDCG results are shown in Table 11).
Implementation details. See Appendix D.2.3 for the detailed introduction. TensorFlow-style implementation of our TranSUN and GTS is exhibited in Code 1. Some optional techniques for optimizing TranSUN's online performance are introduced in Appendix A.4. Moreover, the efficiency analysis of our method is demonstrated in Appendix A.3.
5.2 Results
Effectiveness on eradicating retransformation bias. Since these target data are right-skewed, commonly-used concave functions, i.e. logarithm, square, and arctan transformation, are adopted for performance comparison between transformed MSE and our TranSUN. Because retransformation bias can be viewed as fitting deviation, evaluations are conducted on the training sets of CIKM16 and DTMart. As shown in Table 3, transformed MSE exhibits significant bias issues, with arctan transformation being the most severe. Differently, TranSUN significantly mitigates the bias (mostly -70.0% ()) for all transformations. Furthermore, we assessed their performance on different target bins on Indus, where bins obtained by dividing ascending targets into equal frequencies. In Fig. 3c, LogMSE and LogSUN denotes transformed MSE and TranSUN with T(y) = In + 1). respectively, with Signed TRE used metric. As illustrated, LogSUN substantially alleviated bias across all bins compared to LogMSF. Moreover, Log s bias issue gets more severe when the target value grows larger, and meanwhile, our LogSUN's debiasing intensity gets higher well. Fig. 3c further shows gradually decreases as target y increases, to provide relatively stable x - y for smoothing Lla
Comparison with post-hoc correction methods. To further demonstrate the debiasing capability of our method, our LogSUN is compared against two classic bias correction methods, i.e. Normal Theory Estimates (NTE) [11] and Smearing [12], alongside mainstream calibration method, i.e. SIR [10], on C1KM16 test. Different from LogSUN, all the baselines are post-hoe methods, which naturally confer them an advantage in the comparison. Nevertheless, as shown in Table 4, our method achieves comparable performance with these baselines. Among them, the poor performance of NTE
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Table 4: Comparison with the post-hoc correc- tion methods on CIKMI6 test. The best are in boldface and the second best are underlined.
Table 5: Comparison of LogSUN's different bias modeling schemes on CIKMI6 test, where bold indi- cates the best.
Models
Correction mathods
TRF 1
MRF.
NRMSF 1
NMAF 1
Sc
NiMbb.
NMAE
LogMSE
0.3451
0.3667
0.6189
0,4588
80089
0.3829
06123
IUTII
LogMSE
NTB [11]
0.1262
0.1442
0,5718
0,4309
pp2tt 91
LoMSS
Smncaing [12]
D4175
0.0477
0,5617
D.435
LogMSe
SIR (19)
03098
0.0236
0.5821
0,4399
B3123
6,535
64533
1ATH
LogSUN
0.0133
0.0199
0.5625
0.4333
Table 6: Results of extending our method to advanced regression models on CIKM16 test. XAUC, metric gains are statistically significant at 0.05 level.
Except for
Extensions
TRE 4
MRE 4
NRMSE L
NMAE L
XAUC 1
WLR [9] + GTS
0,0286 1-88.72%)
0.0714 (-78.36%)
0,5814 20%)
0.4735 (-22.42%)
0.6737 (-0.07%)
ZILN [40] + GTS
0.0250 (-94.31%)
0.0223 (-95 04%)
0.5580(-12.81%)
0.4308 (-7.53%)
0.6745 (0.01%)
MDME [21] + GTS
0.0828 (-81.38%)
0,0254 (-73.989 98%%
1.0458 (-33.60%)
0.7874 (-30.85%)
0.6743 (0.1%)
OptDist [41] + GTS
0.0234 (-93.88%)
0.0248 (-94.96%)
0.5604 (-10.84%)
0.4375 (4.666%)
0.6748 (-0.09%)
Table Comparison results of advanced regression methods on CIKM16 test and DTMart test. The best results are in boldface and the second best are underlined.
CIKMI6 test
DTMart test
Models
TRE
MRE L
NRMSE
NMAE
XAUC
TRE L
MRE
NRMSE 1
NMAE
XAUC
MSE
0.1139
0.1687
0.6192
0.5024
0.6693
0.1028
0.1349
0.4893
0.2579
0,9369
MAB
0.0819
0.1281
0.6837
0.4285
0.6747
0.1655
0.0917
0.4940
0.2237
0,9388
LogMSE
0.3451
0.3667
0.6189
0.4528
0.6745
0,2889
0.1448
0.5232
0,2494
0,9440
SqnMSB
0.1339
0.1509
0.5839
0.4222
0.6753
0.4392
0.3445
0.5621
0.3115
0,9422
WLR [9]
0,2536
0.3299
0.8703
0.6103
0.6742
0.0916
0.7488
1.01788
0.5770
0,9249
ZILN [40]
0.4391
0.4498
0,6400
0.4659
0.6744
0.1165
0.0838
0,5107
0.2119
0.9445
MDME [21]
0.4448
0.0976
1.5749
1.1387
0.6730
0,2149
0.0861
0.9654
0.3395
0,9296
TPM [23]
0,0278
0.0548
0,5632
0.4358
0.6758
0.0742
0,0802
0,4998
0.2064
0,9443
CREAD [38]
0.0232
0.0639
0.5639
0,4274
0.6753
0.1533
0.1574
0.4409
0,2583
0,9443
Opt [41]
0.3825
0.4920
0.6285
0.4589
0.6754
0,1422
0.0850
0.4418
0.2121
0,9450
LogSUN
0.0123
0.0439
0.5625
0.4333
0.6740
0.0731
0.0790
0.4151
0,1994
0,9394
SqriSUN
0.0347
0.0545
0.5527
0.4212
0.6752
0,0890
0.0656
0.4194
0.2031
0,9391
is attributed to the transformed target not adhering to the Gaussian distribution assumptions. In contrast, Smearing and SIR exhibit superior results, they are free from distributional assumptions.
Performance comparison with state-of-the-arts. Our TranSUN is compared against common regression loss (e.g. MSE. MAE), transformed models (e.g. LogMSE, SqrtMSE), advanced classification-base regression models (e.g. TPM, MDME), and fancy value regression models (e.g. ZILN, OptDist) on CIKM16 test and DTMart test. In Table 7, LogSUN and SqrtSUN denote our method with Tςy) set to In(y + 1) and /y. respectively. As illustrated, our method achieves the best performance across TRE and MRE metrics, as well the commonly used NRMSE and NMAE metrics. Note that applying TranSUN usually results in a slight decline in XAUC. However,
Table 8: Comparison of advanced regression methods on Indus test, with bold indicating the best.
Indus test
Indus Top test
Models
TRE
MRE J
NRMSE
NMAE 1
XAUC
TRE 4
MRE
NRMSE 1
NMAE -
XAUC
MSE
0.3253
1.6568
2.4500
0.6018
0.7737
0.7719
2.5136
1.6605
0.5845
0.6703
LogMSE
0.6080
0.7463
2.4105
0.5871
0.7819
1.1334
2.4296
1.6130
0.5475
0.6593
LogMAE
0.4685
0.8314
2.4394
0.5691
0.7816
0.8973
2.5427
1.6427
0,5273
0.6567
WLR [9]
0.6940
0.7399
2.5622
0.6419
0.7751
0.7883
1.3097
1.6403
0.5673
0.6608
ZILN [40]
0.2945
0.4159
2.6586
0.5890
0.7809
0.7547
1,5717
1.5543
0.5277
0.6661
MDME [21]
0.3987
0.4585
2.4880
0.6225
0.7790
0.7986
1.5056
1.5789
0.5494
0.6677
TPM [23]
0.0652
0.1350
2.3981
0.6186
0.7799
0.4218
0.9261
1.5706
0.5052
0.6730
CREAD [38]
0.0917
0.1180
2.3353
0.5815
0.7808
0.6484
1,0733
1,5825
0.5191
0.6693
Opt [41]
0.2867
0.3650
2,3486
0,5780
0.7822
0.7247
1.4571
1.5614
0.5212
0.6679
LogSUN
0.0197
0.0410
2.2765
0,5683
0.7815
0.3730
0.8602
1.4969
0.4801
0.6749
8

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Table 9: Results of the online A/B test, with the 95% confidence interval (CI-95%) and p-value.
Scenarios
Product recommendation
Short video recommendation
A/B tests
Logöt UN (Ours) us. LogMAE (Base)
LogSUN (Ours) vz. LogMSE 15% vs. 9% for week
LogSUN (Ours) us. LogMAE (Base) 6% 6% month
Traffics periods
15% 20% for week
Metries
GMV
GMVPI
GMV
GMVPI
GMV
GMVPI
Gains
+1.0%
+0.92%
+1.0%
+0.75%
+1.3%
+1.57%
95%ECT
[ [0.52%. 1.59%] ]
[0.32% 1.51%)
[0.51%. 1.54% ]
[0.18% 1.32%%
[ [0.50% 3.17% ]
[0.24% , 2.89%)
p-value
0.0001
0,0024
0.0001
0.0096
0.00/65
0.0198
this trade-off remains favorable as discussed in Appendix A.I. Furthermore, as shown in Table consistent superiority of our LogSUN is observed on Indus test, where its XAUC for top high-priced samples also achieves the best performance (> +0.015 uplift to LogMSE).
Extension to state-of-the-arts. To validate the effectiveness of GTS as a debiasing framework, we apply our method to several state-of-the-art models with significant bias issues CIKM16 test, where <[f(;;; 0,)) = (a; 0,) + 1) is adopted in Eq. (9), As depicted in Table 6, the bias issues of classification- models (i.e. MDME, WLR) and value regression models (i.e. ZILN, OptDist) are all significantly mitigated (< -70.0% in TRE and MRE) by integrating our approach.
Online A/B test. In Taobao App (DAU > 300M), our LogSUN is deployed to serve as pointwise ranking model for GMV target in two recommendation scenarios (i.e. product and short video recommendation in Guess What You Like business domain in Taobao App homepage), respectively, to optimize object distribution (see Appendix E.2 for details), which is compared against the previous on- line base (LogMAE) and LogMSE. Two common metrics, GMV and GMVPI (GMV Per Impression), are adopted assess online performance. Due to the large variability of these GMV-related metrics, we allocated either substantial traffic (e.g. 15% of the total traffic for LogSUN) or a sufficiently long period (e.g. one month) for A/B tests obtain statistically significant results. As shown in Table 9, LogSUN achieves significant gains (e.g. > +1.0% % GMV gains) over all the baselines. Now, LogSUN has been deployed to serve the major traffic.
5.3 Ablation studies
Comparison of different GTS instance models. To
S0 Let SAN
offer reference results for GTS's application on real- world data, some common CH, and x are selected to
Sa Lown Blges
build different instances of GTS for comparison. As
shown in Table 10, MSE loss is the best- best-performing L.,, while MAE loss also performs well as the target data are right-skewed, which is consistent with the re- sults in Table 15. Regarding function K, compared to the one used in TranSUN, other candidates all bring about poorer loss convergence, which is probably because the variances of their k y are all too large (shown in Ta- ble 17), leading to an excessively steep optimization landscape for oz.
(a) Loss curves
(b) Metric curves
(c) Binned STRE & (d) Impact of
Figure 3: Visualization results across experiments. (a) Training loss curves for LogSUN with different schemes on
Comparison of different bias modeling schemes. To show the superiority of the multiplicative bias modeling scheme in Eq. (4), two other intuitive schemes are com- pared with ours on the LogSUN model, as presented in Table 5, where notably neither of the scheme candidates (SO, S1) belongs to GTS family. The impact of different schemes on model training is illustrated in Fig. 3a, 3b. As visible, despite theoretically unbiased, SO scheme exhibits poor convergence performance, likely due to the high loss variance caused by its additive modeling scheme. S1 scheme converges well but suffers from significant bias, as it is not theoretically unbiased, as discussed in Sec. 3.2. contrast, our scheme (S2) achieves both superior convergence and theoretical unbiasedness.
CIKM16. (b) Training curves of TRE and MRE for LogSUN with different schemes on CIKM16. (c) Signed TRE (STRE) and average slope R on divided target bins of Indus test. (d) The sensitivity of LogSUN to on CIKM16 test.

---

Table 10: Comparison of different GTS instances (T(y) In + 1)) on CIKM16 test The best results are in boldface and the second best are underlined.
Lx,
x(-)
TRE :
MRE. +
NRMSE
NMAR
XAUC 1
MSE
<<()) 1/1 [()
0.0123
0.0439
0,5625
0.4333
0,6740
MAE
<(a) 1/(T-] (u)
0,0145
0.0370
0.5627
0.4336
0,6725
MSPE
<(a)= 1/(TT (u)
0.1077
0.0679
0.5856
0.4595
0,6731
MAPE
<(u)= 1/([T' (0)
0,0340
0.0692
0,5630
0,4316
0,6734
MSE
<(U) 1/(Mu ++)
0.0399
0.0680
0.5898
0.4753
0.6708
MSE
((U) [4]
0.1810
0.2483
0.6328
0.5423
0.6633
Architectural sensitivity. Since our method introduces an extra bias learning branch to transformed MSE, we explore the impact of different parameter sharing schemes between the added branch and the original model, which is conducted on the LogSUN model. In Table 16, sharing parameters from bottom layers (e.g. embedding layers) has minimal impact on performance, whereas further sharing more parameters within MLP results in noticeable performance degradation, which might be inferred that the added task primarily affects the downstream MLP-modeled fitting function rather than the distribution of latent embedding.
Impact of hyperparameters. We study the impact of the only hyperparameter e on the Log- SUN model using CIKMI6. As visible in Fig. 3d, LogSUN stably demonstrates superior perfor- mance when e is between 0.01 and 1.0. As e further approaches zero, the performance rapidly degrades. This may be because T (f; 8)) tends to be near zero at the early stages of training, thus (f I + e) gets extremely large when é is close to zero as well, causing significant loss oscillation and hindering model convergence. Conversely, performance also degrades when c 2 100, likely due to y 3 (=;; 0)) + <) being too small to be learned within the fitting scope of 2 [x; f2), thus leading to the model underfitting.
Conclusion
In this paper, we propose a novel preemptive paradigm to eradicate retransformation bias intrinsically from the regression models to challenge the conventional ones, as the first work in the recommender system field to address the long-neglected bias problem. Specifically, a novel method, TranSUN, proposed with joint bias learning manner offer theoretically guaranteed unbiasedness under empirical superior convergence. It is further generalized into novel generic regression model family, Generalized TranSUN (GTS), which not only offers theoretical insights into TranSUN but also serves as a generic framework for flexibly developing various bias-free models. Extensive experiments demonstrate the superiority and broad applicability of our methods.
Limitations and future works. Regarding real-world applications, although the effectiveness of TranSUN has been validated across data from various domains, these target distributions are all right-skewed. Hence, we expect more exploration for its application where the target distributions not right-skewed. Moreover, a limitation of our method is the decline in XAUC, which conforms to the No Free Lunch (as discussed in Appendix A.1), thus integrating isotonicity into TranSUN is challenging but interesting direction. the future, we plan to investigate GTS further, e.g. exploring general methodology to identify the optimal point Q and function K on any given data.
Acknowledgments
We deeply appreciate Han Wu, Chi Li, Kun Yuan, Runfeng Zhang, Weiqiu Wang, Longbin Li, Xin Yao, Nan Hu, Chuan Wang, and Hanqi Jin for their insightful suggestions and discussions. We thank Kewei Zhu, Yuxin Duan, Hao Fang, and Gaofeng Li for necessary supports about online serving. We thank anonymous reviewers for their constructive feedback and helpful comments.
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NeurIPS Paper Checklist
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A Frequently Asked Questions (FAQ)
A.1 Root reason for the trade-off between point accuracy (e.g. NRMSE) and XAUC
Here we elaborate on the root cause of the trade-off phenomenon between point accuracy and XAUC, and further highlight the limitations of XAUC. This limitation leads the inconsistency between the offline XAUC metric and online business metrics (as shown in Table 9), making XAUC no longer suitable for offline assessment. To address this, we supplemented the offline evaluation with two more consistent offline metrics, high-value XAUC (as shown in Table 8) and commonly used ranking metric NDCG (as shown in Table 11), on both of which our model demonstrates superior performance. For clarity, let us start with a concrete case as follows.
An illustrative case for trade-off: We first sample two inputs x2] ~ P(X). and then sample 3 groups of target y from (() and ((2).)) respectively, and let the samples be (3,3,3) 3, 3} ~ P(Y x1) and (8,1, ~ P(Y(=2), and let T(x) log(z). Then, 1) The LogMSE prediction is f(1 = T (E (E m1)) exp((log(3) + log(3) + log(3))/33 = 3. f(x2) T T (E(T(Y)) [22]) cxp((1o(()) + log(1) + log(1))33 = 2. where f(x1) > f and the bias occurs on the sample X = 22: 2) The TranSUN/GTS prediction is f((1) = E| =
(3 + 3 + 3)/3 3, (x²) = [2] +1+1+ 8)/3 10/3, where f(x) [x2);; 3) The descending ranking result of Log is TRE 4/15, while the result of TranSUN/GTS is {8, 1, 3,3,, with XAUC = 0.233, NRMSE
1,1 with = NRMSE 0.324, and
0.301,, and TRE- = 0: 4) It is observed that a trade-off occurs between point accuracy (NRMSE, TRE) and XAUC, i.e. TranSUN/GTS achieves better point accuracy (NRMSE, TRE) while XAUC worsens.
Root cause of the trade-off: 1) Reason for the improvement of high-value XAUC & overall point accuracy metric: TranSUN/GTS compensates underestimation brought by retransformation bias, resulting in better point and rank accuracy of high-value samples (e.g. for sample (1z,,),, relative error improves from 0.75 to 0.58, and its rank order moves from 4th to 1st, consistent with results on Indus Top (Table 8)), which significantly improves the overall point accuracy (e.g. improvements in NRMSE & TRE in the above case) since these metrics are value-aware (i.e. metric calculation aware of absolute value of sample label); 2) Reason for the drop of overall XAUC: Correcting retransformation bias also leads to some hard low-value samples being overestimated (e.g. predictions for the two samples (122, 1) increase from 2 to 10/3, consistent with Fig. 3c), which dominates the overall XAUC drop since there are far more hard low-value samples than high-value ones in highly right-skewer data and XAUC metric is value-agnostic (i.e. metric calculation only aware of the relative rank order of sample label but not aware to its absolute value).
Overall XAUC is inconsistent with online metrics, thus we use high-value XAUC and NDCG: 1) The core goal of a recommender system is to improve online business metrics, while XAUC is merely an intermediate metric. For business target modeled by regression (GMV, watch time, etc.), the event of ranking high-valued samples in the correct position is far more important for online metrics than that of low-valued samples. However, these two events are equally weighted (i.e. value-agnostic) in the calculation of XAUC, thereby being dominated by abundant low-valued samples when data are highly right-skewed, which probably contribute only a small portion of online metries (e.g. 70% of the top low-valued samples contribute only 20% of GMV in Indus). Therefore, overall XAUC is no longer consistent with online metrics; 2) To address this, we supplemented the offline assessment with more consistent metric. high-value XAUC (Table 8), based on which we achieved improved online results (Table 9). Additionally, NDCG also addresses XAUC's limitation, so we also provide their results. As shown in Table 11, NDCG is computed within all samples (NDCG@ All) and the top 10% high-value ones (NDCG@ @ 10%), respectively. Key observations include: a) TranSUN performs better in NDCG @ All than in XAUC since NDCG is more robust to low-value samples. b) TranSUN shows superior performance NDCG@ 10,, consistent with the reasons described in the 2nd point.
A.2 Convergence analysis for CT CT CNSE and LMSE
As for convergence rate bound, since their loss formulations are all squared errors, the theoretical convergence rate bound using SGD is ( under the Lipschitz assumption, where K is update it- eration number, according to [6]. The key difference in the convergence performance of CTT.. CusE
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Table 11: NDCG metric results of our method and advanced baselines on CIKM16 and DTMart test. The best results are in boldface.
CIKM16 test
DTMart test
Model
NDCG@ All
NDCG@ 10%
NDCG@ All
NDCG@ 10%
MSE
0,9180
0.5201
0.9770
0.9692
MAE
0,9497
0.5654
0.9867
0,9665
LogMSE
0.9498
0.5517
0.9960
0.9736
WLR [9]
0,9475
0,5433
0.9693
0,9609
ZILN [40]
0.9485
0,5781
0.9963
0,9756
MDME [21]
0,9391
0.5671
0.9763
0,9639
TPM [23]
0,9502
0.5888
0.9960
0.9772
CREAD [38]
0.9504
0.5881
0.9962
0.9774
OptDist [41]
0.9500
0.5852
0.9965
0.9770
LogSUN 0.9499
0.5904
0.9967
0.9779
and LMSE lies in their smoothness. This because the variance and the outlier proportion of the target are different, resulting in optimization landscapes with different degrees of smoothness. As shown in Table 12, we present the target variance (Var), the variance divided by squared expectation (V/E2), and the outlier proportion (Outlier %) outside of times the standard deviation of the three losses, where T(x) = log(z). As shown, L has smaller variance and better outlier distribution than the vanilla MSE, thus CT converges more smoothly (Fig. 1). Therefore, TranSUN/GTS essentially decomposes difficult task into two easier and smoother tasks.
Table 12: Convergence analysis for LT MSE. and CMSE
CIKM16
DTMart
Losses
Var
V/E2
Outlier%
Var
V/E2
Outlier%
LMSE
16440
0.41
1.03%
97494
12.1
0.78%
Cln
0.63
0.36
0.59%
2.327
0.93
0.32%
sun
MSE
0.62
0.02
0.29%
1.87
0.15
0.28%
A.3 Efficiency analysis for the proposed TranSUN
As different parameter sharing architectures of TranSUN are explored Appendix E.4, here we supplement the results (Table 16) with TranSUN's ss additional memory (Mem) and computational overhead (MFLOPS), and calculate the relative increase (OH) compared with T-MSE, As shown in Table 13, the till--sharing-embdddin architecture scheme is the most cost-effective, maintaining optimal performance while introducing much little overhead. On the other hand, we provide additional information the resource overhead associated with the online TranSUN model in the e-commerce platform's recommendation system, which achieves high ROI measure (with Table 9): 1) Training: Under the same resources (800 workers). the update iteration (global step) number per second of LogMSE and TranSUN were 89.2 and 86.8, respectively. Therefore, applying TranSUN only reduces the training speed by 2.7%, with the training time increased by 2.78%; 2) Inference: The mean and p99 latency of the LogMSE were 27.8ms and 49.8ms, respectively. while the mean and p99 latency of TranSUN were 28. 38.lms and 51.6ms, respectively: 3) Deployment: In the online service with 300 million daily active users, deploying TranSUN did not increase CPU resources and only increased GPU resources by 5%.
A.4 Optional techniques for optimizing I LogSUN's online performance
As mentioned in Appendix A, TranSUN likely results in certain decrease in the overall XAUC, particularly for low-priced orders. Although these orders only contribute 20% of the total GMV, they represent the majority in view of the total number of transaction orders. Therefore, the reduced
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Table 13: Comparison results of the LogSUN model under different parameter sharing architectures on CIKM16 test. "X/Y" denotes sharing the first X-th layers of the network with totally Y layers. The results with the best ROI are in boldface.
Parameter sharing schemes
Mem (MB)
OH (%)
MFLOPS
OH (%)
0/1 Embedding + 0/3 MLP
610.46
100.00
350.86
100.00
1/1 Embedding + 0/3 MLP
305.29
0.02
190.52
8.60
1/1 Embedding + 1/3 MLP
305.27
0,01
186.12
6.09
1/1 Embedding + 2/3 MI.P
305.24
0.00
177.62
1.25
1/1 Embedding + 3/3 MLP
305.23
0.00
175.47
0.02
ranking accuracy of these orders' GMV estimates deteriorates the accuracy of their overall ranking score, which in turn deteriorates the online metrics regarding the number of transaction orders. Therefore, it is crucial to lift the ranking accuracy of these samples under TranSUN's modeling, Here are two techniques that have been validated as effective in our scenarios: 1) Selecting a suitable combination of ranking losses: As shown in lines 77-79 of the Code 1, selecting these two ranking losses carefully has been shown to improve the overall XAUC by > +0.01 on our private industrial data. 2) Fusion with the original predictions: As shown in lines 51-52 of the Code 1, pre-defined fusion threshold can be used to restrict TranSUN's functioning scope to high-priced samples, which improved the overall XAUC by > +0.003 on our private data. To select the threshold, we first divided the sample into 50 bins with equal frequency based on their original prediction values in ascending order. Then, we calculated the XAUC results of the original and debiased prediction values within each bin, respectively. We found that as the bin number increased, the XAUC gain of debiasing gradually shifted from negative to positive. Therefore, the left boundary of the bin that first achieved a positive XAUC gain was adopted as the fusion threshold. Once this threshold is determined, it does not need be adjusted anymore, unless the data distribution shifts significantly.
A.5 Comparing GTS with probabilistic modeling methods (PMM), egg. Mixture Density Networks (MDN), Normalizing Flows (NF)
A comprehensive comparison is shown in Fig. 4. Specifically, when our GTS serves a point estimator, has three advantages over PMM: 1) Flexibility: It can be flexibly plugged into any model with minor revision (as validated in Table 6). Another advantage is that in industrial practice TranSUN can be fully warmed-up from the online base model, further accelerating TranSUN's s convergence: 2) Lightweight: It requires much less resource than PMM. For example, MDN's overhead grows linearly with mixture components, and NF incurs significant overhead due to Jacobian computations; 3) Training stability: PMM is much harder to converge than GTS given their complex assumptions. For example, on Indus, OptDist [41] (an MDN case) needs 2. 1.13x the iterations TranSUN requires to reach batcb-NRMSE=3.0.
In addition, with minor revision to GTS's model assumption (i.e. modeling constant in Eq. (11) as a function of z)) GTS can also directly model the conditional probability P(Y|z)) in the CTM manner [16]. Specifically, GTS's assumption formulation turns to
- <z( 0,) + Y,- s(x; x (QQpPP()))) [T())) ~ 10,,
(12)
where szx; 0.) O actually models the reciprocal of the standard deviation (Ir). In training stage, according to [29, 16], one can establish the sorringruule-bssee loss Ler (1, y; h) as
(I, y; h) (
Σ 1l vz) log (h(( v;))) 1y 0.) log(1 0(h(2, +)))]]
(13)
where the 1{-) is the indicator function, {u. N denotes pre-defined ascending grid points of y. & ()) 1 [1 + erf( "),, and h(z, y) is defined as
hnr, u) = - (2;; 0z) + y s(x; 0.) stop_grad (x([(1;;,,)) Therefore, the total loss is formulated as
(14)
CeTS Lr, (z, T(y): 0,) + Cor
(15)
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fot: Se
*
MSE
Appy Tong
T-MSE
Abodyy mmoglltd comppe
NF
Ahweay ouseggilll saa
CTM
-fintesle M
-fixl+ N.0.0
K- a- a-M
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*: & MDM
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GTS
Replacott) (lpp
-19 p Roll Ni
-f10)+ 1100==--A01
" -01-1, aisst
Unblasedness
Convergence
Pluggability
Overhead
Holds all the time
Fast and smooth on skewed data
*
For regression model
Mininal
*: Depends on some designs
Occastonally ly unstable due to complex design
*
For specific models (c.R. Transih is for T-MSF)
* Large in same cases (e-g-
(e-g- 12 and H() (аосси)
grows much)
* Barely holds (e.g. T-RSE is barely linear)
*
Unstable on skowed data
*
pluggable
often significant (e-8-
Jacobian computation in NF)
Figure 4: A graphical comparison of the advantages and model assumptions among Mean Squared Error (MSE), transformed MSE (T-MSE), Normalizing Flow (NF), Conditional Transformation Models (CTM), Conditional Linear Transformation Models (CLTM), Mixture Density Model (MDM), TranSUN, and Generalized TranSUN (GTS).
In inference stage, our GTS models the conditional probability with
P(Y < u|z) = 4 (h(x,v)).
(16)
A.6 Principled guidelines for utilizing GTS
The principled guideline is align the model assumption (Eq.(11)) closely as possible with the real data, though this requires manual trial-and-error. Our experience is to first fit the data solely using mainstream regression model as Q, then analyze the variance, skewness, kurtosis, and outlier distribution of Y * x{Q) to select a suitable x form, which determines the final GTS model. This significantly reduces training resources when tuning A more general methodology is left for future work, as stated in the conclusion section.
B
Mathematical Details in Our Approach
B.1 Derivation of transformed MSE's estimation
The loss function of transformed MSE is exhibited in Eq. (2), Minimizing the loss can result in that
min (ZD ()(=;))T(())>
0
I
min ((.N)-(XN)
(f(z; -T())) p(z ydddyy
[
( (f(x;)) T(w)) ((ylx))d p(x)dr
=min
JEMP(X)
8
= =min Ex)P(X)
[ T(w)
(17)
<Vz PXX), min E E
T(x))²
f(z:0)
* P()), Of Ey-p(Y))) [f((;;)) T(y)) {
*Vz P(X), IE [)))) [2X (f(z;)) T(w)]
<Vr P(X), f(;; Ey-P(Y( [Tw)].
24

---

Therefore, f(z;0) 0) is actually an estimate of PV))) [T(v]]
B.2 Detailed derivation for TranSUN's estimation
A brief derivation for TranSUN's estimate is exhibited in Eq. (7, 8). Following Eq. (17), present detailed derivation for TranSUN's estimate (/ as
min CT
min E DD (z(0;0.) 0.) - -sopp grad (T- (f(x; 0)) + 2) '
y
8,
min E P()) E ((<=;)))) stop grad
T (f (x; 0)) + )"]
</x P(X): min E Ey (=(x; - stop_grad
(f(z; 0)) + 11
=(m;0,))
(18)
</x P(X): 0z(r; 0.) By-PMM - stop_gret
y
T (f(x: 0) 0)) +
=
42x P(X). B Sym [2x (z(x; 0z)
0
[T-1 (f(x;(
4Vx P(X), 2(1; 02) Ey)P(Y
y
E P IT- +
T-1 (f(1; +
<vv P(X), j/r 2(x;0.) (f 0)) +c) By-p(Yla)ll)
B.3 Detailed derivation for estimation from the model with S1 scheme
As mentioned in Sec. 3.2 and Table 4, the SI bias modeling scheme formulates the bias learning loss
[<<(x; stopp_tral T (J(z; 11
4T (S1) = E (a.w)>
(19)
Following Eq. (18), we present detailed derivation for its estimate ø|æ:
min CT (S1)
0.
= mmin ( (((x)))) stop_grad T T- (f(z; 0)) 1)
6,
y
(1(z)0))
(f(2; 0)) ((( 1)
mmi E P(x) B By (=(x;; 02) - grap
T (f(z; 0)) 1)29
0))
@Vr P(X), min Ey-p [ stop grad =(x0,)
y
T (f(z: 0)) (f(=:00) 1) 1===0 =0
(20)
SVx ~ P(X), 02(r; E ( - stop_grad
y
T (f(x;))
*Vr P(X), ( [2X (2(x;02)
)] =0
(J(1;)) 0))
*VI P(X), 2(x;0.) Ey>P(M)=)
-f ((([:()))-BBp((1101 E
y
T (f(()())
*VI~ ~ P(X), 02
2(2
Bypp(y
As shown above, the model prediction 0| is actually estimate of 1/E which is biased.
25

---

B.4 Detailed derivation for GTS's estimation
Owing to the stop_grad operation, the optimization of the total loss LGTS can be decomposed into two independent parts, as
min LoTS < min Lu, + min LiTM 0
(21)
9,
where LH, is the conditional point loss and TTMM is the linear transformation loss. The first term
ming, Cn, learns a conditional point according to Eq. (10), which is independent of (x;; 0z). The second term derives the GTS's estimate ( via
min FiTM 6,
-min E (a. (2(x;(2) - -y stop grad ggadggra[[[((f (,)1)
= =min E Ex) By B ( (z(x;;))) stop [oo_ggra[<([[( 6,))] [1] y stop grad ( (f( 0z)
8.
*/r P(X), min E B s(x:82)
(22)
<Vx ~ P(X), 0z(x;0,) By ( y stop stop_grad[x([1e) 6, (,))) =0
<tx ~ P E p [2 (z(1; 0z) (
*²x P()), 2(2; 02) By-p(( y (f((z) Exppp
2(x;(x)
uVx ~ P(X), ū| x(f(x;b))) Bypp(y
B.5 Discussion for the theoretical correctness of the unbiasedness metrics (TRE and MRE)
Details are shown Appendix D.2.2.
B.6 Utilizing GTS for direct probabilistic modeling
Details are shown in Appendix A.5.
C Challenges of applying external bias correction approaches in industrial recommender systems
Applying external debiasing paradigms from prior works real-world recommender systems neces- sitates the development of an additional online post-processing pipeline after the ranking model's scoring pipeline in the overall online system, which suffers from practical challenges including high development costs, substantial maintenance difficulties, and significant system resource consumption. In addition, since the online calibration pipeline [10] has been commonly utilized in many large-scale recommender systems, an alternative approach is to just let this pipeline itself fit the correction. However, practice, when the retransformation bias problem becomes severe (e.g. TRE is about 0.6 before calibration), this alternative approach is prone to yield unstable online TRE results after the calibration, which are significantly worse than those of our TranSUN method, with the mean being 180% and the standard deviation being 150% of ours. The instability of calibration results might be caused by the excessively large differences between predicted values and true values, which can even affect the robustness of the calibration pipeline. Therefore, as a practical solution, we propose TranSUN and Generalized TranSUN (GTS), an end-to-end in-model correction method address the challenges of existing approaches and provide robust model performance of unbiasedness.
26

---

D Details in Experimental Setting
D.1 Detailed setting on synthetic data
D.1.1 Data and metric
We adopt distributions H(Y from three categories: right-skewed, left-skewed, and symmetric. Specifically, we select some classic exponential family instances (e.g. Gamma, Beta, Normal), multimodal distributions (e.g. bimodal uniform), and industry-prevalen zero-inflated distributions (e.g. ZILN [40] with positive rate p+ = 0.2). Detailed implementations are shown in Code 2. For each distribution, we randomly sample
= 10 instances. Fig. illustrates the density and some statistics of the sampled P. P.(Y(z)) [x). We adopt SRE (Signed Relative Error) as the metric, i.e. (ú v)/y where 9 and y are prediction and ground truth, respectively.
D.1.2 Implementation details
We implement all methods using the Tensorflow toolbox on an M2 Pro CPU with 16 GB. Since the model input is fixed in (Y(Y),, we directly set it 1.0. We also implement some advanced classification-based models [23, 38, 21, 9] for comparison, where only their main classification losses are retained. For TPM [23] and CREAD [38], bin number is set to which is produced via equal-frequency and EAD binning method [38], respectively. MDME [21] adopts an equal- width binning method to determine sub-distributions, each containing 2 buckets. WLR [9] is only evaluated on RS-ZIG since it requires substantial zero values as negative samples. We also implement
ZILN [40] and OptDist [41], which discard classification branches when not evaluated on RS-ZIG. And OptDist is set to adopt& 3 SDNs. We set batch size to 1024 and select the optimal learning rate from {10 (10"")ssis
U (5 10 JISisA. All models are trained for I epoch, with each training repeated 10 times with different random seeds to obtain statistical significance, where the p-value is calculated by the t-test.
D.2 Detailed setting on real-world data
D.2.1
Datasets
We adopt two public datasets (CIKM16, DTMMrt) and one exclusive industrial dataset (abbr: Indus). Specifically, CIKM16 aims to predict the dwell time for each session in online searching. We only use the items in the session as input features. The CIKM16 dataset contains 310,302 sessions and 122,991 items. DTMart aims predict the transaction amount for each order in marketing activities. We use item ID, categories, time taken for procurement, and delivery as input features. The DTMart dataset contains 985,033 orders and 15,546 items. Indus aims to predict the Gross Merchandise Value (GMV) of each order paid in the recommendation scenario of an anonymous e-commerce platform. The Indus dataset contains 132,657, 136 orders, 14,538,759 items, and 67,729,861 users. CIKM16 and DT datasets are both randomly divided into training and testing samples at a ratio of 4:1, ratio of 5:1. Interestingly, we found that the Pareto phenomenon
and the Indus dataset is divided occurred in the Indus dataset, where 80% of the GMV was contributed by the top 30% high-priced orders. Consequently, we further conduct evaluation solely on the top high-priced orders in the testing set, abbr. Indus Top test, to better analyze model performance.
D.2.2 Metrics for assessing unbiasedness
As mentioned in Sec. 5.1, we propose Total Ratio Error (TRE) and Mean Ratio Error (MRE) to assess unbiasedness. These metrics are formulated as
Σ
Us
Vi
TRE
(23)
1=
1 M
91
V/s
MRF
(24)
M
0
1=1
where ÿ is prediction, y4 is ground truth, and M is sample number.
27

---

Firstly, we theoretically prove that achieving either the optimal TRE or MRE metric is neces- sary condition for the model to be unbiased. Specifically, through the definition of the model's unbiasedness, we can derive that
Vx PXX),
i((x)) Ey>p(Y|=))
Vx P(X), By)p(Yls))( y)
(25)
where ((x) æ.. For the TRE metric, optimizing it means that min TRE
(a,))D [(x) yl
(a [0(x]] =0
(26)
+ B(a,)) [5(x) - yy] =0
+ B(x (()))) [8x))= - w| =
< Vo ~ P(X), E B [ū(x) y) = 0.
where the second row in Eq. (26) is derived from the definition TRE using expectation formulation, and the last row comes from Eq. (25). Regarding the MRE metric, optimizing it implies that
min MRE
E B 1
= 0
9(x)
(((x)= - y
<> BxwP(X)
B ByNP(Y(0))
(27)
j((x)
+ Ex)P(X)
E By)P(Y())) [(x)
((x)
Va P(X), E (V)P( [xx) - y) = 0,
where the second row in Eq. (27) is derived from the definition of MRE using expectation formulation, and the last row comes from Eq. (25). Notably, the derivation in Eq. (27) explains the reason that the model prediction (xx) is placed in the denominator position of the metric. Specifically, once the
MRE is modified to swap the numerator and denominator of each item in it, as
MRE (wr)
y1
(28)
y1
then this new metric is no longer suitable for measuring the model unbiasedness, which actually turns necessary condition for the estimation of 1/E,)>P(Y==) as
min (RF(wr)
[1 5(xr) 0
E BLOWNDD
j((x)) ]]
E BymP(Y|a))
0
1
(29)
E ((x) EBy-P(M
=
0
(xx)
y
+ Vr ~ P(X), BYNP(Y
0
((x)
V
Vr P(X), ((x) = Ey-p(M)=)
+
where the second row in Eq. (29) derived from the definition of MRF(wr) using expectation formulation.
Next, we theoretically prove that achieving the optimal NRMSE metric necessary and sufficient condition for the model to be unbiased. Specifically, NRMSE is defined as
Σ
1= (Ur u:)
NRMSE
(30)
1 Vi
28

---

and thus optimizing it means that
min NRMSE
+ min ((eg)) (0(z) - y
+ min P(x) ByNPLY (0)x) y)
+ Vo ~ P(X), min E Bymp(Y))) (0(()) - y)
(31)
+ Vr P(X), 0f((z) E
(0(x)) y)²
+ PXX), E By-)) 2 x (f(x) v)]
Vr- PXX), ((x) By)pP(Y [y],
where the second row in Eq. (31) is derived from the definition of NRMSE using expectation formulation, and the last row indicates that (xx) is an unbiased estimate.
Discussion on not using NRMSE as the primary metric for observing unbiasedness. Since NRMSE is a necessary and sufficient condition for a model be unbiased. intuitively should be preferred over TRE and MRE as the primary metric for observing unbiasedness. However, the NRMSE metric has a significant issue, that its optimal value (i.e. the minimum) is unknown. This problem hinders us from intuitively perceiving the presence and severity of the bias, making it much difficult to verify the capability of different models model iterations towards eradicating bias. In contrast, although TRE and MRE are both necessary conditions for a model to be unbiased, their optimal values (i.e. the minimum) are known, which is 0.0. Therefore, they can both clearly indicate whether model is biased. In our experiments, we take the approach for analyzing unbiasedness where TRE and MRE are initially compared to determine if the model is biased, and then NRMSE is subsequently compared to identify the model with the best unbiasedness. The idea of the analytical approach above is also reflected in our result reporting. For example, NRMSE results are not reported in Table 3 and Fig, 3b, 3c, 3d, which is because the gaps among methods in TRE and MRE are both quite pronounced already.
D.2.3 Implementation details
For public datasets, all methods employ an "Embedding+MLP" architecture, where continuous features are discretized, each feature's s embedding dimension is set to 16, and the MLP has 4 layers with hidden dimensions of 123, 64, and 32. For Indus, all methods employ DIN architecture [49], where continuous features are also discretized, and the MLP has 4 layers with hidden dimensions of 1024, 512, and 256. The bias modeling branch of TranSUN defaults non-shared parameters on public datasets and shares the embedding layer on Indus. The default setting for is 1.0. For other baselines, WLR [9] folows the implementation in [45]. ZILN [40] and OptDist [41] both discard classification branches. The number of bins in TPM [23] and CREAD [38] is set to 16. MDME [21] adopts sub-distributions, each containing buckets, and OptDist adopts SDNs. The cqual-frrquency binning method is adopted for both TPM and MDME, while the EAD method is adopted for CREAD. On public datasets, the SGD optimizer is utilized with batch size of 512 and a learning rate of 0.001. On the Indus, the AdagradDecay optimizer is employed with a batch size of 64 and learning rate of 0.01. All models adopt only one training epoch, and each training is repeated 5 times with different random seeds to obtain statistical significance, where the p-value is calculated by the t-test. We implement all methods using the Tensorflow toolbox. The model training on public datasets is performed on an M2 Pro CPU with 16GB, while the training on the Indus dataset consumes resources including 2000 CPUs with 90 GB. In addition, the statistical significance in the results of the online A/B test (Table 9) is calculated by the z-test.
E
More Experimental Results
F.1 Biasedness comparison of TPM with different bin numbers on synthetic data
As shown in Table 2, TPM [23] underestimates the mean on left-skew and overestimates it on right-skew data, likely because learns the average of quantiles while the bin number only The bin number is set small to amplify the theoretical biasedness problem of TPM, which can be
29

---

significantly alleviated by increasing the bin number, as shown in Table 14. This conclusion also applies CREAD [38].
Table 14: Comparison results of TPM with different bin numbers on synthetic data, where "X "X* #bin" indicates the bin number of TPM is X. Bold indicates the best results, and gray background indicates
that ISREI <1% %
Models
RS-G
RS-BU
RS-ZIG
LS-B
LS-BU
SM-U
SM-TN
SM-BU
TPM (4#bin) [23]
0.8303
0.1670
3,4244
-0.0411
-0.0303
0.0055
0.0080
0.0060
TPM bin) [23]
0.1099
0.0519
0.4874
-0.0094
-0.0157
0,0021
0.0020
0.0033
TPM (256#bin) [23]
0.0281
0.0124
0.0561
-0,0022
-0.0054
0.0013
0.0013
0.0021
E.2 Details for online A/B test
In Taobao App (DAU 300M), our LogSUN model is deployed as GMV prediction models in both product and short video recommendation scenarios in Guess What You Like domain in the homepage, which serve as pointwise ranking models for GMV target in the ranking stage of the recommender systems to optimize object distribution. Notably, in the short video recommendation scenario on the e-commerce platform, all the short videos are product description videos, each of which links to certain product, therefore, the GMV of a short video actually refers to the transaction value of the product described in the video after the short video is clicked.
In the A/B test, our LogSUN is compared against the previous online base (LogMAE) and the commonly used LogMSE. Two common metrics, GMV and GMVPI (GMV Per Impression), are adopted to assess online performance. Due to the large variability of these GMV-related metrics, we allocated either substantial traffic sufficiently long period for A/B tests to obtain statistically significant results. Specifically, we conduct two A/B tests for one week in the product recommendation scenario, with LogSUN serving 15% of the total traffic, LogMAE 20%, and LogMSE 9%. And conduct one A/B test for one month in the short video recommendation scenario, with LogSUN serving 6% of the total traffic, and LogMAE 6%.
As shown in Table 9, LogSUN achieves significant gains (e.g. > +1.0% GMV gains) over the baselines in both recommendation scenarios. We attribute the consistent gains in online metrics to the following two reasons. The first reason is that LogSUN significantly improves the predictive accuracy of samples in each target bin by eradicating the retransformation bias, as shown in Figure 3c. The second is that LogSUN empirically improves the ranking accuracy of the top high-priced samples (e.g. the improvements in AUC on Indus Top test, as shown in Table 8), which contribute 80% of the total GMV though they are small in number. On the other hand, we observed that the GMV gain in the short video recommendation scenario was much larger than that of the product. This is possibly because the retransformation bias problem is much more severe in the short video recommendation scenario (TRE is about 0.6352, nearly 140% of the product's) s). Now, LogSUN has been deployed in the two core recommendation scenarios to serve the major traffic.
E.3 Comparison of GTS instance models on synthetic data
Some common LH, and are selected to devise different instances of GTS, providing reference results for its application. As exhibited Table 15, terms of Lx MSE loss is the most versatile loss as it fastly converges to the unbiased solution in all distributions, whose Q corresponds to the arithmetic mean point. Among other losses, MAE presents better convergence on right-skewed effectively on left-skewed and symmetric data.
data, while MSPE and MAPE both converge Regarding function K, all candidates exhibit unbiasedness consistent with TranSUN. The performance of i. real-world data is shown in Table 10.
E.4 Architectural sensitivity on real-world data
Since our method introduces an extra bias learning branch to transformed MSE, we explore the impact of different parameter sharing schemes between the added branch and the original model, which is conducted on the LogSUN model. In Table 16, sharing parameters from bottom layers (e.g. embedding layers) has minimal impact on performance, whereas further sharing more parameters
30

---

Table 15: Comparison results of different GTS instances (T(y) In y 1)) on synthetic data. Red
boldface indicates that ISREI >1 %.
Cu,
x(()
RS-G
RS-BU
RS-ZIG
LS-B
LS-BU
SM-U
SM-TN
SM-BU
MSE
x(u) = 1/(T
[1)
+
0.0014
0.0013
-0.0010
0.0014
0.0033
-0.0038
-0.0017
-0.0058
MAF
R(u) = 1/(T
(u)
+
0.0042
0.0010
-0.0088
-0.0012
0.0242
0.0177
0.0083
0.0010
MSPE
<(u) 1/(T (a)
+
0.0083
0.0340
-0.0048
-0.0644
-0.0044
-0.0074
0.0059
0.0023
MAPE
R(M) = 1/(T [() +
0.0103
0.0191
-0,0018
-0.0087
-0,0016
-0.0084
0.0047
-0,0061
MSE
R(a) I/(la/
0.0055
0.0044
-0,0011
-0.0020
-0.0032
-0.0034
0.0036
0.0041
MSE
R(U) [M]
0.0018
0.0024
-0.0057
-0.0014
-0.0018
-0.0028
-0.0012
-0.0044
within MLP results in noticeable performance degradation, which might be inferred that the added task primarily affects the downstream moddeled fitting function rather than the distribution of latent embedding.
Table 16: Comparison results of the LogSUN model under different parameter sharing architectures on CIKM16 test. "X/Y" denotes sharing the first X-th layers of the network with totally Y layers. The best results are boldface and the second best are underlined.
Parameter sharing schemes
TRE
MRE 4
NRMSE |
NMAE
XAUC t
0/1 Embedding 0/3 MLP
0.0123
0.0439
0.5625
0.4333
0.6740
1/1 Embedding 0/3 MLP
0.0147
0.0353
0.5624
0.4305
0.6743
1/1 Embedding + 1/3 MLP
0.0316
0.0413
0,5672
0.4356
0.6707
1/1 Embedding + 2/3 MLP
0.0490
0.0686
0.5684
0.4455
0,6702
1/1 Embedding 3/3 MLP
0.1063
0.0955
0.5951
0.4775
0.6658
E.5
Comparison of GTS instances with different functions real-world data
As shown Table 10, compared to the one used in TranSUN, other x candidates all bring about poorer loss convergence, which is probably because the variances of their k all too large (Table 17), leading to an excessively steep optimization landscape for 0..
Table 17: Comparison of the variances of к in GTS instances with different x functions (T In + 1) and Lx, is set MSE loss) on CIKM16 train.
(())
Var(x y)
Var(x w)/(B[x w))?
n(u) 1/([T (w)) +e)
0.6329
0.3610
k(u ( 1/([u +
417.67
0,3829
n(u) [u]
461790.3
0.4447
F
Broader Impacts
We think that there is no societal impact of the work performed. Though our method has been applied in two core recommendation scenarios leading e-comeerce platform (DAU 300M) serve the major online traffic, there are no obvious paths that lead to potential harm, since our work just presents unbiased regression methodology and is not tied to particular applications.
31

---

Code 1: TensorFlow-style implementation for our TranSUN and GTS.
import numpy as np
import tensorflow. compat.....mmat..oooo v1 as tf
tf disable__2_
5 from tensorflon keras layers import Dropout
def transun_nodel (x, y y_label, mlp_units, trans, dropout, feat_num, feat_dim, rmask, imask, reuse is_training,
kkargg)):
with tf. variablbee__scpp ('transun', reuse=reuse);
# embed pool
enbedding-paran t.. wtf.get_.ariable
shape=[
feat_num, feat_
feas - w embedding.lookup (ids-x, params
onbedding.paraml
(bsz 20, 10,teat_dim
requesta tf reduceeeuaaaumeee (feas(:: :10, :] expand
rmask, -1), 1) / tf reduce_e__mm (rmask, 1, keepdims=True)
# avg pooling items = ref.reddue_ccm _um (feas 10:, :] tf. expand_dimss imask, -1), 1) / tf. reduce____uud (imask, 1, keepdims-True)
feas concat ([requests, items], 1) # (baz 2+feat_dim) # mlp, main branch
18
drpt Dropout (rate-dropout) fc feas
for idx, num_unit
enumerate (mlp_units):
fc linear (fc, num_unit, ('dense(idx)"" reuse)
23
fo = tf.nn.reell relu
fc = drct training=isstraininn
logits linear 1, "output", reuse)
# mlp, sun branch fci feas
27
28
for idx, num_ unit in enumerate aalp_units):
fcl = linear (fe1, num_unit, f" f"sunfidx3", reuse)
fcl
tn. tf. relu(fc1)
fcl (fct trainingris_training
32
sun = linear (fci, 1, "sun_out", reuse)
bias 1.0
36
if trans 'log'; ori pre_ = tf math. exp (tf. math. minimum (10.0, tf mn. relu (logits)))
final_pred (ori_pred bias) tn. (aun) elif trans 'qrrt'
40
ori-pred tf. (logiiss)) ** 2
final_pred (ori_pred bias) * tf ft.nn de.nn.rew relu elif trans == 'atan':
ori_pred tf.math. tan tan (tf. clip_ by_pbbyyaalleee value (logits, 0.0,
up. atan (10000)))
44
final-pred (ori_pred bias) tf.nn mn relu relu (sun)
elif trans == tanh':
ori_pred tf math atanh (tf. biiipby_vvlrre (logits, 0.0,
np. tanh (800)))
47
final_pred (ori_pred bias) df.nn.reluce
else:
raise NotimmpeeeetteErrrr
FUSE_ THRES 54.0 fused_pred tf. where fori_pred FUSE_ ori-pred, final_pred)
52
32

---

if is_training: if trans '1og':
56
sun sun_label=tf Bttpolit..too__rrdiiieee (y_adient(y_labe)) (tf.ex) bias))
logits)
mse loss tf reducedue_ssu (tf squ.rquure (tf log (yg(y_labe)
1) logits))
loss tf reduce. sum (tf. square sun label )
elif trans = 'aqrt':
sun sun_label label - tf stop_gradient (y_label / (logits **
2 bias))
mse_loss reduce_s_s (tf square (tf math. sqrt
suuuauuarr y.label) logits))
sun loss = tf reduce_ sum (tf... square (sun sun sun label
))
elif trans 'atan':
sun sun_label=tf
wawaabllt..stopgrreeeeeeo stop-gradient
y_label (tf. tan wtf.clffppp clip_byy balvalue (logits atan((0000)) )) + bias))
0.0, sse_loss tf reduce__u_uu (tf square (tf math atan y_label) logits))
sun loss tf reduce_ sum (tf.. equare(sur sun_label
))
elif trans == 'tanh'
label tf. stop_grddie (y_label / (tf math.
atanh (tf. cla.bbbyyyyaaluue (logits, 0.0, up. tanh (800))) ) bias))
mse mse_loss loss tf. reduce____su (tf. square (tf, math. tanh y_label) logits))
sun_loss tf reduce (tf. square
sun sun_label)
73
else:
raise NotInplonentedError
77
rank rank_loss0 loss0 _rank_loss (sun, sun_label)
78
rank lossl -ran_llass (logits, y y_label)
rank rank_lose loas
#+ rank cank_lossi
return {'los': mse_loss
sun_loss
82
2 "mse_ mase_loss?; mse_loss.
2 ssnn_loss" loss,
# "rank_loss":rank_
86
"gt_mean': ....ff.......... rewuceeeeeaaeeeeeeeeeeeeeeeeeeee
'sun.gt_mean'; tf rerrddce_mea (sun_ label), (aun__aabll)), 2 'sun_pree_mman'' re.ureuce_meann (sun), 'pred_mean't tf. reduee mean mea 'ori_pred_mean' reduce mean (ori_pred),
90
91
'pred': final_pred,
'g';: y_label. 2 ori orrippee''' ori_pred
95
96
else:
return {"pred"; final_pred, " "fused_pred": fused_pred, "ori_pred"; ori_pred]
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def gts_model (x, y_label, alp_units,
dropout, feat_num, feat_din rmask, imask, reuse, is_training, location= mse', k_func=0, trans= log', **kvargs):
104
with tf va.variable_scope ('gts', reuse=reuse)
33

---

005
embedding-paran tf. se.gge_variable feat_num feat_dim])
shape=[
106
feas ttf.nn.. embeddng
embedding.param (id (ids=x, params=
20, feat_dim
007
requests tf rf.reduce_sune "reduce_suu(feassl:
(feas(: :10, :] * tf expand_dims (
rmask, -1), 1) / re.reduce_sus (rmask, 1, Keepdims-True)
# avg pooling
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items tf. reduredece__eee sum (feas 10:, :] tf tf. ex.eepaadd_die
imask, -1), 1) / tf. tf. reduceec__aul suntuuce_smmmmsse (imask, 1, keepdims-True)
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feas = tf. concat (crequesss,ssss items], 1) # 2+sz,2ffeat_dnn # mlp, main branch
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drpt Dropout (rate=dropout) fc feas
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for idx, num_unit in enumerate (mlp_units);
fc = linear (fc, num_umit, f ('dense(idx)", reuse) fc re..nfrelu(fc)
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beining=is.trainie logits = linear (fc, 1, "output", reuse) fc feas
fc drpt
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for idx, num_unit in enumerate (mlp_units);
20
fe linear (fc, num_unit, ('dense_suniddx" reuse)
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fc tn.nn. reln
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fc = drpt training=is. tasiiinitnnn))
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sun linear (fc, 1, "sun", reuse)
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assert location in ['mse', 'mae', 'mspe', 'mape'] assert k_func in [0, 1, 2] assert trans in ['log']
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if trans 'log':
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label tf. tf. 1) ori_pred = tf exp (logits)
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if location 'mse';
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location_loss
(tuuuu reauce_mean (tf. square (logits
label))
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elif location == 'mae':
docation_loss loss = tf reduce_ (tf abs (logits label))
elif location 'mspe':
38
location_loss tf reducedee_mmar (tf. square ((logits
label) / (label + 1)))
elif location == 'mape':
location_los losss re.reduce_men (tf abs ((logits label) (label 1)))
441
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if k_func -= 0: sun label tf grapenee ly_label * tf exp (-logits)
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y-pred tf exp (tf math minimum (10.0, logits)) tn. relu))un)
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elif k_funt == 1:
sun sun_label tf stop_gadieet (y_label / (1 + tf abs logits)))
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y-pred (1 tf abs
tf nn relu (sun)
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elif k. fufunc == 2:
sun_label tf stapige (y_label * tf abs (logits))
y-pred tf.nn df..n.ree relu / (1e-12+tf. abs (logitts) sun redurececmmmane square (sun sun_label))
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522
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loss = location_loss sun_loss
if is is_training: {'los': loss,
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# Frank_loss.
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'location_los l location,loss
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sunn_loss' soss,
34

---

139
# 'rank_loss' :
"gt_mean': tf reduce___mnan (ean(y_laaee)))) ssun_gt_mean tf. re..redue_mean (sun_ (eunneeeaann 'sun_pred_mean'
161
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re..ceeee_mea (sun),
16
'pred_mean': tf wew.uce_meanyy_ 'ori_pred_mean's tf re.uceuc__men (ori_pred), # 'grad_mainn_mbb" tf gradientd ([aun_loas] embedding.param))
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# 'grad_aun_emb'. tf. gradieddientt ([sun_ [[sun_loas],
embedding-param))
# gradd_min__ooitt" tf. gradients logits),
68
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'pred': y-pred,
gt':: y.label, ori-ppedd; ori-pred
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else: return ("pred": y-pred, "ori.pred"; ori-pred}
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def linear (inpute, units, name, reuse=None):
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with tf www.vaarallaapppppeeeeee (name, reuse=reuse)
input_dim inputs. get_shape () [-1] value
weights tf. t get_variablee
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'weights', shape= units], initializer=
he he_initializer)
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biases = tf.get_variable.
'biases", shape=[units], initializer=tf.
zeros_initializer())
884
outputs tf.matmul (inputs, weights) biases return outputs
885
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def _rank_loss (logits, labels):
189
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@params:
991
logits: (bsz
labels: (baz,1)
193
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pairwise_logits = logits tf. transpose (logits)
995
pairwise_mask tf greater (labels tf transpose (labels), 0)
pairwise_logits = bf.boolean_man (pairwise_
pairwise_mask)
997
pairise..puuo_labil. of.ones_lii like (pairvise_logits)
998
rank_loss - reddruuc__mean(t.. nn.
logiasspairriis__looiss
200
labelsspairriee.paddd. labels
201
))
202
# set rank loss to zero if batch has no positive sample. rank_lose tf. where (tf.is_ is_nnann (rank_loss), tf zeros_like rank_loash rank_loss)
004
return rank_loo loss
35

---

Code 2: Python codes for generating synthetic data.
import numpy as np
from scipy stats import beta, gamma, uniform, skew, truncnorm
n_samples 1000000 zero_inflate_ratio 0.8
def Emorraee_disttiiitiionoo distributions [] [(title, samples, mean, skewn, var, caption)]
(a) RS-C
d gamma (a=2, scale=1)
samples d.rv (n_
true_mean d. mean skewn d.stats (moments='s")
var - var
distributions appreennn.appedddeeoo (("Right- Senght-Skeee Skewed: samples, true_mean, akeun, var, (RS
(b) RS-BU
1o samples uniform (1oc=11, scale=10) rva (int (n_samples 0.9))
high_sample uniform (1oc=90 scale=10) (int (n_samples 0.1))
21 samples up concatenate (a1ore(((o______ee__ high_ samples] true_mean = 0.9 * 6 0.1 * 95
skewn (ske (samples))
var np var (samples)
25
distributions append (("Righ (eRight-Skewede Bii-Unifor"" samples,
aaprrbbtionn..ppedddll true_mean, skewn, var, 2 (b) URS-BU))
(c) RS-ZIG
28
base_samples gamma scale=1) rvs
29
zero mask = random rand (n_ samples) < zero inrrtiinnnatteratioo
samples base_samples (1 mask)
gamma scale=1) mean () (1
zoro_inflate_ratio)
32
skewn = skew ssempeapllss
var = up var (samples)
distributions append (( ("Right Skewed: : Inf.-naddlddanneee samples, true_mean, skewn, var, RR) ZIG
35
36
(d) LS-B
d beta(a=3, b=1.5) samples (n true_mean m) skewn tnstatt(mmmentss-....
40
var = var
distributions append (("Left- Seeeett-kkeed:: BBeta", samples, true_mean, skeun, var, (d))
43
44
(e) LS-BU
lo low_samples uniform (1oc=1, scale=10). rvs (int (n_samples 0.1))
high_samples uniform (1oc=90 scale-10) rvs (int (n_samples 0.9))
samples up concatenate (11o__ssp1sssssee high.samples]) true_mean = 0.1 * 6 0.9 95 skewn float (skew (samples))))) var np var var (samples)
51
distributions append ((" -eeeet-Skwwed::. ; ;,ii: Uniforr'""" samples, true_mean skevn, var, BB)
36

---

58 # (f) SM-U
uniform (loc=0, scale=100) samples d.v (n_saplles) true_mean d. mean
55
56
skewn d.stats (ecatssmmmenttta (moments='s')
- ()
distributions append ( ((" ("Symmetric: samples, true_mean skewn, var, (M-)))
60
(g) SM-TN
(0 50) / 10, (100 50) / 10
samples truncnorm (a, b, loc=50, scale=10) rvs (a_samlles) true_ment mean
64
skewn skev (samples)
= d. da ()
distributions apperd ( Styymettriciuuuuu-oooooo true_mean, skewn, var, (g) USM-TH))
samples,
68
# (h) SM-BU
sampsemeles iniform(oc=1,, scale-10) rvs (int (n_samples 0.5))
71
high_samples uniform (1ooor0 scale=10) rvs (int (n_samples 0.5))
samples up concatenaaae ((1ovssaaee high_ saghee]m) true_mean 0.5 skewn float (skew (samples)))))))
0.5 95
75
var = np. var (samples)
76
distributions aap.end (("Smmeetiicc :ii- samples, true_mean, skewn, var, (h) LMM-BU
return distributions
79
dist generate__dstrrbuttiirs. ()
37


Reviews:
[{"review_id": "wqwiDINAXF", "reviewer": "Reviewer_mPVQ", "summary": "TranSUN introduces a preemptive retransformation bias correction paradigm by jointly training a primary branch that predicts the transformed target and an auxiliary branch that learns a corrective factor, thereby achieving theoretically guaranteed unbiased regression with strong empirical convergence. The approach is further generalized into the GTS framework, enabling plug-and-play loss functions and correction schemes, and demonstrates substantial improvements across synthetic benchmarks, public datasets, and large-scale industrial A/B tests.", "questions": "The authors observe that while TranSUN improves outcome regression accuracy, it may degrade ranking performance, a phenomenon worthy of deeper investigation. In simplified ranking scenarios (e.g., pairwise comparisons), this reduces to a binary decision task, and prior work has shown that more accurate outcome regression does not necessarily lead to better decision quality. Could the authors elaborate on this point?", "limitations": "In the conclusion, the authors acknowledge key limitations, including the lack of evaluation on non-right-skewed distributions and the observed performance drop in ranking metrics such as XAUC.", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "S1: The research topic is valuable, as preemptive debiasing is indeed more practical than post-hoc correction methods that require substantial computational resources in industrial recommender systems.\nS2: The motivation behind TranSUN is clearly articulated, and the method is conceptually simple and easy to implement, yet supported by solid theoretical foundations. Moreover, the authors explicitly state the modeling assumptions and provide proofs for unbiasedness.\nS3: Extensive experiments are conducted on synthetic data, public datasets, and large-scale industrial A/B tests, offering solid empirical support for the method's effectiveness.\n\nW1: A key claimed advantage of TranSUN is its strong convergence properties. However, this is only demonstrated empirically, and no formal convergence analysis or theoretical guarantees (e.g., convergence rate bounds) are provided.\nW2: The theoretical guarantee of unbiasedness implicitly relies on the assumption that training and test data are independently and identically distributed (i.i.d.), which is not explicitly stated. In practice, if distribution shift occurs at deployment, the unbiasedness claim may no longer hold.\nW3: Beyond the i.i.d. assumption, achieving unbiasedness requires that the auxiliary model accurately estimates the correction factor (slope model). This implicitly assumes that the learned slope approximates the true ground-truth ratio, which is itself a non-trivial task.", "was_revised": true, "final_justification": "TranSUN tackles an important topic and shows promising empirical results, but key concerns remain. The claimed convergence is only demonstrated empirically, with no formal theoretical guarantees. The unbiasedness relies on i.i.d. assumptions and accurate correction factor estimation, both of which are not sufficiently addressed and may not hold in practice. These theoretical gaps limit the reliability and generalizability of the method.\nTherefore, I do not recommend acceptance.", "rebuttal": "We thank all the reviewers for their time and insightful feedback to help improve our work. We appreciate that the reviewers recognized our research problem as practically valuable and our method as simple, effective, theoretically grounded, and \"of broad practical potential\", supported by exhaustive validation. We have carefully considered all the comments and addressed them in this rebuttal, which will be incorporated into the revised version. If any further clarification is required, please do not hesitate to contact us. Below we address your questions (Q) and weaknesses (W).\n> ### Q1: The reason for the trade-off between point accuracy and XAUC\n\nHere we elaborate on the cause of the trade-off phenomenon between point accuracy and XAUC, and further highlight the limitations of XAUC. This limitation leads to the inconsistency between the offline XAUC metric and online business metrics (see Tab6), making XAUC no longer suitable for offline assessment. To address this, we supplemented offline evaluation with two more consistent offline metrics, high-value XAUC (L565-568, Tab 8) and a commonly used ranking metric NDCG, on both of which our model demonstrates superior performance. For clarity, let us start with a concrete case:\n 1. **A case of trade-off**: We first sample two inputs {x1, x2} ~ P(X), and then sample 3 groups of target y from P(Y|x1) and P(Y|x2) respectively, and let the samples be {3,3,3} ~ P(Y|x1) and {8,1,1} ~ P(Y|x2), and let T(x)=log(x). Then:\n\t- The LogMSE prediction is $f(x_1)=\\mathrm{T}^{-1}(\\mathbb{E}[\\mathrm{T}(\\mathrm{Y})|x_1])=\\exp((\\log(3)+\\log(3)+\\log(3))/3)=3$, $f(x_2)=\\mathrm{T}^{-1}(\\mathbb{E}[\\mathrm{T}(\\mathrm{Y})|x_2])=\\exp((\\log(8)+\\log(1)+\\log(1))/3)=2$, where $f(x_1)>f(x_2)$ and the bias occurs on the sample X=x2\n\t- The TranSUN/GTS prediction is $f(x_1)=\\mathbb{E}[\\mathrm{Y}|x_1]=(3+3+3)/3=3, f(x_2)=\\mathbb{E}[\\mathrm{Y}|x_2]=(1+1+8)/3=10/3$, where $f(x_1)<f(x_2)$\n\t- The descending ranking result of LogMSE is {3, 3, 3, 8, 1, 1}, with XAUC = 0.333, NRMSE = 0.324, and TRE = 4/15, while the result of TranSUN/GTS is {8, 1, 1, 3, 3, 3}, with XAUC = 0.233, NRMSE = 0.301, and TRE = 0. \n\t- It is observed that **a trade-off occurs** between point accuracy (NRMSE, TRE) and XAUC, i.e. TranSUN/GTS achieves better point accuracy (NRMSE, TRE) while XAUC worsens.\n 2. **Root cause of the trade-off:**  \n\t - TranSUN/GTS compensates underestimation brought by retransformation bias, resulting in better point and rank accuracy of high-value samples  (e.g., for sample $(x_2,8)$, relative error improves from 0.75 to 0.58, and its rank order moves from 4th to 1st, consistent with results on Indus Top(Tab8)), which significantly improves the overall point accuracy (e.g. improvements in NRMSE & TRE in the case) since these metrics are **value-aware** (i.e. metric calculation aware of absolute value of sample label)\n\t -  Correcting retransformation bias also leads to some hard low-value samples being overestimated (e.g., predictions for the two samples $(x_2,1)$ increase from 2 to 10/3, consistent with Fig3c), which dominates the overall XAUC drop since there are far more hard low-value samples than high-value ones in highly right-skewed data and XAUC metric is **value-agnostic** (i.e. metric calculation only aware of the relative rank order of sample label but not aware to its absolute value)\n3. **Overall XAUC is inconsistent with online metrics, thus we use high-value XAUC and NDCG**: \n\t- The core goal of a recommender system is to improve online business metrics, while XAUC is merely an intermediate metric. For business target modeled by regression (GMV, watch time, etc.), the event of ranking high-valued samples in the correct position is far more important for online metrics than that of low-valued samples. However, these two events are equally weighted (value-agnostic) in the calculation of XAUC, thereby being dominated by abundant low-valued samples when data are highly right-skewed, which probably contribute only a small portion of online metrics (e.g. 70% of the top low-valued samples contribute only 20% of GMV in Indus). Therefore, overall XAUC is no longer consistent with online metrics\n\t- To address this, we supplemented the offline assessment with a more consistent metric, high-value XAUC (L565-568, Tab8), based on which we achieved improved online results (Tab6). Additionally, NDCG also addresses XAUC's limitation, so we also provide their results. In the table below, NDCG is computed within all samples (NDCG@all) and the top 10% high-value ones (NDCG@10%) respectively. Key observations include: 1) TranSUN performs better in NDCG@all than in XAUC since NDCG is more robust to low-value samples. 2) TranSUN shows superior performance in NDCG@10%, consistent with the reasons described in the 2nd point\n\n| Model | NDCG@all (CIKM16) | NDCG@10%(CIMK16) | NDCG@all (DTMart) | NDCG@10% (DTMart) |\n|---|:---:|:---:|:---:|:---:|\n| MSE | 0.9180 | 0.5201 | 0.9770 | 0.9692 |\n| MAE | 0.9497 | 0.5654 | 0.9867 | 0.9665 |\n| LogMSE | 0.9498 | 0.5517 | 0.9960 | 0.9736 |\n| WLR | 0.9475 | 0.5433 | 0.9693 | 0.9609 |\n| ZILN | 0.9485 | 0.5781 | 0.9963 | 0.9756 |\n| MDME | 0.9391 | 0.5671 | 0.9763 | 0.9639 |\n| TPM | 0.9502 | 0.5888 | 0.9960 | 0.9772 |\n| CREAD | **0.9504** | 0.5881 | 0.9962 | 0.9774 |\n| OptDist | 0.9500 | 0.5852 | 0.9965 | 0.9770 |\n| **LogSUN** | 0.9499 | **0.5904** | **0.9967** | **0.9779** |\n\n> ### W1: Lack of convergence analysis for $L_{sun}^{\\mathrm{T}}$\n\nWe add the convergence analysis:\n1. For convergence rate bound, T-MSE (Eq2) = $L_{sun}^{\\mathrm{T}}$ (Eq4) = MSE: Under the Lipschitz assumption, since the loss formulations of $L_{sun}^{\\mathrm{T}}$, MSE, and T-MSE are all squared errors, the theoretical convergence rate bound using SGD is $O(\\frac{1}{\\sqrt{K}})$, where $K$ is update iteration number, according to [1]. \n2. **For convergence smoothness, T-MSE > L_{sun} > MSE**: The key difference in the convergence performance of $L_{sun}^{\\mathrm{T}}$, MSE, and T-MSE lies in their smoothness. This is because the variance and the outlier proportion of the target are different, resulting in optimization landscapes with different degrees of smoothness. The table below shows the target variance (Var), the variance divided by squared expectation (V/E2), and the outlier proportion (Outlier%) outside of 3 times the standard deviation when T(x)=log(x). As shown, the target of $L_{sun}^{\\mathrm{T}}$ has a smaller variance and a better outlier distribution than the vanilla MSE, thus $L_{sun}^{\\mathrm{T}}$ converges more smoothly (Fig1). Therefore, TranSUN/GTS essentially decomposes a hard task into two easier and smoother tasks\n\n| Loss (CIKM16) | Var | V/E2 | Outlier% |\n|---|:---:|:---:|:---:|\n| MSE | 16440 | 0.41 | 1.03% |\n| $L_{sun}^{\\mathrm{T}}$ | 0.63 | 0.36 | 0.59% |\n| LogMSE | 0.62 | 0.02 | 0.29% |\n\n| Loss (Indus) | Var | V/E2 | Outlier% |\n|---|---|---|---|\n| MSE | 97494.16 | 12.10 | 0.78% |\n| $L_{sun}^{\\mathrm{T}}$ | 2.327 | 0.93 | 0.32% |\n| LogMSE | 1.87 | 0.15 | 0.28% |\n\n> ### W2: Unbiasedness relies on I.I.D. assumption\n\nWe beg to differ.\n1. Theoretical unbiasedness in our paper defines that the model prediction f(x0) for any training sample x0 is equal to the conditional expectation E(Y|x0) under the distribution of the training data (Eq13). So our unbiasedness is completely independent to the distribution of the test data (e.g. whether the training-test distribution violates IID).\n2. IID violation is a problem that neither TranSUN nor any existing post-hoc debiasing and calibration methods can address, and is completely beyond the scope of this paper.\n\nWe will clarify this in the revised version.\n\n> ### W3: Unbiasedness requires that the ratio estimation is accurate, which is non-trivial\n\nOne point needs clarification: theoretical unbiasedness is an intrinsic theoretical property of TranSUN/GTS and is unaffected by model convergence (L164-165). An example is that the theoretically unbiased MSE fails to converge when modeling high-skewed data, exhibiting quasi-biased performance (Fig1, Tab7). Therefore, I understand your underlying concern is the difficulty of learning the non-trivial ratio estimation task. Regarding this:\n\n 1. **The task is easier** for model than the vanilla MSE, since $L_{sun}^{\\mathrm{T}}$ can converge much smoother than the vanilla task (according to the reply to W1), which was also carefully selected from three bias modeling schemes (Tab5, Fig3a&b)\n 2. The comparisons with post-hoc debiasing and calibration methods (Tab4) show that the model is **indeed capable of grasping this task**\n\nWe will clarify this in the revised version.\n\n# Ref\n\n[1] Bottou L et al. Optimization methods for large-scale machine learning. 2018"}, {"review_id": "bH3F3E0FLh", "reviewer": "Reviewer_Fv4e", "summary": "This paper addresses the retransformation bias problem in regression models, which is especially important in recommender systems where data is highly skewed. The authors propose TranSUN, a preemptive method that eradicates this bias intrinsically during training. TranSUN augments standard model with an auxiliary branch that jointly learns a correction factor, ensuring the final prediction is an unbiased estimate of the target's expectation. The paper further generalizes this idea into the Generalized TranSUN (GTS) framework, which reveals that the core mechanism for unbiasedness is \"conditional linearity\" and provides a flexible approach to debias various regression models. The method's effectiveness is demonstrated on synthetic and real-world datasets, with a successful large-scale deployment in two recommendation scenarios on e-commerce platform.", "questions": "See weakness", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "### Strengths\n1. **Practical Problem:** The paper tackles retransformation bias, a theoretically well-known but practically critical issue in industrial recommender systems that directly impacts the accuracy of predicted values like GMV or user engagement. \n\n2. **Theoretically Sound Method:** The proposed TranSUN method is simple yet effective, and its claim of unbiasedness is supported by theoretical derivations. The generalization to the GTS framework provides a deeper understanding of the solution space. \n3. **Comprehensive Evaluation:** The experimental validation is quite comprehensive.\n    (1) The use of synthetic data with diverse distributions demonstrates the bias in baselines and the unbiasedness of the proposed method.\n    (2) The experiments on public and a large-scale proprietary industrial dataset show consistent and significant improvements in bias-related metrics (TRE, MRE) and often in standard regression metrics (NRMSE, NMAE).\n    (3) The successful, large-scale online A/B test with significant GMV lift shows promising real-world impact.\n\n### Weaknesses\n1. **Lack of Efficiency Analysis:** The paper introduces an auxiliary model branch, which presumably adds computational overhead. While Table 13 explores architectural choices, it focuses on accuracy, not efficiency. \n\n2. **Limited Discussion on Ranking Performance Trade-off:** The results (e.g., Table 7) show that while the method improves value prediction, it can sometimes lead to a slight decrease in ranking performance (XAUC). The authors acknowledge this as a limitation, but a deeper discussion would be beneficial. For example, why does correcting for value bias sometimes harm the relative ordering of items? The fact that XAUC improves for high-value items on the Indus dataset (Table 8) is an interesting counterpoint that is not fully explored. A more thorough analysis of this trade-off would be valuable.", "was_revised": false, "final_justification": "", "rebuttal": "We thank all the reviewers for their time and insightful feedback to help improve our work. We appreciate that the reviewers recognized our research problem as practically valuable and our method as simple, effective, theoretically grounded, and \"of broad practical potential\", supported by exhaustive validation. We have carefully considered all the comments and addressed them in this rebuttal, which will be incorporated into the revised version. If any further clarification is required, please do not hesitate to contact us. Below we address your questions (Q) and weaknesses (W).\n> ### W1: Lack of efficiency analysis in Tab13\n\nIn the table below, we supplemented Tab13 with TranSUN's additional memory (Mem) and computational overhead (MFLOPS), and calculated the relative increase (OH) compared with T-MSE. As shown, the only-sharing-embedding architecture scheme is the most cost-effective, maintaining optimal performance while introducing much little overhead.\n\n| Archs on CIKM16 | Mem (MB) | OH (%) | MFLOPS | OH (%) |\n|---|:---:|:---:|:---:|:---:|\n| 0/1 Emb + 0/3 MLP | 610.46 | 100.00 | 350.86 | 100.00 |\n| **1/1 Emb + 0/3 MLP** | **305.29** | **0.02** | **190.52** | **8.60** |\n| 1/1 Emb + 1/3 MLP | 305.27 | 0.01 | 186.12 | 6.09 |\n| 1/1 Emb + 2/3 MLP | 305.24 | 0.00 | 177.62 | 1.25 |\n| 1/1 Emb + 3/3 MLP | 305.23 | 0.00 | 175.47 | 0.02 |\n\nWe also provide additional information on the resource overhead associated with the online TranSUN model in the e-commerce platform's recommendation system, which achieves a **high ROI** measure (with Tab6):\n1. **Training**: Under the same resources (800 workers), the update iteration (global step) number per second of LogMSE and TranSUN  were 89.2 and 86.8, respectively. Therefore,  applying TranSUN only reduces the training speed by 2.7%, with the training time increased by 2.78%.\n2. **Inference**: The mean and p99 latency of the LogMSE were 27.8ms and 49.8ms, respectively, while the mean and p99 latency of TranSUN were 28.1ms and 51.6ms, respectively.\n3. **Deployment**: In the online service with 300 million daily active users, deploying TranSUN did not increase CPU resources and only increased GPU resources by 5%.\n\n> ### W2: Limited discussion on the trade-off between point accuracy and XAUC\n\nHere we elaborate on the cause of the trade-off phenomenon between point accuracy and XAUC, and further highlight the limitations of XAUC. This limitation leads to the inconsistency between the offline XAUC metric and online business metrics (see Tab6), making XAUC no longer suitable for offline assessment. To address this, we supplemented the offline evaluation with two more consistent offline metrics, high-value XAUC (L565-568, Tab 8) and a commonly used ranking metric NDCG, on both of which our model demonstrates superior performance. For clarity, let us start with a concrete case:\n 1. **A case of trade-off**: We first sample two inputs {x1, x2} ~ P(X), and then sample 3 groups of target y from P(Y|x1) and P(Y|x2) respectively, and let the samples be {3,3,3} ~ P(Y|x1) and {8,1,1} ~ P(Y|x2), and let T(x)=log(x). Then:\n\t- The LogMSE prediction is $f(x_1)=\\mathrm{T}^{-1}(\\mathbb{E}[\\mathrm{T}(\\mathrm{Y})|x_1])=\\exp((\\log(3)+\\log(3)+\\log(3))/3)=3$, $f(x_2)=\\mathrm{T}^{-1}(\\mathbb{E}[\\mathrm{T}(\\mathrm{Y})|x_2])=\\exp((\\log(8)+\\log(1)+\\log(1))/3)=2$, where $f(x_1)>f(x_2)$ and the bias occurs on the sample X=x2\n\t- The TranSUN/GTS prediction is $f(x_1)=\\mathbb{E}[\\mathrm{Y}|x_1]=(3+3+3)/3=3, f(x_2)=\\mathbb{E}[\\mathrm{Y}|x_2]=(1+1+8)/3=10/3$, where $f(x_1)<f(x_2)$\n\t- The descending ranking result of LogMSE is {3, 3, 3, 8, 1, 1}, with XAUC = 0.333, NRMSE = 0.324, and TRE = 4/15, while the result of TranSUN/GTS is {8, 1, 1, 3, 3, 3}, with XAUC = 0.233, NRMSE = 0.301, and TRE = 0. \n\t- It is observed that **a trade-off occurs** between point accuracy (NRMSE, TRE) and XAUC, i.e. TranSUN/GTS achieves better point accuracy (NRMSE, TRE) while XAUC worsens.\n 2. **Root cause of the trade-off:**  \n\t - *Reason for the improvement of high-value XAUC & overall point accuracy metric*: TranSUN/GTS compensates underestimation brought by retransformation bias, resulting in better point and rank accuracy of high-value samples  (e.g., for sample $(x_2,8)$, relative error improves from 0.75 to 0.58, and its rank order moves from 4th to 1st, consistent with results on Indus Top(Tab8)), which significantly improves the overall point accuracy (e.g. improvements in NRMSE & TRE in the case) since these metrics are **value-aware** (i.e. metric calculation aware of absolute value of sample label)\n\t -  *Reason for the drop of overall XAUC*: Correcting retransformation bias also leads to some hard low-value samples being overestimated (e.g., predictions for the two samples $(x_2,1)$ increase from 2 to 10/3, consistent with Fig3c), which dominates the overall XAUC drop since there are far more hard low-value samples than high-value ones in highly right-skewed data and XAUC metric is **value-agnostic** (i.e. metric calculation only aware of the relative rank order of sample label but not aware to its absolute value)\n3. **Overall XAUC is inconsistent with online metrics, thus we use high-value XAUC and NDCG**: \n\t- The core goal of a recommender system is to improve online business metrics, while XAUC is merely an intermediate metric. For business target modeled by regression (GMV, watch time, etc.), the event of ranking high-valued samples in the correct position is far more important for online metrics than that of low-valued samples. However, these two events are equally weighted (value-agnostic) in the calculation of XAUC, thereby being dominated by abundant low-valued samples when data are highly right-skewed, which probably contribute only a small portion of online metrics (e.g. 70% of the top low-valued samples contribute only 20% of GMV in Indus). Therefore, overall XAUC is no longer consistent with online metrics\n\t- To address this, we supplemented the offline assessment with a more consistent metric, high-value XAUC (L565-568, Tab8), based on which we achieved improved online results (Tab6). Additionally, NDCG also addresses XAUC's limitation, so we also provide their results. In the table below, NDCG is computed within all samples (NDCG@all) and the top 10% high-value ones (NDCG@10%) respectively. Key observations include: 1) TranSUN performs better in NDCG@all than in XAUC since NDCG is more robust to low-value samples. 2) TranSUN shows superior performance in NDCG@10%, consistent with the reasons described in the 2nd point\n\n| Model | NDCG@all (CIKM16) | NDCG@10%(CIMK16) | NDCG@all (DTMart) | NDCG@10% (DTMart) |\n|---|:---:|:---:|:---:|:---:|\n| MSE | 0.9180 | 0.5201 | 0.9770 | 0.9692 |\n| MAE | 0.9497 | 0.5654 | 0.9867 | 0.9665 |\n| LogMSE | 0.9498 | 0.5517 | 0.9960 | 0.9736 |\n| WLR | 0.9475 | 0.5433 | 0.9693 | 0.9609 |\n| ZILN | 0.9485 | 0.5781 | 0.9963 | 0.9756 |\n| MDME | 0.9391 | 0.5671 | 0.9763 | 0.9639 |\n| TPM | 0.9502 | 0.5888 | 0.9960 | 0.9772 |\n| CREAD | **0.9504** | 0.5881 | 0.9962 | 0.9774 |\n| OptDist | 0.9500 | 0.5852 | 0.9965 | 0.9770 |\n| **LogSUN** | 0.9499 | **0.5904** | **0.9967** | **0.9779** |"}, {"review_id": "CCitwpRDsR", "reviewer": "Reviewer_1oaS", "summary": "This paper focuses on addressing the **re-transformation bias** issue in regression models for recommendation systems. This problem arises when functions like the logarithm are used to transform target values with skewed distributions (e.g., GMV) to stabilize training. When the model's predictions are transformed back to the original scale, a systematic bias is introduced. The authors propose a \"proactive\" method called **TranSUN**, which introduces a jointly trained auxiliary model branch to learn and correct this bias from the ground up, thereby theoretically guaranteeing an unbiased prediction. This method is further generalized into the **GTS (Generalized TranSUN)** framework, providing a universal approach for designing unbiased regression models. The paper validates the effectiveness of its method through synthetic data, public datasets, and a large-scale online A/B test on a leading e-commerce platform.", "questions": "1. **On the Root Cause of Ranking Performance Degradation:** You mentioned that the decrease in XAUC is an acceptable trade-off. Could you please elaborate on why a method designed for more \"accurate\" predictions leads to a decline in ranking ability? Does this imply that the model, in correcting for large biases on a few high-value samples, sacrifices its ranking discrimination for the majority of samples? Would this limit its general applicability? Additionally, you mentioned that a part of it increased; could you explain what happened there? You state the drop in XAUC is \"acceptable given the improvement on TRE\" (§5.2). Does this imply unbiasedness hurts ranking? Please analyze the correlation between prediction error reduction (TRE) and ranking metrics (XAUC) to clarify this trade-off.\n2. **Comparison with Direct Probabilistic Modeling Methods:** Your method can be viewed as a sophisticated correction to a Gaussian distribution assumption. How do you see it comparing to methods that directly model p(y|x) using more powerful distributional assumptions (e.g., via MDNs or Normalizing Flows)? The latter can obtain unbiased expected predictions in one step without introducing extra tricks like `stop_grad` or auxiliary networks. In your view, what advantages does TranSUN offer over these methods (e.g., in terms of training stability, computational overhead, ease of integration)?\n3. Can you prove that the linear transformation assumption (Eq. 11) holds under non-Gaussian noise or multi-modal target distributions (e.g., RS-BU in Fig. 2)? If not, what are the theoretical guarantees when this assumption is violated?\n4. **Necessity of the GTS Framework:** You generalized TranSUN to the GTS framework. However, the experimental section mainly validates TranSUN and its variants. Beyond theoretical elegance, what unique and validated practical value does the GTS framework offer beyond TranSUN? Is there a specific scenario where standard TranSUN would fail, and one must leverage the GTS framework to design a specific, non-trivial instance to solve the problem?\n5. How much additional training time and computational cost does TranSUN introduce during training? Is this mentioned in the paper? Could you provide an example to give a concrete sense of the scale? Does this impact computational performance and speed in industrial scenarios? The auxiliary branch (Eq. 4) and dynamic slope (Eq. 9) inevitably add computational load. Please quantify: (a) the inference latency (in ms) of TranSUN vs. LogMSE on the Indus dataset, and (b) the extra CPU/GPU resources consumed during online serving at the scale of over 300 million DAU.\n6. Are there principled guidelines for determining the optimal $L_v$ (e.g., MAE for right-skewed data) and $\\Psi$ functions, or is manual trial-and-error the only way? Does this limit the method's applicability in resource-constrained environments?", "limitations": "Yes. The authors discuss limitations in Section 6. However, I believe the discussion of the core limitation—the degradation in ranking performance (XAUC)—is too understated. The authors attribute it to the \"no free lunch\" theorem but fail to sufficiently explore the severity of this issue. For a paper on recommendation systems, harming the core ranking metric is a very serious problem. This needs to be discussed more explicitly and deeply as a core limitation, with an analysis of how it restricts the method's scope of application.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**Pros:**\n\n1. **Addresses a Practical Problem:** The paper accurately identifies and solves a concrete technical problem prevalent in the industry (especially in e-commerce, video streaming, etc.). Eliminating systematic bias has clear business value for scenarios requiring precise prediction of business metrics (e.g., GMV, user watch time). The paper introduces an auxiliary branch to learn the bias, supervised by a multiplicative bias modeling scheme aimed at capturing the ratio between predicted and true values. This approach tackles the model performance degradation caused by right-skewed data distributions in real-world applications and provides a detailed theoretical foundation.\n2. **Exhaustive Experimental Validation:** The experimental work in this paper is very solid, particularly the evaluation on large-scale industrial datasets and the successful deployment in an online A/B test. This directly proves the method's utility and effectiveness in specific business scenarios. This is the most commendable part of the paper. The method is not limited to e-commerce platforms and can be applied to recommendation systems in various other domains, showing its broad practical potential.\n\n**Cons:**\n\n1. **Limited Research Paradigm and Problem Significance:** Although re-transformation bias exists, it is fundamentally a product of the traditional \"predict-then-rank\" paradigm. Compared to concurrent cutting-edge research in recommendation systems, this paradigm itself is being challenged. Much of the frontier work is shifting towards **end-to-end Learning-to-Rank** frameworks that directly optimize ranking metrics (like NDCG). These frameworks may not rely on precise point estimates of continuous values from the outset, thus naturally circumventing the re-transformation bias problem. From this perspective, the paper's effort to patch a problem within a specific paradigm makes its significance and novelty relatively limited.\n2. The study primarily relies on TRE and MRE as core unbiasedness metrics (§5.1), justifying their necessity through the derivations in Appendix C.2.2 (Eq. (21)-(22)). However, these metrics are necessary but not sufficient conditions for unbiasedness: even if they reach their optimal value (zero), it does not guarantee the absence of bias across all data subgroups. For instance, systematic prediction errors might persist in local data distributions undetected by TRE/MRE.\n3. **Limited Methodological Innovation:** The core idea of TranSUN—introducing an auxiliary network to learn a correction term—is not uncommon in the broader machine learning field. It can be seen as a direct application of residual fitting, the **boosting idea** from ensemble learning, or an auxiliary task that provides corrections for a primary task in multi-task learning. The authors have skillfully applied it to the specific problem of re-transformation bias, but its methodological originality is relatively modest.\n4. **At the Cost of Core Ranking Performance:** This is one of the paper's weaknesses. The paper explicitly states that while the method improves the accuracy of point estimates, it harms the core task of the recommendation system—its ranking ability (as indicated by the drop in the XAUC metric). The authors acknowledge this trade-off but fail to provide an effective solution or an in-depth analysis of its causes, which may make the method unacceptable in the vast majority of recommendation scenarios where ranking performance is the priority.\n5. **Gap with Frontier Probabilistic Modeling Methods:** Compared to contemporary research, the paper's reliance on a \"transform-correct\" method appears somewhat conservative. Currently, using deep probabilistic models like **Mixture Density Networks (MDNs) or Normalizing Flows** to directly model the complex, skewed raw data distribution p(y|x) has become a significant research direction. These methods can directly and unbiasedly compute the conditional expectation E[y|x] and provide richer probabilistic information (such as uncertainty), fundamentally avoiding the re-transformation problem. In contrast, TranSUN/GTS remains a point estimation model, lagging behind these advanced methods in terms of model expressiveness and the richness of its output information.\n6. While the paper highlights that TranSUN is deployed on an e-commerce platform with over 300 million daily active users (DAU) (§5.2), it fails to quantify the computational overhead introduced by its key components: the auxiliary branch (Eq. 4) and the dynamic slope (Eq. 9). Crucially, the paper does not provide a comparison of inference latency against baseline methods.", "was_revised": true, "final_justification": "The authors have resolved most of my concerns. I decided to keep my score.", "rebuttal": "We thank all the reviewers for their time and insightful feedback to help improve our work. We appreciate that the reviewers recognized our research problem as practically valuable and our method as simple, effective, theoretically grounded, and \"of broad practical potential\", supported by exhaustive validation. We have carefully considered all the comments and addressed them in this rebuttal, which will be incorporated into the revised version. If any further clarification is required, please do not hesitate to contact us. Below we address your questions (Q) and weaknesses (W).\n\n> ### W1: Limited research paradigm & problem significance\n\nWe beg to differ. ***As currently all large-scale recommender systems adopt \"predict-then-rank\" paradigm, our research problem on point accuracy has high practical value.*** This is because such platforms serve plentiful business targets (clicks, pays, duration, etc.) & types (products, videos, ads, etc.), which are diverse & frequently updated, making unifying them into an e2e LTR framework impractical. The practical approach is to first model each business type & target separately in ranking stage, then unify them in a upstream re-ranking stage where they compete with each other for traffics. For fair competition, two core demands arise: 1) alignment of values across business types; 2) target score must match real value for physical definition. Both require point accuracy. Under this background, impactful works (e.g. SIR [1] in calibration topic) have emerged in industry.\n\n> ### W2: TRE and MRE are just necessary conditions\n\nThis concern is addressed in detail in L588-606. In short, we first examine TRE and MRE to detect model bias, then compare NRMSE (a necessary and sufficient condition) to identify the best unbiased model.\n\n> ### W3: The core idea of TranSUN is residual fitting, whose originality is relatively modest\n\nWe beg to differ. Our method's true spirit is **conditional linearity**, i.e. treating the original model $f$ as a conditional slope generator and applying \"piecewise\" linear transformation on target $y$ in the \"residual\" branch, which is what we deeply hope readers take away. As discussed in L135-141, bias learning/residual fitting is only a superficial description of TranSUN and does not ensure theoretical unbiasedness. For instance, the $L_{sun}^{\\mathrm{T}}$ variant in Eq14 is also residual fitting but is not theoretically unbiased (L502-506, Tab5).\n\n> ### W4&Q1: At the cost of core ranking performance & Root cause of XAUC degradation\n\nFirst, we clarify that ***the only core goal of recommender system is online business metric***. The observed inconsistency (offline XAUC drops while online metric improves (Tab6)) shows that ***XAUC is no longer suitable for offline evaluation***. Next, we elaborate on the cause of the trade-off between point accuracy and XAUC, and highlight XAUC's limitation. To address this, we adopted two more consistent offline metrics, high-value XAUC (L565-568, Tab 8) and a common rank metric NDCG, on which our model exhibits superior performance. For clarity, we start with a case:\n1. **Trade-off case**: We first sample inputs {x1, x2} ~ P(X), then sample 3 target y from P(Y|x1) and P(Y|x2) respectively: {3,3,3} ~ P(Y|x1), {8,1,1} ~ P(Y|x2), and let T(x)=log(x). Then:\n\t- LogMSE prediction is $f(x_1)=\\mathrm{T}^{-1}(\\mathbb{E}[\\mathrm{T}(\\mathrm{Y})|x_1])=\\exp((\\log(3)+\\log(3)+\\log(3))/3)=3$, $f(x_2)=\\mathrm{T}^{-1}(\\mathbb{E}[\\mathrm{T}(\\mathrm{Y})|x_2])=\\exp((\\log(8)+\\log(1)+\\log(1))/3)=2$; here f(x1)>f(x2), bias on X=x2\n\t- TranSUN/GTS prediction is $f(x_1)=\\mathbb{E}[\\mathrm{Y}|x_1]=(3+3+3)/3=3, f(x_2)=\\mathbb{E}[\\mathrm{Y}|x_2]=(1+1+8)/3=10/3$; f(x1)<f(x2)\n\t- LogMSE's descending ranking result is {3, 3, 3, 8, 1, 1}, XAUC = 0.333, NRMSE = 0.324, TRE = 4/15; TranSUN/GTS's is {8, 1, 1, 3, 3, 3}, XAUC = 0.233, NRMSE = 0.301, TRE = 0\n\t- Thus, **a trade-off occurs** : TranSUN/GTS achieves better point accuracy (NRMSE, TRE) while XAUC worsens\n 2. **Root cause**:  \n\t - TranSUN/GTS corrects underestimation from RetransBias, improving point & rank accuracy of high-value samples  (e.g.  (x2,8): relative error 0.75 → 0.58, rank 4th → 1st, as in Tab8 (Indus Top)), which boosts the overall point accuracy (e.g. NRMSE & TRE gains in case) since these metrics are **aware of label's absolute value**\n\t -  Correction also overestimates some hard low-value samples (e.g. two (x2,1)'s pred rise from 2 to 10/3, as in Fig3c), dominating overall XAUC drop since such samples far outnumber high-value ones in highly right-skewed data and XAUC metric is **only aware of label's relative rank but not of its absolute value**\n3. **Overall XAUC is inconsistent with online metrics, thus we use high-value XAUC and NDCG**: \n\t- The core goal of recommender system is to improve online metrics, while XAUC is an intermediate metric. For regression targets (GMV, time, etc.), correctly ranking high-value samples matters much more than low-value ones for online metrics. However, XAUC weighs both equally (value-agnostic), so in right-skewed data, low-value samples dominate XAUC but contribute little online (e.g. 70% low-valued samples bring only 20% GMV in Indus). Thus, overall XAUC fails to align with online metrics\n\t- To address this, we supplement with a more consistent metric, high-value XAUC (L565-568, Tab8), based on which we achieved improved online results (Tab6). NDCG also addresses XAUC's limitation, so we further attach its results. In the table below, NDCG is computed for all samples (NDCG@all) and the top 10% high-value ones (NDCG@10%). Key observations: 1) TranSUN performs better in NDCG@all than in XAUC, as NDCG is more robust to low-value samples. 2) TranSUN shows superior performance in NDCG@10%, consistent with the 2nd point\n\n| Model | NDCG@all (CIKM16) | NDCG@10%(CIMK16) | NDCG@all (DTMart) | NDCG@10% (DTMart) |\n|---|:---:|:---:|:---:|:---:|\n| MSE | 0.9180 | 0.5201 | 0.9770 | 0.9692 |\n| MAE | 0.9497 | 0.5654 | 0.9867 | 0.9665 |\n| LogMSE | 0.9498 | 0.5517 | 0.9960 | 0.9736 |\n| WLR | 0.9475 | 0.5433 | 0.9693 | 0.9609 |\n| ZILN | 0.9485 | 0.5781 | 0.9963 | 0.9756 |\n| MDME | 0.9391 | 0.5671 | 0.9763 | 0.9639 |\n| TPM | 0.9502 | 0.5888 | 0.9960 | 0.9772 |\n| CREAD | **0.9504** | 0.5881 | 0.9962 | 0.9774 |\n| OptDist | 0.9500 | 0.5852 | 0.9965 | 0.9770 |\n| **LogSUN** | 0.9499 | **0.5904** | **0.9967** | **0.9779** |\n\n> ### W5&Q2: Gap & Comparison with probabilistic modeling methods (PMM), e.g. MDN, NF\n\nWhen GTS serves as a point estimator, we acknowledge that PMM offers richer probability information. However:\n\n1. Inspired by your comment, GTS can, with minor changes (modeling $\\sigma$ in Eq11 as a function of $x$), model P(Y|x) in the CTM[2] manner. Specifically, GTS’s assumption becomes:  $-z(x)+Y_x*\\kappa(\\mathbb{Q})*s(x)\\sim N(0,1)$, where $s(x)>0$ is the inverse of the std. GTS can then learn P(Y<v|x) using CTM loss formulas (Eq12 in CLTM[3]). Detailed derivation will be added to the appendix.\n\n2. As a point estimator, GTS has three advantages over PMM:\n\n\t- **Flexibility**: It can be flexibly plugged into any model with minor revision (L172-176, Tab9). Another advantage is that in industrial practice TranSUN can be fully warmed-up from the online base model, further accelerating TranSUN's convergence\n\t- **Lightweight**: It requires much less resource than PMM. For example, MDN’s overhead grows linearly with mixture components, and NF incurs significant overhead due to Jacobian computations\n\t- **Training stability**: PMM is much harder to converge than GTS given their complex assumptions. For example, on Indus, OptDist[4] (an MDN case) needs 2.13x the iterations TranSUN requires to reach batch-NRMSE=3.0\n\n> ### W6&Q5: Lack of overhead analysis\n\nWe provide resource overhead date for the online TranSUN model in the e-commerce platform's recommender system, which achieves a ***high ROI*** (with Tab6):\n1. **Training**: With 800 workers, LogMSE and TranSUN achieve 89.2 and 86.8 update iterations per second, respectively; thus, TranSUN reduces training speed by only 2.7% and increases training time by 2.78%\n2. **Inference**: LogMSE has mean/p99 latencies of 27.8ms/49.8ms, while TranSUN’s are 28.1ms/51.6ms\n3. **Deployment**: On a platform with 300 million DAU, TranSUN required no extra CPU and only 5% more GPU resources\n\n> ### Q3: What are the theoretical guarantees when Eq11 is violated\n\nAs noted in L164-165, violating the model assumption does not invalid its intrinsic theoretical unbiasedness. As shown in Tab1, TranSUN and MSE remain theoretically unbiased regardless of the real data distribution (L195-198)\n\n> ### Q4: Necessity of GTS\n\nAs a supplement to L169-176, we further discuss GTS's practical value beyond TranSUN.\n1. TranSUN can only be applied to T-MSE, while GTS to any regression model (Tab9)\n2. TranSUN may face convergence issues when model assumption is severely violated, though we haven't met this yet. In such cases, one can customize $\\mathbb{Q}$ and $\\kappa$ to better align its assumption with the real data distribution (L165-168), thereby improving convergence\n\n> ### Q6: Principled guidelines for GTS\n\nThe principled guideline is to align the model assumption (Eq11) as closely as possible with the real data, though this requires manual trial-and-error. Our experience is to first fit the data solely using a mainstream regression model as $\\mathbb{Q}$, then analyze the skewness and kurtosis of $Y*\\kappa(\\mathbb{Q})$ to select a suitable $\\kappa$ form, which determines the final GTS model. This significantly reduces training resources when tuning $\\kappa$. A more general methodology is left for future work (L341-342).\n\n# Ref\n[1] Deng et al. Calibrating user response predictions in online advertising. 2020\n\n[2] Hothorn et al. Conditional transformation model. 2014\n\n[3] Möst et al. Predicting birth weight with conditionally linear transformation models. 2016\n\n[4] Weng et al. Optdist: Learning optimal distribution for customer lifetime value prediction. 2024"}, {"review_id": "GWGmDbL28X", "reviewer": "Reviewer_xLUq", "summary": "This paper proposes a novel preemptive paradigm called TranSUN to address the long-neglected retransformation bias problem in regression models for recommender systems. TranSUN introduces a joint bias learning approach, ensuring theoretically guaranteed unbiasedness and superior empirical convergence. The paper also generalizes TranSUN into a generic regression model family, Generalized TranSUN (GTS), which offers more theoretical insights and serves as a flexible framework for developing various bias-free models. Extensive experiments demonstrate the superiority and broad applicability of the proposed methods.", "questions": "- How proposed method performs w.r.t other ranking metrics (such as NDCG .etc)? \n- How to theoretically explain the improvement on pairwise/listwise ranking metrics?\n- How to resolve  the aforementioned paradox between the high-skewed distribution and retransformation bias?", "limitations": "N/A", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- This paper is clearly written and well organized.\n- The retransformation bias is a crucial problem but neglected by most recommendation methods, so the motivation of this paper is interesting. \n- The experimental results are promising.\n\nConcerns:\n- In recommendation tasks, we often use pairwise or listwise ranking metrics (e.g. XAUC adopted by authors) for evaluation.  However, the function T can only affect the labels y in a pointwise manner (Eq.(1) in this paper), but not change their relative ranking orders( E[sign(y_1>y_2)] <=> E[sign(T(y_1)>T(y_2)] ). In this way, I wonder how the retransformation bias affect the model performance w.r.t the ranking metrics. I hope the authors could provide some theoretical justification on this point. Otherwise, we can reasonably speculate that the improvement on AUC does not stem from the proposed strategy, and thus its application scope might be limited.\n- By introducing T(y), the model can adapt the high-skewed distribution of y, but this operation leads to a Jensen gap (Eq.(3)). To fill this gap, the author proposes Eq.(9). However, the optimization of L_{sun} in Eq.(9) might also be affected by high-skewedness of y in turn. This seems to be a paradox.\n\n-----!!!\n\nIn the rebuttal phase, the response from the authors have resolved all my concerns above. Therefore, I intend to improve the rating of this paper.", "was_revised": true, "final_justification": "The authors' responses have clarified all my concerns. Therefore, I am now inclined to raise the evaluation score for this paper.", "rebuttal": "We thank all the reviewers for their time and insightful feedback to help improve our work. We appreciate that the reviewers recognized our research problem as practically valuable and our method as simple, effective, theoretically grounded, and \"of broad practical potential\", supported by exhaustive validation. We have carefully considered all the comments and addressed them in this rebuttal, which will be incorporated into the revised version. We would be grateful if you could reconsider our work in light of these explanations and the provided evidence. If any further clarification is required, please do not hesitate to contact us. Below we address your questions (Q) and weaknesses (W).\n> ### W1&Q2: Since retransformation bias (RB) does not change label rank order in the listwise manner, how does it affect XAUC?\n\nSince our model is trained in a pointwise manner, retransformation bias (RB) can affect the rank order of model predictions, which in turn affects the rank metrics. That is, $\\mathbb{E}[\\mathrm{Y}|x_1]<\\mathbb{E}[\\mathrm{Y}|x2] \\not \\Leftrightarrow \\mathrm{T}^{-1}(\\mathbb{E}[\\mathrm{T}(\\mathrm{Y})|x1])<\\mathrm{T}^{-1}(\\mathbb{E}[\\mathrm{T}(\\mathrm{Y})|x2])$. For clarity, let’s start with a case study, then we clarify the reasons for the improvement/drop of XAUC, and finally introduce how we address the relationship between XAUC and online metrics in real-world industrial recommendation systems.\n\n1. **Case study**: We first sample two inputs {x1, x2} ~ P(X), and then sample 3 groups of target y from P(Y|x1) and P(Y|x2) respectively, and let the samples be {3,3,3} ~ P(Y|x1) and {8,1,1} ~ P(Y|x2), and let T(x)=log(x). Then:\n\t- The LogMSE prediction is $f(x_1)=\\mathrm{T}^{-1}(\\mathbb{E}[\\mathrm{T}(\\mathrm{Y})|x_1])=\\exp((\\log(3)+\\log(3)+\\log(3))/3)=3$, $f(x_2)=\\mathrm{T}^{-1}(\\mathbb{E}[\\mathrm{T}(\\mathrm{Y})|x_2])=\\exp((\\log(8)+\\log(1)+\\log(1))/3)=2$, where $f(x_1)>f(x_2)$ and the bias occurs on the sample X=x2\n\t- The TranSUN/GTS prediction is $f(x_1)=\\mathbb{E}[\\mathrm{Y}|x_1]=(3+3+3)/3=3, f(x_2)=\\mathbb{E}[\\mathrm{Y}|x_2]=(1+1+8)/3=10/3$, where $f(x_1)<f(x_2)$\n\t- The descending ranking result of LogMSE is {3, 3, 3, 8, 1, 1}, with **XAUC = 0.333**, NRMSE = 0.324, and TRE = 4/15, while the result of TranSUN/GTS is {8, 1, 1, 3, 3, 3}, with **XAUC = 0.233**, NRMSE = 0.301, and TRE = 0\n\t- It is obviously observed that XAUC metric is affected by the retransformation bias problem\n 2. **Reason for the improvement of high-value XAUC**: TranSUN/GTS compensates underestimation brought by retransformation bias, resulting in better point and rank accuracy of high-value samples  (e.g., for sample $(x_2,8)$, relative error improves from 0.75 to 0.58, and its rank order moves from 4th to 1st, consistent with results on Indus Top(Tab8)), which significantly improves the overall point accuracy (e.g. improvements in NRMSE & TRE in the case) since these metrics are **value-aware** (i.e. metric calculation aware of absolute value of sample label)\n 3. **Reason for the drop of overall XAUC**: Correcting retransformation bias also leads to some hard low-value samples being overestimated (e.g., predictions for the two samples $(x_2,1)$ increase from 2 to 10/3, consistent with Fig3c), which dominates the overall XAUC drop since there are far more hard low-value samples than high-value ones in highly right-skewed data and XAUC metric is **value-agnostic** (i.e. metric calculation only aware of the relative rank order of sample label but not aware to its absolute value)\n3. **Overall XAUC is inconsistent with online metrics, thus we use high-value XAUC and NDCG**: \n\t- The core goal of a recommender system is to improve online business metrics, while XAUC is merely an intermediate metric. For business target modeled by regression (GMV, watch time, etc.), the event of ranking high-valued samples in the correct position is far more important for online metrics than that of low-valued samples. However, these two events are equally weighted (value-agnostic) in the calculation of XAUC, thereby being dominated by abundant low-valued samples when data are highly right-skewed, which probably contribute only a small portion of online metrics (e.g. 70% of the top low-valued samples contribute only 20% of GMV in Indus). Therefore, overall XAUC is no longer consistent with online metrics\n\t- To address this, we supplemented the offline assessment with a more consistent metric, high-value XAUC (L565-568, Tab8), based on which we achieved improved online results (Tab6). Additionally, NDCG also addresses XAUC's limitation, so we also provide their results (shown in the reply to Q1)\n\n> ### W2&Q3: The optimization of $L_{sun}^{\\mathrm{T}}$ in Eq(9) might also be affected by high-skewedness of y, which seems to be a paradox\n\nWe beg to differ. **The convergence smoothness of $L_{sun}^{\\mathrm{T}}$ is more superior than that of the vanilla MSE (using target y).** This is because the variance and the outlier proportion of the their targets are quite different, resulting in optimization landscapes with different degrees of smoothness. The table below shows the target variance (Var), the variance divided by squared expectation (V/E2), and the target outlier proportion (Outlier%) outside of 3 times the standard deviation of MSE, T-MSE, and $L_{sun}^{\\mathrm{T}}$, where T(x)=log(x). As shown, the target of $L_{sun}^{\\mathrm{T}}$ has a smaller variance and a better outlier distribution than the vanilla MSE, thus $L_{sun}^{\\mathrm{T}}$ converges more smoothly (Fig1). Taking a step back, even if the target formulation of $L_{sun}^{\\mathrm{T}}$ encounters convergence difficulties, it can be addressed by optimizing the $\\kappa$ function of GTS (L165-168). Therefore, TranSUN/GTS essentially decomposes a hard task into two easier and smoother tasks, rather than the paradox problem you mentioned.\n\n| Loss (CIKM16) | Var | V/E2 | Outlier% |\n|---|:---:|:---:|:---:|\n| MSE | 16440 | 0.41 | 1.03% |\n| $L_{sun}^{\\mathrm{T}}$ | 0.63 | 0.36 | 0.59% |\n| LogMSE | 0.62 | 0.02 | 0.29% |\n\n| Loss (Indus) | Var | V/E2 | Outlier% |\n|---|---|---|---|\n| MSE | 97494.16 | 12.10 | 0.78% |\n| $L_{sun}^{\\mathrm{T}}$ | 2.327 | 0.93 | 0.32% |\n| LogMSE | 1.87 | 0.15 | 0.28% |\n\n> ### Q1: Performance on NDCG\n\nWe provide the NDCG metric results of our TranSUN and other baselines on the CIKM16 test and DTMart test in the table below. NDCG is computed within all samples (NDCG@all) and the top 10% high-value ones (NDCG@10%) respectively. Key observations include: \n 1. TranSUN performs better in NDCG@all than in XAUC, probably because that NDCG is more robust to the low-value samples than XAUC\n 2. TranSUN shows superior performance in NDCG@10%, consistent with the 2nd reason stated in the reply to W1&Q2\n\n| Model | NDCG@all (CIKM16) | NDCG@10%(CIMK16) | NDCG@all (DTMart) | NDCG@10% (DTMart) |\n|---|:---:|:---:|:---:|:---:|\n| MSE | 0.9180 | 0.5201 | 0.9770 | 0.9692 |\n| MAE | 0.9497 | 0.5654 | 0.9867 | 0.9665 |\n| LogMSE | 0.9498 | 0.5517 | 0.9960 | 0.9736 |\n| WLR | 0.9475 | 0.5433 | 0.9693 | 0.9609 |\n| ZILN | 0.9485 | 0.5781 | 0.9963 | 0.9756 |\n| MDME | 0.9391 | 0.5671 | 0.9763 | 0.9639 |\n| TPM | 0.9502 | 0.5888 | 0.9960 | 0.9772 |\n| CREAD | **0.9504** | 0.5881 | 0.9962 | 0.9774 |\n| OptDist | 0.9500 | 0.5852 | 0.9965 | 0.9770 |\n| **LogSUN** | 0.9499 | **0.5904** | **0.9967** | **0.9779** |"}]

Author rebuttal:

Meta-review: This paper proposes TranSUN, a preemptive paradigm to intrinsically eradicate retransformation bias in regression models for recommender systems, along with its generalization (GTS), backed by solid theoretical guarantees, comprehensive experiments across synthetic, public, and industrial data, and successful deployment in real-world e-commerce scenarios.

The reviews highlight the work’s strengths: addressing a valuable and practically critical problem, with a simple yet effective method supported by strong theoretical foundations and extensive empirical validation. Key concerns raised by reviewers included convergence analysis of $L_{sun}^{T}$, the trade-off between point accuracy and ranking metrics (e.g., XAUC), efficiency overhead, reliance on the "predict-then-rank" paradigm, and comparisons with probabilistic modeling methods. After reading the rebuttal and discussions, I think the authors adequately addressed these concerns by supplementing theoretical analysis and experimental evidence. Although some extra concerns are raised during the discussion period, they are not highly related to the core novelty and scientific soundness of the paper. Overall, I recommend that this paper be accepted.
Decision: Accept (poster)