# Exploiting Sample Uncertainty for Domain Adaptive Person Re-Identification

Kecheng Zheng1, Cuiling Lan2, Wenjun Zeng2, Zhizheng Zhang1, Zheng-Jun Zha1†
This work was done when Kecheng Zheng was an intern at MSRA.Corresponding
Author

###### Abstract

Many unsupervised domain adaptive (UDA) person re-identification (ReID)
approaches combine clustering-based pseudo-label prediction with feature fine-
tuning. However, because of domain gap, the pseudo-labels are not always
reliable and there are noisy/incorrect labels. This would mislead the feature
representation learning and deteriorate the performance. In this paper, we
propose to estimate and exploit the credibility of the assigned pseudo-label
of each sample to alleviate the influence of noisy labels, by suppressing the
contribution of noisy samples. We build our baseline framework using the mean
teacher method together with an additional contrastive loss. We have observed
that a sample with a wrong pseudo-label through clustering in general has a
weaker consistency between the output of the mean teacher model and the
student model. Based on this finding, we propose to exploit the uncertainty
(measured by consistency levels) to evaluate the reliability of the pseudo-
label of a sample and incorporate the uncertainty to re-weight its
contribution within various ReID losses, including the identity (ID)
classification loss per sample, the triplet loss, and the contrastive loss.
Our uncertainty-guided optimization brings significant improvement and
achieves the state-of-the-art performance on benchmark datasets.

Figure 1: Observations on the relations between the correctness of pseudo
labels and the uncertainty (which we measure by the inconsistency level of the
output features of two models, i.e., the student model and the teacher model
based on the mean teacher method (Tarvainen and Valpola 2017) for the target
domain samples (obtained from Duke$\to$Market). We found the uncertainty for
samples with wrong/noisy pseudo labels (red curve) is usually larger than
those (green curve) with correct/clean pseudo labels.

##  1 Introduction

Person re-identification (ReID) is an important task that matches person
images across times/spaces/cameras, which has many applications such as people
tracking in smart retail, image retrieval for finding lost children. Existing
approaches achieve remarkable performance when the training and testing data
are from the same dataset/domain. But they usually fail to generalize well to
other datasets where there are domain gaps (Ge, Chen, and Li 2020). To address
this practical problem, unsupervised domain adaptive (UDA) person ReID
attracts much attention for both the academic and industrial communities,
where labeled source domain and unlabeled target domain data are exploited for
training.

Typical UDA person ReID approaches (Ge, Chen, and Li 2020; Zhai et al. 2020a;
Zhong et al. 2019; Zheng et al. 2020; Song et al. 2020) include three steps:
feature pre-training with labeled source domain data, clustering-based pseudo-
label prediction for the target domain data, and feature representation
learning/fine-tuning with the pseudo-labels. The last two steps are usually
iteratively conducted to promote each other. However, the pseudo-labels
obtained/assigned through clustering usually contain noisy (wrong) labels due
to the divergence/domain gap between the source and target data, and the
imperfect results of the clustering algorithm. Such noisy labels would mislead
the feature learning and harm the domain adaptation performance. Thus,
_alleviating the negative effects of those samples with unreliable/noisy
pseudo labels is important for the success of domain adaptation_.

The challenge lies in 1) how to identify samples that are prone to have noisy
pseudo labels; 2) how to alleviate their negative effects during the
optimization. In this paper, to answer the first question, we have observed
abundant samples and analyzed the relationship between the characteristics of
the samples and the correctness of pseudo labels. Based on the theory on
uncertainty (Kendall and Gal 2017), a model has uncertainty on its prediction
of an input sample. Here, we measure the inconsistency level of the output
features of two models (the student model and the teacher model based on the
mean teacher method (Tarvainen and Valpola 2017)) and take it as the estimated
uncertainty of a target domain sample. As shown in Fig. 1, we observe the
distribution of the uncertainty (inconsistency levels) for correct/clean
pseudo labels and wrong pseudo labels. We found that the uncertainty values
for the samples with wrong pseudo labels are usually larger than those with
correct pseudo labels. This motivates us to estimate and exploit the
uncertainty of samples to alleviate the negative effects of noisy pseudo
labels, enabling effective domain adaptation. We answer the second question by
carefully incorporating the uncertainty of samples into classification loss,
triplet loss, and contrastive loss, respectively.

We summarize our main contributions as follows:

  * •

We propose a network named Uncertainty-guided Noise Resilient Network (UNRN)
to explore the credibility of the predicted pseudo labels of target domain
samples for effective domain adaptive person ReID.

  * •

We develop an uncertainty estimation strategy by calculating the inconsistency
of two models in terms of their predicted soft multilabels.

  * •

We incorporate the uncertainty of samples to the ID classification loss,
triplet loss, and contrastive loss through re-weighting to alleviate the
negative influence of noisy pseudo labels.

Extensive experiments demonstrate the effectiveness of our framework and the
designed components on unsupervised person ReID benchmark datasets. Our scheme
achieves the state-of-the-art performance on all the benchmark datasets.

##  2 Related Work

###  2.1 Unsupervised Domain Adaptive Person ReID

Existing unsupervised domain adaptive person ReID approaches can be grouped
into three main categories.

Clustering-based methods in general generate hard or soft pseudo labels based
on clustering results and then fine-tune/train the models based on the pseudo
labels (Fan et al. 2018; Zhang et al. 2019; Yang et al. 2019b; Ge, Chen, and
Li 2020; Yu et al. 2019; Zhong et al. 2019; Song et al. 2020; Jin et al.
2020). They are widely used due to their superior performance. PUL (Fan et al.
2018) iteratively obtains hard clustering labels and trains the model in self-
training manner. SSG (Yang et al. 2019b) exploits the potential similarity for
the global body and local body parts, respectively, to build multiple
independent clusters. These clusters are then assigned with labels to
supervise the training. PAST (Zhang et al. 2019) optimizes the network with
triplet-based loss function (to capture the local structure of target-domain
data points) and classification loss by appending a classification layer (to
use global information about the data distribution) based on clustering
results.

Pseudo label noise caused by unsupervised clustering is always an obstacle to
the self-training. Such noisy labels would mislead the feature learning and
impede the achievement of high performance. Recently, some methods introduce
mutual learning among two/three collaborative networks to mutually exploit the
refined soft pseudo labels of the peer networks as supervision (Ge, Chen, and
Li 2020; Zhai et al. 2020c). To suppress the noises in the pseudo labels, NRMT
(Zhao et al. 2020) maintains two networks during training to perform
collaborative clustering and mutual instance selection, which reduces the
fitting to noisy instances by using the mutual supervision and the reliable
instance selection. These approaches need mutual learning of two or more
networks and are somewhat complicated. Besides, the selection of reliable
instances in NRMT (Zhao et al. 2020) is a hard rather than a soft selection,
which requires a careful determination of threshold parameters and may lose
the chance of exploiting useful information of the abandoned samples.

Different from the above works, in this paper, we propose a simple yet
effective framework which estimates the reliability of the pseudo labels
through uncertainty estimation and softly exploit them in the ReID losses to
alleviate the negative effects of noise-prone samples. Note that we do not
need two networks for mutual learning. We build our framework based on the
mean teacher method, which maintains a temporally averaged model of the base
network during the training, to facilitate the estimation of the uncertainty
of each target domain sample.

Domain translation-based methods (Deng et al. 2018a; Huang et al. 2020b; Wei
et al. 2018; Ge et al. 2020) transfer source domain labeled images to the
style of the target domain images and use these transferred images and the
inherited ground-truth labels to fine-tune the model. However, the quality of
translated images is still not very satisfactory which hinders the advancement
of these approaches.

Memory bank based methods have been widely used for unsupervised
representation learning which facilitates the introduction of contrastive loss
(He et al. 2020) for the general tasks. He et al. leverage the memory bank to
better train the model to exploit the similarity between a sample and the
instances in the global memory bank (He et al. 2020). Wang et al. propose to
use memory bank to facilitate hard negative instance mining across batches
(Wang et al. 2020). ECN (Zhong et al. 2019) leverages memory bank to enforce
exemplar-invariance, camera-invariance and neighborhood-invariance over global
training data (instead of local batch) for UDA person ReID. We introduce
contrastive loss to the target instance memory bank to enable the joint
optimization of positive pairs and negative pairs for a query/anchor sample
over all the samples in the memory bank, which serves as our strong baseline.

Figure 2: Overview of the proposed Uncertainty-guided Noise Resilient Network
(UNRN) for UDA person ReID. We build our baseline framework with the mean
teacher method (where the mean teacher model is a temporally moving average of
weights of the student network) together with contrastive loss (supported by a
memory bank). Our method belongs to clustering-based methods. In the model
pre-training stage, we pre-train the network using source domain labeled data.
In the clustering stage, we do clustering on the unlabeled target domain data
using the more accurate features from the mean teacher model and assign pseudo
labels based on the clustering results. Because of domain gap, some of the
pseudo-labels are noisy/incorrect. In the joint fine-tuning stage, we propose
to exploit the estimated uncertainty to evaluate the reliability of the
pseudo-labels to alleviate the negative influence of the samples with error-
prone pseudo-labels, by carefully incorporating the uncertainty to re-weight
the contribution of samples in ID classification loss, triplet loss, and
contrastive loss, respectively. Stage 2 and Stage 3 are performed
alternatively.

###  2.2 Uncertainty Estimation

Uncertainty modeling helps us to understand what a model does not know (or is
not confident). In order to suppress the noise during the training, existing
works (Kendall and Gal 2017; Chang et al. 2020; Zheng and Yang 2020; Zheng,
Zha, and Wei 2019) have explored uncertainty estimation from different
aspects, such as the data-dependent uncertainty, model uncertainty, and the
uncertainty on annotation. For fully supervised learning tasks with clean
groudtruth labels, some works learn the data-dependent uncertainty in an end-
to-end manner to alleviate the influence of observation noise of an input
sample for better network optimization (Kendall and Gal 2017; Chang et al.
2020). Zheng et al. (Zheng and Yang 2020) use an extra auxiliary classifier to
help estimate the uncertainty of the predicted pseudo labels for semantic
segmentation. For clustering-based UDA person ReID, some of the pseudo labels
generated by clustering are incorrect/noisy. However, the investigation on how
to softly evaluate the reliability of clustering-generated pseudo labels is
still underexplored. In this work, we explore the reliability estimation of
the clustering-generated pseudo labels and alleviate the influence of noise-
prone samples by re-weighting their contributions in ReID losses.

##  3 Uncertainty-guided Noise Resilient Network

Unsupervised domain adaptive person ReID aims at adapting the model trained on
a labeled source domain dataset
$\mathbb{D}_{s}\\!\\!=\\!\\!\left\\{\\!\\!\left.\left(\boldsymbol{x}_{i}^{s},{y}_{i}^{s}\right)\right|_{i=1}^{N_{s}}\\!\right\\}$
of $C_{s}$ identities to an annotation-free target domain dataset
$\mathbb{D}_{t}\\!\\!=\\!\\!\left\\{\\!\left.\boldsymbol{x}_{i}^{t}\right|_{i=1}^{N_{t}}\right\\}$.
$N_{s}$ and $N_{t}$ denote the number of samples. $\boldsymbol{x}_{i}$ denotes
a sample and ${y}_{i}$ denotes its groudtruth label. Fig. 2 shows an overview
of our proposed Uncertainty-guided Noise Resilient Network (UNRN) for UDA
person ReID. We aim to address the negative influence of noise-prone pseudo
labels during adaptation/fine-tuning under the clustering-based framework. We
build a clustering-based strong baseline scheme _SBase._ for UDA person ReID.
On top of the strong baseline, we introduce an uncertainty calculation module
to estimate the reliability of psedudo labels and incorporate the uncertainty
into the ReID losses (ID classification loss (ID loss), triplet loss, and
contrastive loss, respectively) to alleviate the influence of noise-prone
pseudo labels. Our uncertainty-guided optimization design brings significant
improvement on top of this strong baseline. We introduce the strong baseline
in Section 3.1 and elaborate on our proposed uncertainty-guided noise-
resilient optimization designs in Section 3.2.

###  3.1 Clustering-based Strong Baseline

We build a clustering-based strong baseline scheme _SBase._ for UDA person
ReID. We follow the general pipeline of clustering-based UDA methods (Fan et
al. 2018; Song et al. 2020; Jin et al. 2020) which consists of three main
stages, i.e., model pre-training, clustering, and fine-tuning. As shown in
Fig. 2, we exploit the labeled source domain data for fine-tuning, incorporate
contrastive loss, and leverage the simple yet effective mean teacher method to
have a strong baseline. We will present the ablation study of each component
in the experimental section.

In the model pre-training stage, we pre-train the network using source domain
labeled data. In the clustering stage, we do clustering on the unlabeled
target domain data using the more accurate features from the mean teacher
model and generate pseudo labels based on the clustering results.

Joint fine-tuning using source data. In the fine-tuning stage (Zhang et al.
2019), most works fine-tune the networks only using target domain pseudo
labels. Here, we also re-use the valuable source domain data with reliable
groudtruth labels. For a source sample, we add ID classification loss, where
maintained $C_{s}$ class centers are used as the classification weight vectors
for classification.

Contrastive loss across memory bank. For image retrieval task, to enable the
pair similarity optimization over informative negative instances, Wang et al.
propose a cross-batch memory mechanism that memorizes the feature embeddings
of the past iterations to allow collecting sufficient hard negative pairs
across the memory bank for network optimization (Wang et al. 2020). Motivated
by this, for a target domain query sample $a$, we add contrastive loss to
maximize the within-class similarity and minimize the between-class similarity
across the memory bank. Particularly, the memory bank consists of $N$ target
domain instances (which is maintained similar to (Wang et al. 2020)) and
$C_{s}$ source class center features (as the negative samples). Based on the
pseudo labels of the target domain samples and the additional source class
centers, we have $N_{a}^{+}$ positive samples and
$N_{a}^{-}=N-N_{a}^{+}+C_{s}$ negative samples. We optimize their similarities
with respect to the query sample. Following circle loss (Sun et al. 2020), we
use self-paced weighting to softly emphasize harder sample pairs by giving
larger weights to them to get effective update.

Mean teacher method. Mean teacher is a method that temporally averages model
weights over training steps, which tends to produce a more accurate model than
using the final weights directly (Tarvainen and Valpola 2017). As illustrated
in Fig. 2, there is no gradient back-propagation over the teacher model which
just maintains a temporal moving average of the student model. This method is
simple yet effective. We use the features from the teacher model to perform
clustering and the final ReID inference.

###  3.2 Uncertainty-guided Optimization

Figure 3: Uncertainty estimation module. For a sample $\boldsymbol{x}_{i}$ and
its feature $\boldsymbol{\tilde{f}}_{i}$ from the mean teacher model and
feature $\boldsymbol{f}_{i}$ from the student model, we estimate the
uncertainty of its pseudo label by calculating the KL divergence of their soft
multilabels.

The noisy pseudo labels would mislead the feature learning in the fine-tuning
stage and hurt the adaptation performance. We aim to reduce the negative
influence of noisy pseudo labels by evaluating the credibility of the pseudo
label of each sample and suppress the contributions of samples with error-
prone pseudo labels in the ReID losses.

Uncertainty estimation. Intuitively, the higher of the uncertainty the model
has on its output of a sample, the lower of the reliability (larger of
observation noise) of the output and it is more likely to have incorrect
pseudo labels through clustering. We have observed in Fig. 1 that the samples
with wrong pseudo labels in general have higher uncertainty values than those
with correct pseudo labels. We leverage the uncertainty to softly assess the
credibility of samples.

We estimate the uncertainty based on the output consistency between the mean
teacher model and the student model. For a sample $\boldsymbol{x}_{i}$ of the
target domain, we denote the extracted feature from the student model as
$\boldsymbol{f}_{i}\in\mathbb{R}^{D}$ of $D$ dimensions, and the feature from
the teacher model as $\boldsymbol{\tilde{f}}_{i}\in\mathbb{R}^{D}$. One
straightforward solution to calculate the consistency between the mean teacher
model and the student model is to calculate the distance (e.g., cosine
distance) between the two features. However, this is clustering ignorance
which does not capture/explore the global distribution of the target domain
samples.

In MAR (Yu et al. 2019), they measure the class likelihood vector (i.e., soft
multilabel) of a person image with a set of reference persons (from an
auxiliary domain). The inconsistency with the soft multilabel vector of an
anchor sample is used to mine the hard negative sample that is visually
similar to the anchor image but is of a different identity. Inspired by this,
we propose to evaluate the uncertainty based on the inconsistency of the two
features $\boldsymbol{f}_{i}$ and $\boldsymbol{\tilde{f}}_{i}$, by calculating
the distance (e.g., KL distance, L1 distance) of their soft multilabels with
respect to the same set of cluster centers. Particularly, as illustrated in
Fig. 3, we use the class centers of source dataset and the cluster centers of
the target domain data together to form the set of “reference persons”. The
soft multilabel agreement is analog to the voting by the “reference persons”
to evaluate the relative consistency. Besides, through the comparison with the
cluster centers of the target domain data, the soft multilabel captures some
global information of the clustering centers which is related to pseudo label
assignment. As an auxiliary domain, the source centers provide additional
references.

Let ${R}=[R_{t},R_{s}]\in\mathbb{R}^{K_{r}\times D}$ denote a matrix which
stores the features of the $K_{r}$ “reference persons”, with each column
denoting the feature of a “reference person”. $R_{t}\in\mathbb{R}^{K_{t}\times
D}$ denotes the $K_{t}$ cluster centers of the target domain data, and
$R_{s}\in\mathbb{R}^{K_{s}\times D}$ denotes the $K_{s}$ class centers of the
source domain data (which are obtained from the weights of the fully-connected
layer of the ID classifier). $K_{r}=K_{t}+K_{s}$.

For a feature $\boldsymbol{f}_{i}\in\mathbb{R}^{D}$ from the student model, we
calculate the similarity to the $K_{r}$ “reference persons” and obtain the
soft multilabel (likelihood vector) as:

$\boldsymbol{p}_{i}={\rm{Softmax}}\left(R\cdot\boldsymbol{f}_{i}\right),$ (1)

where Softmax($\cdot$) denotes softmax function which normalizes the
similarity scores. Similarly, for the feature $\boldsymbol{\tilde{f}}_{i}$
from the mean teacher model, we obtain its soft multilabel as
$\boldsymbol{\tilde{p}}_{i}$. We use KL divergence to measure the difference
between the two probability distributions from the two models as the
uncertainty $u_{i}$ of the sample $\boldsymbol{x}_{i}$:

$u_{i}=D_{KL}(\boldsymbol{\tilde{p}}_{i}||\boldsymbol{p}_{i})=\sum_{k=1}^{K_{r}}\tilde{p}_{i,k}\log\frac{\tilde{p}_{i,k}}{p_{i,n}}.\\\
$ (2)

Optimization. We have observed that a sample with a wrong pseudo-label
(through clustering), in general, has a higher uncertainty. Based on this
observation, we propose to exploit the uncertainty to estimate the
unreliability of the pseudo-label of a sample and use it to re-weight the
contributions of samples in various ReID losses. For a sample
$\boldsymbol{x}_{i}$ with high uncertainty, we will reduce its contribution to
the losses. Therefore, we could assign $\omega_{i}=1/u_{i}$ as the credibility
weight. To enable more stable training, we adopt the policy in (Kendall and
Gal 2017) and define $\omega_{i}={\rm{exp}}({-u_{i}})$. We incorporate the
uncertainty-guided optimization in the classification loss, triplet loss, and
contrastive loss, respectively.

For _ID Classification loss_ , we define the uncertainty-guided ID
classification loss in a min-batch of $n_{t}$ target domain samples as

$\mathcal{L}_{UID}=-\frac{1}{n_{t}}\sum_{i=1}^{n_{t}}\mathcal{\omega}_{i}\log
p\left(\tilde{y}_{i}|\boldsymbol{x}_{i}\right),$ (3)

where $p\left(\tilde{y}^{t}_{i}|\boldsymbol{x}^{t}_{i}\right)$ denotes the
probability of being class $\tilde{y}^{t}_{i}$, where $\tilde{y}^{t}_{i}$
denotes the pseudo groudtruth class (based on the pseudo label assigned after
clustering). For a sample with high uncertainty, a smaller weight is used to
reduce its contribution to the overall loss to reduce its negative effect.

As a typical sample-pair similarity optimization, triplet loss is widely used
in ReID to make the similarity between an anchor sample and a positive sample
to be much larger than that between this anchor sample and negative sample.
For the $j^{th}$ triplet of an anchor sample, a positive sample and a negative
sample that correspond to three pseudo labels, we approximate the reliability
of a sample pair, e.g., the positive sample pair, by a function of the two
uncertainties as

$\mathcal{\omega}_{ap}^{j}=\varphi(u_{a}^{j},u_{p}^{j}),$ (4)

where $u_{a}^{j}$ and $u_{p}^{j}$ denote the estimated uncertainty for the
anchor sample and positive sample in the $j^{th}$ triplet, respectively. For
simplicity, we define the pair credibility as the average of two credibility
as
$\varphi(u_{a}^{j},u_{p}^{j})=\omega_{a}^{j}+\omega_{p}^{j}={\rm{exp}}({-u_{a}^{j}})+{\rm{exp}}({-u_{p}^{j}})$.
Similarly, we get $\mathcal{\omega}_{an}^{j}$ for the negative sample pair.

For _triplet loss_ , we define the uncertainty-guided triplet loss in a min-
batch of $n_{tr}$ triplets as

$\mathcal{L}_{UTRI}\\!=-\frac{1}{n_{tr}}\sum\limits_{j=1}^{n_{tr}}\log\frac{\omega_{ap}^{j}\exp(s_{ap}^{j})}{\omega_{ap}^{j}\exp(s_{ap}^{j})\\!+\\!\omega_{an}^{j}\exp(s_{an}^{j})},$
(5)

where $s_{an}^{j}$ denotes the similarity for the $j^{th}$ positive sample
pair. Mathematically, the lower credibility (higher uncertainty) of a sample
pair, the smaller of a weight on the similarity and thus a smaller gradient in
optimization, i.e., contributing smaller to the optimization.

For _contrastive loss_ , given a query/anchor sample $\boldsymbol{x}_{k}$, we
have $N_{k}^{+}$ positive samples and $N_{k}^{-}$ negative samples in the
memory bank. For a batch of $n_{t}$ samples, by introducing the sample pair
credibility weights, the uncertainty-guided contrastive loss is as

$\mathcal{L}_{\text{UCT}}\\!=\\!\frac{1}{n_{t}}{\sum\limits_{k=1}^{n_{t}}}\log\\!\\!\left[\\!\\!1+{\sum\limits_{j=1}^{N_{k}^{-}}\omega_{kj}^{-}{\rm{exp}}(s_{kj}^{-})\sum\limits_{i=1}^{N_{k}^{+}}\omega_{ki}^{+}{\rm{exp}}(-s_{ki}^{+})}\right],$
(6)

where $s_{kj}^{-}$ denotes the similarity between the query sample
$\boldsymbol{x}_{k}$ and the $j^{th}$ negative sample, and $\omega_{kj}^{-}$
denotes the approximated reliability of the sample pair (see (4)). The lower
credibility of a sample pair, the smaller the gradient and the contribution of
this pair to the optimization. Note that similar to our strong baseline, we
also use self-paced weighting (Sun et al. 2020) to softly emphasize harder
sample pairs (whose similarity score deviates far from the optimum) by giving
larger weights to them to get effective update. For simplicity, we do not
present it in (6), where $s_{kj}^{-}$, $s_{ki}^{+}$ denote the similarities
that already re-weighted.

The total loss for the target domain data in the fine-tuning stage could be
formulated as:

$\mathcal{L}_{target}=\mathcal{L}_{UID}+\lambda_{tri}\mathcal{L}_{UTRI}+\lambda_{ct}\mathcal{L}_{UCT}+\lambda_{reg}\mathcal{L}_{reg},$
(7)

where $L_{reg}=\frac{1}{n_{t}}{\sum_{i=1}^{n_{t}}}u_{i}$ is a regularization
loss which prevents large uncertainty (i.e., small credibility which could
reduce the first three losses) all the time. $\lambda_{tri}$, $\lambda_{ct}$,
and $\lambda_{reg}$ are weighting factors.

##  4 Experiments

Table 1: Performance (%) comparison with the state-of-the-art methods for UDA
person ReID on the datasets of DukeMTMC-reID, Market-1501 and MSMT17. We mark
the results of the second best by underline and the best results by bold text.

Methods | DukeMTMC$\to$Market1501 | Market1501$\to$DukeMTMC
---|---|---
mAP |  R1 |  R5 |  R10 |  mAP |  R1 |  R5 |  R10
ATNet (Liu et al. 2019)(CVPR’19) |  25.6 |  55.7 |  73.2 |  79.4 |  24.9 |  45.1 |  59.5 |  64.2
SPGAN+LMP (Deng et al. 2018b)(CVPR’18) |  26.7 |  57.7 |  75.8 |  82.4 |  26.2 |  46.4 |  62.3 |  68.0
CFSM (Chang et al. 2019) (AAAI’19) |  28.3 |  61.2 |  - |  - |  27.3 |  49.8 |  - |  -
BUC (Lin et al. 2019) (AAAI’19) |  38.3 |  66.2 |  79.6 |  84.5 |  27.5 |  47.4 |  62.6 |  68.4
ECN (Zhong et al. 2019) (CVPR’19) |  43.0 |  75.1 |  87.6 |  91.6 |  40.4 |  63.3 |  75.8 |  80.4
UCDA (Qi et al. 2019) (ICCV’19) |  30.9 |  60.4 |  - |  - |  31.0 |  47.7 |  - |  -
PDA-Net (Li et al. 2019) (ICCV’19) |  47.6 |  75.2 |  86.3 |  90.2 |  45.1 |  63.2 |  77.0 |  82.5
PCB-PAST (Zhang et al. 2019) (ICCV’19) |  54.6 |  78.4 |  - |  - |  54.3 |  72.4 |  - |  -
SSG (Yang et al. 2019b) (ICCV’19) |  58.3 |  80.0 |  90.0 |  92.4 |  53.4 |  73.0 |  80.6 |  83.2
ACT (Yang et al. 2019a) (AAAI’20) |  60.6 |  80.5 |  - |  - |  54.5 |  72.4 |  - |  -
MPLP (Wang and Zhang 2020) (CVPR’20) |  60.4 |  84.4 |  92.8 |  95.0 |  51.4 |  72.4 |  82.9 |  85.0
DAAM (Huang et al. 2020a) (AAAI’20) |  67.8 |  86.4 |  - |  - |  63.9 |  77.6 |  - |  -
AD-Cluster (Zhai et al. 2020a) (CVPR’20) |  68.3 |  86.7 |  94.4 |  96.5 |  54.1 |  72.6 |  82.5 |  85.5
MMT (Ge, Chen, and Li 2020) (ICLR’20) |  71.2 |  87.7 |  94.9 |  96.9 |  65.1 |  78.0 |  88.8 |  92.5
NRMT (Zhao et al. 2020)(ECCV’20) |  71.7 |  87.8 |  94.6 |  96.5 |  62.2 |  77.8 |  86.9 |  89.5
B-SNR+GDS-H (Jin et al. 2020)(ECCV’20) |  72.5 |  89.3 |  - |  - |  59.7 |  76.7 |  - |  -
MEB-Net (Zhai et al. 2020c)(ECCV’20) |  76.0 |  89.9 |  96.0 |  97.5 |  66.1 |  79.6 |  88.3 |  92.2
UNRN (Ours) |  78.1 |  91.9 |  96.1 |  97.8 |  69.1 |  82.0 |  90.7 |  93.5

Methods | Marke1501$\to$MSMT17 | DukeMTMC$\to$MSMT17
---|---|---
mAP |  R1 |  R5 |  R10 |  mAP |  R1 |  R5 |  R10
ECN (Zhong et al. 2019) (CVPR’19) |  8.5 |  25.3 |  36.3 |  42.1 |  10.2 |  30.2 |  41.5 |  46.8
SSG (Yang et al. 2019b) (ICCV’19) |  13.2 |  31.6 |  - |  49.6 |  13.3 |  32.2 |  - |  51.2
DAAM (Huang et al. 2020a) (AAAI’20) |  20.8 |  44.5 |  - |  - |  21.6 |  46.7 |  - |  -
NRMT (Zhao et al. 2020)(ECCV’20) |  19.8 |  43.7 |  56.5 |  62.2 |  20.6 |  45.2 |  57.8 |  63.3
MMT (Ge, Chen, and Li 2020) (ICLR’20) |  22.9 |  49.2 |  63.1 |  68.8 |  23.3 |  50.1 |  63.9 |  69.8
UNRN (Ours) |  25.3 |  52.4 |  64.7 |  69.7 |  26.2 |  54.9 |  67.3 |  70.6

###  4.1 Datasets and Evaluation Metrics

We evaluate our methods using three person ReID datasets, including DukeMTMC-
reID (Duke) (Ristani et al. 2016), Market-1501 (Market) (Zheng et al. 2015)
and MSMT17 (Wei et al. 2018). DukeMTMC-reID (Ristani et al. 2016) has 36,411
images, where 702 identities are used for training and 702 identities for
testing. Market-1501 (Zheng et al. 2015) contains 12,936 images of 751
identities for training and 19,281 images of 750 identities for testing.
MSMT17 (Wei et al. 2018) contains 126,441 images of 4,101 identities, where
1,041 identities and 3060 identities are used for training and testing
respectively.

We adopt mean average precision (mAP) and CMC Rank-1/5/10 (R1/R5/R10) accuracy
for evaluation.

###  4.2 Implementation Details

We use ResNet50 pretrained on ImageNet as our backbone networks. As (Luo et
al. 2019), we perform data agumentation of randomly erasing, cropping, and
flipping. For source pre-training, each mini-batch contains 64 images of 4
identities. For our fine-tuning stage, when the source data is also used, each
mini-batch contains 64 source-domain images of 4 identities and 64 target-
domain images of 4 pseudo identities, where there are 16 images for each
identity. All images are resized to 256$\times$128\. Similar to (Ge, Chen, and
Li 2020; Yang et al. 2019b), we use the clustering algorithm of DBSCAN. For
DBSCAN, the maximum distance between neighbors is set to $eps=0.6$ and the
minimal number of neighbors for a dense point is set to 4. ADAM optimizer is
adopted. The initial learning rate is set to 0.00035. We set the weighting
factors $\lambda_{tri}=1$, $\lambda_{ct}=0.05$, and $\lambda_{reg}=1$, where
we determine them simply by making the several losses on the same order of
magnitude.

###  4.3 Comparison with the State-of-the-arts

We compare our proposed UNRN with the state-of-the-art methods on four domain
adaptation settings in Tab. 1. Our UNRN significantly outperforms the second
best UDA methods by $2.1\%$, $3.0\%$, $2.4\%$ and $2.9\%$, in mAP accuracy,
for Duke$\to$Market, Market$\to$Duke, Market$\to$MSMT, and Duke$\to$MSMT,
respectively. SSG (Yang et al. 2019b) performs multiple clustering on both
global body and local body parts. DAAM (Huang et al. 2020a) introduces an
attention module and incorporates domain alignment constraints. MMT (Ge, Chen,
and Li 2020) use two networks (four models) and MEB-Net (Zhai et al. 2020b)
use three networks (six models) to perform mutual mean teacher training, which
have high computation complexity in training. Our UNRN uses only one network
(two models) in training but still significantly outperforms the best-
performing MEB-Net (Zhai et al. 2020b).

###  4.4 Ablation Studies

Table 2: Ablation studies on the effectiveness of components in our proposed UNRN on Market and Duke. Source: source data is also used in fine-tuning stage with ID classification loss. Contrastive loss (CT): pair similarity optimization across the memory bank. Mean teacher: use mean teacher method where a temporally moving averaged model is taken as the mean teacher. ID: target domain identity classification loss. UID: ID loss with _uncertainty_. TRI: target domain triplet loss. UTRI: target domain triplet loss with _uncertainty_. UCT: contrastive loss with _uncertainty_. Methods | Duke$\to$Market | Market$\to$Duke
---|---|---
mAP |  R1 |  mAP |  R1
Supervised learning |  85.7 |  94.1 |  75.8 |  86.2
Model pretraining |  32.9 |  62.6 |  35.2 |  53.3
Baseline |  68.2 |  87.9 |  60.4 |  75.9
+Source |  70.4 |  88.3 |  61.3 |  76.4
+Contrastive loss |  72.1 |  88.7 |  62.1 |  77.6
+Mean teacher (SBase.) |  75.4 |  89.8 |  64.8 |  79.7
SBase. (ID+TRI+CT) |  75.4 |  89.8 |  64.8 |  79.7
SBase. w/ UID |  77.3 |  91.2 |  68.2 |  81.3
SBase. w/ UTRI |  76.1 |  90.9 |  66.3 |  81.0
SBase. w/ UID+UTRI |  77.8 |  91.5 |  68.9 |  81.7
SBase. w/ UID+UTRI+UCT |  78.1 |  91.9 |  69.1 |  82.0

Effectiveness of components in our strong baseline. We build our basic
baseline _Baseline_ following the commonly used baselines in UDA methods (Ge,
Chen, and Li 2020; Song et al. 2020; Jin et al. 2020), where in the fine-
tuning stage, the identity classification loss and triplet loss are used to
fine-tune the network based on the pseudo labels for the target domain data.
On top of _Baseline_ , we add three components (as described in Section 3.1.
Tab. 2 shows that each component brings additional significant gain and
finally we have a strong baseline _SBase._.

Effectiveness of our uncertainty-guided optimization. We validate the
effectiveness of our proposed design on top of a strong baseline _SBase._. In
general, the stronger of a baseline, the harder one can achieve gains since
the cases easy to address are mostly handled by the strong baseline. Once the
new design is complementary to the strong baseline, it is valuable to advance
the development of techniques.

In the strong baseline _SBase._ , for the target domain samples, identity
classification loss (ID), triplet loss (TRI), and contrastive loss (CT) are
used for supervision based on pseudo labels. To alleviate the negative
influence of noisy/wrong pseudo labels, we exploit uncertainty to re-weight
the contributions of samples. Tab. 2 shows the comparisons. When we replace ID
loss by UID loss, which is the ID loss with uncertainty, the mAP accuracy is
significantly improved by 1.9% and 3.4% for Duke$\to$Market and
Market$\to$Duke, respectively. When we replace triplet (TRI) loss by UTRI
loss, similar improvements are observed. We have our final scheme _UNRN_ when
the uncertainty-guided optimization is applied to all the three losses and it
achieves 2.7% and 4.3% improvement in mAP accuracy over _SBase._ for
Duke$\to$Market and Market$\to$Duke, respectively.

###  4.5 Design Choices

Influence of different designs in uncertainty estimation. We have discussed
the estimation of uncertainty in Section 3.2. There are some design choices
and Tab. 3 shows the comparisons. 1) _UNRN-feat. consist._ denotes that we
estimate the uncertainty based on the distance of the features
$\boldsymbol{\tilde{f}_{i}}$ and $\boldsymbol{{f}_{i}}$ instead of the
distance of derived soft multilabels. We can see that the gain over _SBase._
is negligible due to the poor estimation of uncertainty. In contrast, using
the consistency between soft multilabels (i.e._UNRN- $R$ (Ours)_) captures
global information of the target cluster centers and brings significant
improvement. 2) When we estimate the uncertainty, we leverage a set of
“reference persons” to get the soft multilabels. _UNRN- $R_{t}$_ denotes the
scheme when only the target cluster centers (see Fig. 3) are used as
“reference persons”. _UNRN- $R_{s}$_ denotes the scheme when only the source
centers are used as “reference persons”. _UNRN- $R$_ denotes both are used as
“reference persons”. We can see that the performance of _UNRN- $R_{s}$_ is
very similar to that of _SBase._ , where the source centers only cannot
provide the clustering information of target domain data and is helpless to
estimate the reliability of pseudo labels. _UNRN- $R_{t}$_ outperforms
_SBase._ significantly, which captures the target domain global clustering
information that is helpful to estimate the reliability of pseudo labels.
Interestingly, _UNRN- $R$_ which jointly considers the target cluster centers
and source centers provides the best performance. That may be because the
source centers provide more references which enables the soft multilabels more
informative.

Influence of regularization loss $\mathcal{L}_{reg}$. The regularization loss
$\mathcal{L}_{reg}$ prevents larger uncertainty all the time. As shown in Tab.
3, our final scheme _UNRN- $R$_ outperforms _UNRN w/o $\mathcal{L}_{reg}$_ by
0.6% and 1.1% in mAP accuracy for Duke$\to$Market and Market$\to$Duke,
respectively.

Table 3: Influence of different designs in uncertainties estimation, and the influence of regularization loss $\mathcal{L}_{reg}$ on performance under our framework. Methods | Duke$\to$Market | Market$\to$Duke
---|---|---
mAP |  R1 |  mAP |  R1
SBase. |  75.4 |  89.8 |  64.8 |  79.7
UNRN w/o $\mathcal{L}_{reg}$ |  77.5 |  91.4 |  68.0 |  81.4
UNRN-feat. consist. |  76.5 |  91.0 |  66.7 |  80.9
UNRN-$R_{s}$ |  76.0 |  91.3 |  66.6 |  81.0
UNRN-$R_{t}$ |  77.8 |  91.7 |  68.3 |  81.7
UNRN-$R$ (Ours) |  78.1 |  91.9 |  69.1 |  82.0

Influence of size of memory bank. We use a queue to maintain $N$ target domain
instances in the memory bank. Tab. 4 shows that as the queue length $N$
increases, the performance increases but saturates when the size is around
8192.

Table 4: Influence of the number ($N$) of target instances in the memory bank. We study this on top of baseline scheme _Baseline+Source+Contrastive loss_ (see Tab. 2). “All” denotes the size is equal to the size of target training dataset. Size of memory bank | Market$\to$Duke
---|---
0 | 1024 | 4096 | 8192 | All
mAP | 62.8 | 63.4 | 63.9 | 64.8 | 64.5
R1 | 77.9 | 78.9 | 79.3 | 79.7 | 79.3

##  5 Conclusion

In this paper, for clustering-based UDA person ReID, we aim to alleviate the
negative influence of wrong/noisy labels during the adaptation. We have
observed that a sample with a wrong pseudo-label through clustering in general
has a weaker consistency between the output of the mean teacher model and the
student model. Based on this finding, we propose to exploit the uncertainty
(measured by consistency levels) to evaluate the reliability of the pseudo-
label of a sample and incorporate the uncertainty to re-weight its
contribution within various ReID losses, including the ID classification loss
per sample, the triplet loss, and the contrastive loss. Our uncertainty-guided
optimization brings significant improvement over our strong baseline and our
scheme achieves the state-of-the-art performance on benchmark datasets.

##  6 Acknowledgments

This work was in part supported by the National Key R$\&$D Program of China
under Grand 2020AAA0105702, National Natural Science Foundation of China
(NSFC) under Grants U19B2038 and 61620106009.

##  7 Ethical Impact

Our method is proposed to help match/identify different persons across images,
which can facilitate the development of smart retail systems in the future.
When the person re-ID system is used to identify the pedestrian, it may cause
a violation of human privacy. Therefore, governments and officials need to
carefully formulate strict regulations and laws to ensure the legal use of
ReID technology and strictly protect the data.

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# Popularity Debiasing from Exposure to Interaction in Collaborative Filtering

Yuanhao Liu  Data Intelligence System Research Center, Institute of Computing
Technology, CAS University of Chinese Academy of Sciences, Beijing, China
<EMAIL_ADDRESS>,  Qi Cao  Data Intelligence System Research Center,
Institute of Computing Technology, CAS<EMAIL_ADDRESS>,  Huawei Shen  Data
Intelligence System Research Center, Institute of Computing Technology, CAS
University of Chinese Academy of Sciences, Beijing, China<EMAIL_ADDRESS>,  Yunfan Wu  Data Intelligence System Research Center, Institute of Computing
Technology, CAS University of Chinese Academy of Sciences, Beijing, China
<EMAIL_ADDRESS>,  Shuchang Tao  Data Intelligence System Research
Center, Institute of Computing Technology, CAS University of Chinese Academy
of Sciences, Beijing, China<EMAIL_ADDRESS>and  Xueqi Cheng  CAS Key
Lab of Network Data Science and Technology, Institute of Computing Technology,
CAS University of Chinese Academy of Sciences, Beijing, China<EMAIL_ADDRESS>
(2023)

###### Abstract.

Recommender systems often suffer from popularity bias, where popular items are
overly recommended while sacrificing unpopular items. Existing researches
generally focus on ensuring the number of recommendations (_exposure_) of each
item is equal or proportional, using inverse propensity weighting, causal
intervention, or adversarial training. However, increasing the exposure of
unpopular items may not bring more clicks or interactions, resulting in skewed
benefits and failing in achieving real reasonable popularity debiasing. In
this paper, we propose a new criterion for popularity debiasing, i.e., _in an
unbiased recommender system, both popular and unpopular items should receive
Interactions Proportional to the number of users who Like it, namely IPL
criterion_. Under the guidance of the criterion, we then propose a debiasing
framework with IPL regularization term which is theoretically shown to achieve
a win-win situation of both popularity debiasing and recommendation
performance. Experiments conducted on four public datasets demonstrate that
when equipping two representative collaborative filtering models with our
framework, the popularity bias is effectively alleviated while maintaining the
recommendation performance.

collaborative filtering, popularity debiasing, new criterion

††journalyear: 2023††copyright: rightsretained††conference: Proceedings of the
46th International ACM SIGIR Conference on Research and Development in
Information Retrieval; July 23–27, 2023; Taipei, Taiwan††booktitle:
Proceedings of the 46th International ACM SIGIR Conference on Research and
Development in Information Retrieval (SIGIR ’23), July 23–27, 2023, Taipei,
Taiwan††doi: 10.1145/3539618.3591947††isbn: 978-1-4503-9408-6/23/07††ccs:
Human-centered computing Collaborative filtering

##  1\. Introduction

Recommender systems aim to help users find interesting items and are used in
various online services, e.g., online shopping (Wu et al., 2019; Kim et al.,
2002, 2009), social networks (Debnath et al., 2008; Walter et al., 2008; Wang
et al., 2012), and video sites (Davidson et al., 2010; Deldjoo et al., 2016;
Mei et al., 2011). Collaborative filtering, a widely used recommendation
approach (Koren et al., 2009; He et al., 2020; Wu et al., 2016; Huang et al.,
2023), learns models for recommendation from user-item interactions.
Unfortunately, since the user-item interactions usually exhibit long-tail
distribution in terms of item popularity (Zhang et al., 2021a; Li et al.,
2019), the models trained via the skewed interactions are often observed to
further amplify the popularity bias by over-recommending popular items and
under-recommending unpopular items (Mansoury et al., 2020; Abdollahpouri et
al., 2019). Such popularity bias may lead to terrible results such as Matthew
Effect (Perc, 2014), hindering the long-term and sustainable development of
recommender systems.

Researchers propose different methods for popularity debiasing. Early works
generally follow a paradigm of inverse propensity weighting (Kamishima et al.,
2014; Schnabel et al., 2017; Liang et al., 2016; Brynjolfsson et al., 2006;
Krishnan et al., 2018), i.e., increase the weight of unpopular items during
training. Later, researchers introduce causal methods to remove the harmful
impact of popularity (Zhang et al., 2021b; Zheng et al., 2021; Wei et al.,
2021; Zhao et al., 2021). Adversarial learning is also used to enhance the
distribution similarity of prediction scores between items to alleviate
popularity bias (Zhu et al., 2020; Liu et al., 2022).

Figure 1. The proportion of items that get the unbiased (a) exposure (b)
interaction amount before and after debiasing. The unbiased number of
exposures/interactions of the item is proportional to the item’s popularity.
Popular items are the ones whose popularity exceeds 80% items.

Despite the various existing methods, they generally focus on making the
number of recommendations (the _exposure_) of items equal to each other or
proportional to their popularity (Wei et al., 2021; Liang et al., 2016). Fig.
1(a) shows the ratio of items that get unbiased exposure amount in existing
representative debiasing method (Wei et al., 2021), which helps 23% unpopular
items avoid being under-recommended. However, blindly increasing the exposure
of unpopular items may not significantly increase their interactions 111User
_interactions_ , such as clicking, purchasing, or expressing liking for the
recommended item, can directly represent that the item benefits from the
recommendation., since they may be recommended to users who dislike them.
Taking two similar books as an example, one is recommended to users who like
it and the other is recommended more to those who don’t like it. Although they
are treated similarly in exposure, the latter is likely to earn less because
fewer users will buy it, and thus still be plagued by popularity bias. As
shown in Fig. 1(b), there are hardly any extra unpopular items (less than
0.01) that can get an unbiased amount of interactions through existing
debiasing methods. In other words, simply increasing the exposure of unpopular
items in existing methods may not necessarily lead to more clicks or
interactions, resulting in skewed benefits and failing in achieving real
reasonable popularity debiasing.

In this paper, we propose a new criterion for popularity debiasing, i.e., in a
popularity unbiased recommender system, both popular and unpopular items
should receive _interactions_ _proportional_ to the number of users who _like_
it, namely IPL criterion. We propose a regularization-based debiasing
framework following this criterion. However, in offline scenarios, we cannot
observe the number of interactions that items can get in recommendation. In
addition, due to the missing-not-at-random phenomenon of data, users who like
the item are also invisible. In order to estimate both the number of
interactions and users who like the items using observational data, we propose
an inverse-propensity-score-based estimation method and use it to formalize
the IPL regularization term for debiasing.

We conduct experiments on four public datasets and equip our framework with
the representative matrix factorization (Koren et al., 2009) and the state-of-
the-art LightGCN (He et al., 2020) for collaborative filtering. Experimental
results show that our framework achieves the best effectiveness of debiasing
while even further improving the recommendation performance. Further analysis
is also offered to deepen the understanding of the success of our framework.

In summary, the contribution of this work is threefold.

  * •

We propose a new criterion for popularity debiasing, i.e., an item should
receive interactions proportional to the number of users who like it.

  * •

We propose an estimation method to measure IPL in offline data, and further
propose a debiasing framework, which is theoretically shown to achieve a win-
win situation of both popularity debiasing and recommendation performance.

  * •

Experiments conducted on four public datasets demonstrate the effectiveness of
our framework when equipped with two representative collaborative filtering
models.

##  2\. Method

This section describes the problem formulation and the proposed new criterion
for popularity debiasing, as well as a general debiasing framework.

###  2.1. Collaborative Filtering

Suppose we have $N$ users $\mathcal{U}=\\{u_{1},u_{2},...,u_{N}\\}$ and $M$
items $\mathcal{I}=\\{i_{1},i_{2},...,i_{M}\\}$, collaborative filtering aims
to predict the preference score $\widehat{y}_{u,i}$ of item $i$ by user $u$
based on observed interactions. For training a collaborative filtering model,
Bayesian Personalized Ranking (BPR) (Rendle et al., 2009) is one of the most
widely adopted training loss,

$\small\vspace{-3pt}L_{\text{BPR}}=-\sum_{u\in\mathcal{U}}\sum_{\begin{subarray}{c}i^{+}\in\mathcal{I}_{u}^{+}\end{subarray}}\sum_{i^{-}\in\mathcal{I}/\mathcal{I}_{u}^{+}}\ln(\sigma(\widehat{y}_{u,i^{+}}-\widehat{y}_{u,i^{-}})+\lambda_{\Theta}\lVert\Theta\rVert^{2}_{F},\vspace{-3pt}$

where $\mathcal{I}_{u}^{+}$ is the set of items interacted with $u$ in
training data.

###  2.2. New Criterion for Popularity Debiasing

The new criterion is defined as a popular or unpopular item should receive
interactions proportional to the number of users who like it, namely IPL
criterion, which is formally defined as:

(1) $\small\vspace{-3pt}\forall
i,j\in\mathcal{I}^{\text{pop}}or\mathcal{I}^{\text{unpop}},\frac{C_{i}}{Q_{i}}=\frac{C_{j}}{Q_{j}},$

where $\mathcal{I}^{pop}$ and $\mathcal{I}^{unpop}$ are popular and unpopular
items respectively, $C_{i}$ is the number of interactions $i$ can get from
recommendation, and $Q_{i}$ is the number of interactions that $i$ can get
when exposed to all users, reflecting the number of users who like item $i$.
Such a criterion takes into account two aspects:

  * •

The benefit of an item in recommendation is more about the interactions it
receives, instead of massive useless recommendations. Hence, we take the
interactions as the indicator.

  * •

The more users like an item, the more interactions it deserves. Hence, an
unbiased recommendation should ensure interactions is proportional to the
users who like the item.

A recommender system is ideally unbiased if it satisfies the IPL criterion
above, which not only provides a more reasonable goal for debiasing but also
eliminates the trade-off between debiasing and recommendation performance (see
Section 2.5).

###  2.3. Estimation in offline data

The IPL criterion provides a great goal for popularity debiasing. However, due
to the incomplete observation in offline data, it is hard to obtain the real
number of interactions received from recommendations ($C_{i}$) and from all
users ($Q_{i}$). Although some methods tried to consider interaction amount in
debiasing (Zhu et al., 2020, 2021), they generally obtain the $C_{i}$ directly
in the online scenario or ignore the incompleteness of the data, making it
difficult to apply offline.

To solve the above problem, we propose an estimator for $C_{i}$ and $Q_{i}$
based on the inverse-propensity-score (IPS) (Joachims and Swaminathan, 2016)
technique.

For estimating $C_{i}$, note that $C_{i}=\sum_{u\in\mathcal{U}_{i}}R_{u,i}$,
where $\mathcal{U}_{i}$ is users interact with $i$ when $i$ is exposed to all
users, and $R_{u,i}=1$ if $i$ is recommended to $u$ otherwise $0$. Given
$C_{i}^{\text{IPS}}=\sum_{u\in\mathcal{U}_{i}}\frac{O_{u,i}}{P_{u,i}}R_{u,i}$
where $P_{u,i}=\text{Pr}(O_{u,i}=1)$ and $O_{u,i}$ is a binary variable of
which $1$ means that an interaction between $u$ and $i$ is observed, we can
easily have $\mathbb{E}_{O}\left[C_{i}^{\text{IPS}}\right]=C_{i}$. In other
words, $C_{i}^{\text{IPS}}$ is an unbiased estimation of $C_{i}$. For
estimating $P_{u,i}$ in $C_{i}^{\text{IPS}}$, we follow the broadly adopted
approach in (Yang et al., 2018), which assume that
$P_{u,i}=P_{*,i}=p^{\text{expose}}_{*,i}*p^{\text{like}}_{*,i}$, where
$p^{\text{expose}}_{*,i}$ and $p^{\text{like}}_{*,i}$ are the probability that
item $i$ is exposed and liked, and $p^{\text{like}}_{*,i}$ is estimated to be
proportional to $Q_{i}=|\mathcal{U}_{i}|$. Then we have $P_{*,i}\propto
p_{*,i}^{\text{expose}}*Q_{i}$. Denoting the observed popularity of item $i$
as $Q_{i}^{*}=|\mathcal{U}_{i}^{*}|$, we have a binomial distribution of
$Q_{i}^{*}\sim\mathcal{B}(Q_{i},p_{*,i}^{\text{expose}})$. Then we have
$Q_{i}^{*}=p_{*,i}^{\text{expose}}*Q_{i}\propto P_{*,i}$, and

(2)
$\small\vspace{-5pt}C_{i}^{\text{IPS}}=\sum_{u\in\mathcal{U}_{i}}\frac{O_{u,i}}{P_{u,i}}R_{u,i}=\sum_{u\in\mathcal{U}_{i}^{*}}\frac{R_{u,i}}{P_{u,i}}=\frac{\sum_{u\in\mathcal{U}_{i}^{*}}R_{u,i}}{P_{*,i}}\propto\frac{C_{i}^{*}}{Q_{i}^{*}},$

where $C_{i}^{*}=\sum_{u\in\mathcal{U}_{i}^{*}}R_{u,i}$ is the number of
observed interactions in recommendation.

To estimate $Q_{i}$, recall that $Q_{i}=Q_{i}^{*}/p_{*,i}^{\text{expose}}$. We
assume that
$p_{*,i}^{\text{expose}}\\!\propto\\!\left(Q_{i}^{*}\right)^{\gamma}$ (Yang et
al., 2018), where $\gamma$ characterizes the popularity bias during data
generation (Steck, 2011), and can be estimated by fitting the data. Then we
have

(3)
$\small\vspace{-5pt}Q_{i}=\frac{Q_{i}^{*}}{p_{*,i}^{\text{expose}}}\propto{(Q_{i}^{*})}^{1-\gamma}.$

With observed $C_{i}^{*}$ and $Q_{i}^{*}$ in offline data, we can measure the
IPL criterion by
$\frac{C_{i}^{\text{IPS}}}{Q_{i}}\propto\frac{C_{i}^{*}}{\left(Q_{i}^{*}\right)^{2-\gamma}}=r_{i}$.
Then we can rewrite Eq. (1) as:

(4) $\small\vspace{-5pt}\forall
i,j\in\mathcal{I}^{\text{pop}}or\mathcal{I}^{\text{unpop}},r_{i}=r_{j}.\vspace{-5pt}$

###  2.4. Debiasing Framework

We further propose a debiasing framework with a regularization term
considering the IPL criterion during model training.

Considering a recommender model with parameter $\Theta$, we have

$\displaystyle\widehat{r}_{i}=\mathbb{E}[r_{i}|\Theta]=\frac{\mathbb{E}\left[\left.C_{i}^{*}\right|\Theta\right]}{\left(Q_{i}^{*}\right)^{2-\gamma}}=\frac{\sum_{u\in\mathcal{U}^{*}_{i}}\text{Pr}\left(\left.u,i\right|\Theta\right)}{\left|\mathcal{U}^{*}_{i}\right|^{2-\gamma}}=\frac{\sum_{u\in\mathcal{U}^{*}_{i}}\sigma(\widehat{y}_{u,i})}{\left|\mathcal{U}^{*}_{i}\right|^{2-\gamma}},$

where $\sigma(\widehat{y}_{u,i})$ indicates the probability that $i$ will be
recommended to $u$, $\mathcal{U}_{i}^{*}$ is all the users observed interact
with $i$ in training data.

Then the regularization term ensures IPL criterion is written as:

(5)
$\small\vspace{-3pt}L_{\text{IPL}}=std_{i\in\mathcal{I}}(\widehat{r}_{i})=\sqrt{\frac{1}{M}\sum_{i\in\mathcal{I}}(\widehat{r}_{i}-\frac{1}{M}\sum_{i\in\mathcal{I}}\widehat{r}_{i})^{2}},$

which aims to reduce the $r_{i}$ gap between all the $M$ items according to
Eq. (4) to achieve unbiased recommendation under the IPL criterion.

The final loss function for debiasing model training is:

(6)
$\small\min_{\Theta}L_{\text{debias}}=L_{\text{BPR}}+\lambda_{f}*L_{\text{IPL}},$

where $\lambda_{f}$ controls the strength of popularity debiasing.

###  2.5. Theoretical Analysis

Generally, popularity debiasing may bring a decrease in recommendation
performance. In this section, we give a theoretical analysis to show that our
proposed criterion can achieve a win-win situation for both recommendation
performance and popularity debiasing.

###### Proposition 2.1.

Given an acceptable recommendation performance with $\text{recall}=c$, there
always exists a recommendation result that satisfies the requirements of both
the recall $c$ and the IPL criterion.

###### Proof.

For recommendations with recall
$c=\frac{\sum_{i\in\mathcal{I}}C_{i}}{\sum_{i\in\mathcal{I}}Q_{i}}$, to meet
the IPL criterion, we should have $\forall
i\in\mathcal{I},r_{i}=\frac{C_{i}}{Q_{i}}=\frac{\sum_{i\in\mathcal{I}}C_{i}}{\sum_{i\in\mathcal{I}}Q_{i}}=c$.

Given $k\in\\{1,2,...,M\\}$ denoting the number of items recommended to each
user, if a recommendation with recall $c$ cannot meet the IPL criterion, then
there always exists a discriminated item $i$ that has
$r_{i}=\frac{C_{i}}{Q_{i}}=\frac{C_{i}}{|\mathcal{U}_{i}|}<c$. In other words,
there are at least $(1-c)|\mathcal{U}_{i}|$ users like item $i$ while cannot
further have $i$ in their recommendation list, which means that such a user
$u$ will necessarily lose the recommendation of another item
$j\in\mathcal{I}_{u}$ ($u$ likes $j$) and make $r_{j}<c$ if adding item $i$
into the recommendation list of user $u$. For better understanding, we denote
the set of items at risk of discrimination (like $j$) as
$\mathcal{I}^{-}{\triangleq}\left\\{j\left|\frac{|\mathcal{U}^{-}\cap\mathcal{U}_{j}|}{|U_{j}|}>1-c\right.\right\\}$,
where
$\mathcal{U}^{-}{\triangleq}\left\\{u\big{|}|\mathcal{I}_{u}|>k\right\\}$. The
above-mentioned user $u$ likes at least $k$ items in $\mathcal{I}^{-}$. Now we
consider the existence of $u$, which is the necessary condition for the
existence of the discriminated item $i$:

(7) $\small\textbf{condition-1}:\exists
u\in\mathcal{U},|\mathcal{I}_{u}\cap\mathcal{I}^{-}|>k.\vspace{-3px}$

Given $|\mathcal{I}_{u}|$ follows Pareto distribution
$\text{Pr}(|\mathcal{I}_{u}|\\!=\\!x)\\!=\\!(\beta-1)x^{-\beta}$ with
$\beta>1$, the probability that user $u\in\mathcal{U}^{-}$ equals to
$p=\text{Pr}(|\mathcal{I}_{u}|\\!>\\!k)=k^{1-\beta}$. Therefore we have
$\text{Pr}(|\mathcal{U}^{-}\\!\cap\\!\mathcal{U}_{i}|\\!=\\!x)\sim
B(x;|\mathcal{U}_{i}|,p)$, where $B(\cdot;n,p)$ is the Binomial distribution
with the number of experiments $n$ and the probability of success $p$. Then we
have
$\text{Pr}(i\in\mathcal{I}^{-})=\text{Pr}\left(|\mathcal{U}^{-}\cap\mathcal{U}_{i}|\\!>\\!(1-c)|\mathcal{U}_{i}|\right)<F(c|\mathcal{U}_{i}|;|\mathcal{U}_{i}|,1-p)$,
where $F(\cdot;n,p)$ is the cumulative distribution function of
$B(\cdot;n,p)$. With the Chernoff bound
$F(x;n,p)\leq\exp\left(-nD(\frac{x}{n}||p)\right)$, where
$D(a||p)=a\log\frac{a}{p}+(1-a)\log\frac{1-a}{1-p}$, we further have
$\text{Pr}(i\in\mathcal{I}^{-})\leq\exp\left(-\left((1-c)\log\frac{(1-c)}{p}+c\log\frac{c}{1-p}\right)\right)$.

Then the probability that satisfying condition-1 is:

(8) $\displaystyle
1{-}\prod_{u\in\mathcal{U}\atop{|\mathcal{I}_{u}|>k}}\left(1{-}\sum_{j=k+1}^{|\mathcal{I}_{u}|}\tbinom{|\mathcal{I}_{u}|}{j}\text{Pr}(i\in\mathcal{I}^{-})^{j}(1-\text{Pr}(i\in\mathcal{I}^{-}))^{|\mathcal{I}_{u}|-j}\right)$
$\displaystyle\leq$ $\displaystyle
1{-}\prod_{u\in\mathcal{U}\atop{|\mathcal{I}_{u}|>k}}\left(1{-}\sum_{j=k+1}^{|\mathcal{I}_{u}|}\tbinom{|\mathcal{I}_{u}|}{j}\text{Pr}(i\in\mathcal{I}^{-})^{j}\right)$
$\displaystyle\leq$ $\displaystyle
1{-}\prod_{u\in\mathcal{U}\atop{|\mathcal{I}_{u}|>k}}\left(1{-}\sum_{j=k+1}^{|\mathcal{I}_{u}|}\tbinom{|\mathcal{I}_{u}|}{j}\exp\left(-\left((1{-}c)\log\frac{(1{-}c)}{p}{+}c\log\frac{c}{1{-}p}\right)\right)^{j}\right)$

Taking real-world datasets as an illustration, when specifying interaction
recall $c=0.99$, the probability of condition-1 $<10^{-10}$ on MovieLens-1M.
Similar results were shown on other datasets. This show that there is almost
always a recommendation result that satisfies IPL criterion while ensuring
recommendation performance. ∎

##  3\. Experimental results

Table 1. Performance of recommendation and debiasing. Bold and underlined
scores are the best and second-best performances.

| MovieLens-1M | Gowalla | Yelp | Amazon book
---|---|---|---|---
| Pre$\uparrow$ | Recall$\uparrow$ | NDCG$\uparrow$ | MI$\downarrow$ | DI$\downarrow$ | Pre$\uparrow$ | Recall$\uparrow$ | NDCG$\uparrow$ | MI$\downarrow$ | DI$\downarrow$ | Pre$\uparrow$ | Recall$\uparrow$ | NDCG$\uparrow$ | MI$\downarrow$ | DI$\downarrow$ | Pre$\uparrow$ | Recall$\uparrow$ | NDCG$\uparrow$ | MI$\downarrow$ | DI$\downarrow$
MF | 19.977 | 27.685 | 30.777 | 2.138 | 3.723 | 4.738 | 17.763 | 13.149 | 0.601 | 3.067 | 2.557 | 10.871 | 6.848 | 0.782 | 3.989 | 2.618 | 12.066 | 7.979 | 0.757 | 3.061
PO | 17.329 | 23.097 | 25.877 | 1.997 | 3.461 | 4.442 | 16.862 | 12.374 | 0.593 | 2.918 | 1.951 | 8.075 | 5.078 | 0.742 | 4.594 | 2.606 | 12.021 | 7.965 | 0.742 | 2.928
DPR | 16.630 | 23.010 | 25.240 | 1.985 | 3.467 | 3.983 | 14.404 | 10.862 | 0.611 | 4.042 | 2.104 | 8.485 | 5.407 | 0.766 | 5.757 | 2.238 | 10.219 | 7.596 | 0.728 | 5.194
IPW | 16.350 | 22.110 | 23.540 | 2.073 | 3.500 | 4.021 | 15.151 | 10.360 | 0.588 | 2.974 | 1.950 | 8.081 | 4.813 | 0.718 | 3.882 | 2.220 | 8.751 | 7.011 | 0.735 | 3.004
MACR | 17.248 | 23.253 | 25.782 | 2.211 | 3.458 | 3.977 | 14.694 | 10.879 | 0.584 | 2.905 | 1.685 | 6.732 | 4.285 | 0.747 | 4.891 | 2.140 | 11.875 | 7.889 | 0.726 | 3.173
IPL | 20.397 | 28.642 | 31.397 | 1.942 | 3.254 | 5.136 | 19.220 | 14.450 | 0.559 | 2.882 | 2.715 | 11.578 | 7.278 | 0.625 | 3.808 | 2.891 | 13.274 | 8.914 | 0.725 | 2.889
LGCN | 19.808 | 27.217 | 30.599 | 2.010 | 4.032 | 5.381 | 19.894 | 15.355 | 0.719 | 2.623 | 2.934 | 12.410 | 7.948 | 0.723 | 4.403 | 2.905 | 12.978 | 8.805 | 0.777 | 3.016
PO | 19.830 | 27.206 | 30.475 | 1.998 | 3.356 | 5.221 | 18.373 | 15.176 | 0.692 | 3.131 | 2.861 | 12.220 | 7.767 | 0.738 | 4.487 | 2.880 | 11.675 | 7.992 | 0.720 | 3.031
DPR | 17.682 | 22.861 | 28.199 | 1.922 | 3.417 | 4.533 | 16.654 | 12.458 | 0.638 | 2.760 | 2.106 | 11.255 | 6.152 | 0.728 | 6.809 | 2.422 | 9.427 | 6.854 | 0.736 | 4.334
IPW | 13.689 | 16.700 | 19.590 | 1.959 | 3.777 | 2.950 | 10.960 | 8.340 | 0.685 | 3.357 | 1.913 | 9.159 | 5.822 | 0.722 | 6.026 | 2.075 | 8.427 | 6.999 | 0.716 | 4.922
MACR | 18.724 | 26.251 | 27.945 | 1.985 | 3.180 | 5.183 | 19.022 | 14.831 | 0.630 | 3.058 | 2.335 | 11.684 | 7.702 | 0.725 | 4.651 | 2.108 | 10.133 | 7.255 | 0.757 | 3.799
IPL | 19.979 | 27.545 | 30.949 | 1.921 | 3.005 | 5.385 | 19.897 | 15.365 | 0.621 | 2.011 | 2.954 | 12.440 | 8.013 | 0.720 | 3.848 | 2.913 | 12.991 | 8.844 | 0.704 | 2.886

###  3.1. Experiment Setup

Datasets. We conduct experiments on four public benchmark datasets:
MovieLens-1M (Harper and Konstan, 2015), Gowalla (Cho et al., 2011), Yelp
(yel, 2022), and Amazon Book (He and McAuley, 2016). We uniformly sample
interaction records from each item, splitting them into 70%, 10%, and 20% as
train, validation, and test sets. In addition, we follow (Yang et al., 2018)
and use MF (Koren et al., 2009) to estimate $\gamma$ of the datasets, which
are $1.826$, $1.285$, $1.552$, $1.446$, respectively.

Baselines. We implement our method with MF (Koren et al., 2009) and LightGCN
(He et al., 2020) 222The model implementations are accessible on Github:
https://github.com/UnitDan/IPL, comparing with the following baselines: IPW
(Liang et al., 2016) is a IPS-based re-weighting method. PO (Zhu et al., 2021)
eliminates popularity bias in item ranking by regularization. MACR (Wei et
al., 2021) removes the causal effect of popularity on preference scores. DPR
(Zhu et al., 2020) uses adversarial training for item group fairness. In
addition, we also optimize MF and LightGCN using BPR loss as the basis for
comparison.

Evaluation metrics. We evaluate recommendation performance by Precision@k,
Recall@k and NDCG@k. We set $k=20$ following (Wang et al., 2019), and show all
these metrics after multiplying by 100 (Wu et al., 2022). To evaluate the
effectiveness of popularity debiasing, we use the mutual information (MI)
(Cover, 1999) of $r_{i}$ and item popularity $Q_{i}^{*}$ to measure the
correlation between them. We also propose a metric that is consistent with the
IPL criterion, called Deviation of Interaction distribution (DI).
$DI=\frac{std_{i\in\mathcal{I}}(r_{i})}{mean_{i\in\mathcal{I}}(r_{i})}$. Lower
values of MI and DI indicate less popularity bias in the recommendation
result.

###  3.2. Performance Evaluation

To demonstrate the effectiveness of our method, we evaluate recommendation
performance and debiasing results on four benchmark datasets. As shown in
Table 1, MF and LightGCN achieve good recommendation performance, but with a
serious popularity bias, reflected in a high value of MI and DI. For debiasing
baselines, they mitigate the popularity bias to some extent, however, at the
cost of severely sacrificing recommendation performance. For our method, IPL
shows superiority in both recommendation accuracy and debiasing. Especially,
IPL achieves the best recommendation performance on all datasets, even
outperforming MF and LightGCN. As for debiasing, our IPL performs best on MI
and DI. These results demonstrate the effectiveness of our IPL method in terms
of both recommendation performance and popularity debiasing.

###  3.3. IPL Method Win-Win Evaluation

To verify the conclusion in Section 2.5 that our proposed method can achieve a
win-win situation in recommendation and debiasing, we compared the performance
of IPL with different strengths of popularity debiasing and basic models. We
used $1/DI$ to represent the debiasing performance and an unbiased recall
metric ($Recall_{\text{SNIPS}}$) (Yang et al., 2018) to represent the
recommendation accuracy. We experimented with 20 equally spaced values of
$\lambda_{f}$ on a logarithmic scale from $1e-2$ to $1e-6$. Fig. 2
demonstrates that the experimental results of IPL are consistently located in
the upper right space of the basic model results, indicating that IPL can
simultaneously enhance recommendation and debiasing performance.

Figure 2. Performance of basic models and IPL with different $\lambda_{f}$ on
recommendation and debiasing.

###  3.4. Case Study

Figure 3. Case study. The number of recommendations (blue) is on the left, and
that of effective recommendations (green) is on the right. Users who prefer
unpopular items are bold.

Fig. 3 demonstrates how IPL can achieve a win-win situation using Movie-Lens
as an example. By comparing recommendation lists of two pairs of popular and
unpopular items, we found that MF amplifies popularity bias by over-
recommending popular items (442 and 148) and under-recommending unpopular ones
(1150 and 549). The existing debiasing method (MACR_MF) blindly recommends
more to unpopular items, sacrificing recommendations of popular items. In
contrast, our IPL_MF recommends the unpopular item (1150) to users (U1761 and
U394) who prefer unpopular items, thereby alleviating the popularity bias
while achieving better recommendation accuracy.

##  4\. CONCLUSION

In this work, we propose a new criterion to measure popularity bias, i.e., an
item should get interactions proportional to the number of users who like it
(IPL). We further propose a debiasing framework based on IPL. Both theoretical
analysis and experimental results demonstrate that the proposed method can
achieve a win-win situation for both recommendation boosting and popularity
debiasing.

###### Acknowledgements.

This work is funded by the National Key R&D Program of China (2022YFB3103700,
2022YFB3103701), and the National Natural Science Foundation of China under
Grant Nos. 62272125, U21B2046. Huawei Shen is also supported by Beijing
Academy of Artificial Intelligence (BAAI).

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