Delving into Probabilistic Uncertainty for
Unsupervised Domain Adaptive Person Re-identification

We construct a clustering-based pipeline based on MMT (Ge, Chen, and Li 2020) for UDA person ReID. Following the general pipeline of clustering-based methods, three stages are consisted, such as: source-domain model pre-training, clustering, and target-domain fine-tuning. In the source pre-training stage, two sibling networks are established with the same architecture. They are initialized with different random seeds, trained with the same data yet experienced different data augmentations to reduce the dependence. The networks are optimized by the identity loss $L_{id}$ and triplet loss $L_{tri}$. In the clustering stage, pseudo labels for target-domain data are generated by clustering. In the target fine-tuning stage, two mean teachers $\bar{M_{1}}$ and $\bar{M_{2}}$ are established with the exponential moving average of student models over iterations. The prediction of one teacher model is taken as soft labels to mutually supervise the training of the other student. Apart from the identification and triplet loss with hard pseudo labels provided by clustering, each model is also guided by the Kullback–Leibler (KL) divergence loss $L_{KL}$ and soft triplet loss $L_{stri}$ with the soft labels.

The whole loss function in the fine-tuning stage is as:

$\displaystyle\mathcal{L}=\mathcal{L}_{id}+\lambda_{tri}\mathcal{L}_{tri}+\lambda_{KL}\mathcal{L}_{KL}+\lambda_{stri}\mathcal{L}_{stri}$

(1)

where $\lambda_{tri}$, $\lambda_{KL}$, $\lambda_{stri}$ indicate corresponding loss weights.

For clustering-based UDA person ReID, the pseudo labels are noisy, which would mislead the network training in the target fine-tuning stage and hurt the performance in target domain. To reduce the effects of noise, uncertainty estimation is a natural way to eliminate the unreliable pseudo labels. To establish the uncertainty criterion, we present the output probabilistic distribution of samples with correct and wrong labels for an investigative study. As shown in Figure 3a, the sample with wrong pseudo labels is associated with high probabilistic uncertainty, which has several peaks and generally reaches high in different identities. In contrast, the sample with correct pseudo labels is associated with low probabilistic uncertainty (Figure 3b). The assigned probability peaks high in the correct identity and remains nearly zero in other identities. This is consistent with the intuitive idea that the samples with wrong pseudo labels are ambiguous for model prediction, which is significantly distinct to correct pseudo labels.

Inspired by this observation, we leverage the distribution difference as the probabilistic uncertainty to softly evaluate the noisy level of samples. Each unlabeled sample $x_{i}$ in the target domain is assigned with a pseudo label $\tilde{y}_{i}$ by clustering. Based on the clustering at $t$-th step, we build an external classifier $\phi_{t}(\cdot|w^{cls}_{t})$, where $w^{cls}_{t}\in\mathbb{R}^{c\times d}$ is the parameterized weights of the external classifier. Note that the weights are generated dynamically and don’t need separate training. Here we employ $c$ cluster centroids of $d$ dimensions as classifier weights. For a feature $f_{i}\in\mathbb{R}^{d}$ of sample $(x_{i},\tilde{y}_{i})$ extracted by the mean teacher, we obtain classified probability distributions among identities with this classifier following Eq.2. Here $\alpha$ is the temperature parameter.

$$P{(x_{i},\tilde{y}_{i})}=\phi_{t}(f_{i})=Softmax\left(\frac{w^{cls}_{t}}{||w^{cls}_{t}||}\cdot\frac{f_{i}}{||f_{i}||}\cdot\alpha\right)$$

(2)

In source domain, we obtain a single impulse distribution for samples after symmetrically arranging the probability from large to small while making $y^{s}_{i}$ as the center. This phenomenon motivates us to model the generalized ideal distributions for samples in the target domain. We find that the smoothed $\delta$ distribution associative with large temperature $\alpha$ is highly stable and insensitive to specific datasets. When $\alpha$ decreases ($\alpha$ controls the variety of distributions), another distribution might be better for some cases but hard to generalize. Therefore, we draw the smoothed $\delta$ distribution (Eq.LABEL:eq:qfunc) as the ideal distribution $Q(x_{i},\tilde{y}_{i})$.

$$Q(x_{i},\tilde{y}_{i})=\delta_{smooth}(j-\tilde{y}_{i})=\left\{\begin{aligned} &\quad\epsilon,\quad if~{}~{}j=\tilde{y}_{i}\\ &\frac{1-\epsilon}{c-1},otherwise\\ \end{aligned}\right.$$

(3)

where $j$ is the identity index and $c$ is the number of identities (i.e. the number of clusters). $\epsilon$ is a hyperparameter and is set to 0.99.

We estimate the probabilistic distance of the predicted probability across identities and the ideal distribution to measure the uncertainty of samples. Rather than measuring the feature inconsistency of teacher-student models (Zheng et al. 2021a), we define a criterion named probabilistic uncertainty, which measures the inconsistency between predicted distribution $P{(x_{i},\tilde{y}_{i})}$ and the ideal distribution $Q(x_{i},\tilde{y}_{i})$. Moreover, we leverage the Kullback–Leibler (KL) divergence to measure the inconsistency and establish the probabilistic uncertainty as:

$$U~{}\left(x_{i},\tilde{y}_{i}\right)=D_{KL}\left(Q\left(x_{i},\tilde{y}_{i}\right)||P(x_{i},\tilde{y}_{i})\right)$$

(4)

Larger $U~{}(x_{i},\tilde{y}_{i})$ indicates that the pseudo label generated by clustering is more likely to be wrong, which should be excluded in the target fine-tuning stages. As in Figure 3c, our probabilistic uncertainty is highly related to correctness.

We formulate the uncertainty guided domain adaption mathematically. The model can be denoted as $\emph{M}(\cdot|\mathbf{w})$, where $\mathbf{w}$ is the associated parameters. Each model maps a sample $x_{i}$ to the prediction $M\left(x_{i}|\mathbf{w}\right)$. An uncertainty score can be further obtained, as $u_{i}=U(x_{i},\tilde{y}_{i}|\mathbf{w})$. $U$ is the label uncertainty estimation module. The uncertainty guided learning can be formulated as a joint optimization problem as:

$\displaystyle\min_{\mathbf{w};\mathbf{v}\in{\{0,1\}}^{N}}\mathbb{E}(\mathbf{w},\mathbf{v};\beta)=\sum_{i=1}^{N}v_{i}u_{i}-\beta\sum_{i=1}^{N}v_{i}$

(5)

where $v_{i}\in{\{0,1\}}$ is the indicator for sample selection. $\beta$ is the age parameter to control the learning pace. That is, we need to reduce the overall uncertainty of select samples while selecting as many samples as possible for sufficient training. To optimize the above objective function, we adopt Alternative Convex Search (Gorski, Pfeuffer, and Klamroth 2007). In particular, $\mathbf{w}$ and $\mathbf{v}$ are alternatively optimized while fix the other. With the fixed $\mathbf{w}^{*}$, the global optimum $\mathbf{v}^{*}$ is solved as:

$\displaystyle\mathbf{v}^{*}=\arg\min_{v_{i}\in\{0,1\}}\sum_{i=1}^{N}v_{i}u_{i}-\beta\sum_{i=1}^{N}v_{i}$

(6)

When $\mathbf{v}^{*}$ is fixed, the global optimum $\mathbf{w}^{*}$ is solved as:

$\displaystyle\mathbf{w}^{*}=\arg\min_{\mathbf{w}}\sum^{N}_{i=1}v^{*}_{i}u_{i}$

(7)

The two optimization steps are iteratively conducted, while $\beta$ is gradually increased to add more harder samples.

Uncertainty guided sample selection. With the proposed uncertainty measurement, the solution for Eq.7 is provided by gradient descent based network training. With fixed $\mathbf{w}^{*}$, finding the optimal $\mathbf{v}$ is converted into a combinatorial optimization issue with the linear objective function. We can simply derive the global minimum by setting the partial derivative of Eq.6 to $v_{i}$ as zero. Considering $v_{i}$ is either 0 or 1, we obtain the close-formed solution $\mathbf{v}^{*}$ as:

$$v^{*}_{i}=\left\{\begin{aligned} 1,~{}~{}if~{}~{}u_{i}\leq\beta\\ 0,~{}~{}otherwise\\ \end{aligned}\right.$$

(8)

Since clustering and target fine-tuning stages are iterated in an alternative way for multiple steps, we need to determine how many samples are included. A sequence $\{N\cdot p_{t}\},t=0,1,\cdots,T$ is predefined for this purpose, where $N\cdot p_{t}$ is the number of selected examples at iteration time $t$. Based on the predefined $p_{t}$, the threshold $\beta$ is dynamically updated according to Eq.9 to ensure exactly $N\cdot p_{t}$ samples are assigned with non-zero $v_{i}$.

$$\beta=Sort\{u_{1},u_{2},...,u_{N}\}_{(N\cdot p_{t})}$$

(9)

Note that as the training proceeds, the models become more reliable. Consequently, the measured uncertainty reduces drastically at the beginning, then converges slowly with larger $t$ (Figure 4(left)). As the result, $p_{t}$ should be enlarged as $t$ increases. To be consistent with the trends of uncertainty reduction, we design $p_{t}$ as a rescaled logarithm-exponential function:

$$p_{t}=p(t)=p_{0}+\frac{1}{h}\ln\left(1+\left(e^{h\cdot(1-p_{0})}-1\right)\cdot\frac{t}{T}\right)$$

(10)

$p_{0}$ is the initial proportion of samples for fine-tuning in target domain. The setting of $p_{0}$ enables the model to learn from sufficient easy samples at early steps, to avoid falling into the negative loop of degrading. $h$ is the hyper-parameter to control the increasing rate of samples (Figure 4(right)). Because the rate of adding examples is negatively correlated to the size of the current training set, the number of newly added examples is reduced as the training proceeds. More importantly, the uncertainty decreases dramatically when $t$ is small, we enlarge the set of samples in a fast way. As $t$ increases, the uncertainty converges and the set of samples for fine-tuning increases slowly for stable training. This progressive label refinery would help the model learn sufficiently from the newly added samples in target domain.

We implement our model based on MMT (Ge, Chen, and Li 2020) and train it on four Tesla XP GPUs. ADAM optimizer is adopted to optimize models with the weight decay of 5e-4. We employ ImageNet (Deng et al. 2009) pre-trained ResNet50 (He et al. 2016) as the backbone. We obey normal $P-K$ sampling in person ReID, where $P=4$ and $K=16$ in each mini-batch. Then we perform data augmentation of random cropping, flipping, and erasing. Note that random erasing is not utilized in the source pre-training stage. All person images are resized to $256\times 128$. We use the clustering algorithm of k-means where the number of clusters ($c$) is set as 500, 700, and 1500 for Market, Duke, and MSMT datasets, respectively. The temperature parameter $\alpha$ in Eq.2 is set to 20. The parameter $p_{0}$ and $h$ in Eq.10 are set to 0.3 and 1.5, respectively. Overall alternative optimization steps $T$ are set to 100. In source pre-training stage, the initial learning rate is set to $3.5\times 10^{-4}$ and is decreased by 1/10 on the 40th and 70th epoch in the total 80 epochs. In target fine-tuning stage, the learning rate is fixed to $3.5\times 10^{-4}$.

We evaluate our method on three main-stream person ReID datasets, i.e., Market-1501 (Market) (Zheng et al. 2015), DukeMTMC-reID (Duke) (Ristani et al. 2016), and MSMT17 (MSMT) (Wei et al. 2018). The Market-1501 dataset contains 32,668 annotated images of 1,501 identities shot from 6 cameras, where 12,936 images of 751 identities are used for training and 19,732 images of 750 identities for testing.The DukeMTMC-reID dataset consists of 36,411 images collected from 8 cameras, where 702 identities are used for training and 702 identities for testing. MSMT17 is the most challenging and largest person ReID dataset consisting of 126,441 images of 4,101 identities, where 1,041 identities and 3,060 identities are used for training and testing, respectively. We adopt mean average precision (mAP) and CMC Rank-1/5/10 (R1/R5/R10) accuracy without re-ranking (Zhong et al. 2017) for evaluation.

We compare our method against the state-of-the-art (SOTA) methods on four UDA ReID settings and present the results in Table 1. Among existing methods for UDA person ReID, DAAM (Huang et al. 2020a) introduces domain alignment constraints and an attention module. SSG (Fu et al. 2019), MMT (Ge, Chen, and Li 2020), MEB-Net (Zhai et al. 2020b), and UNRN (Zheng et al. 2021a) are all clustering-based methods. SSG (Fu et al. 2019) employs both global body and local body part features for clustering and evaluation. We construct the baseline based on MMT (Ge, Chen, and Li 2020) which introduces mutual mean teacher for UDA person ReID. Compared to the baseline MMT (Ge, Chen, and Li 2020), our proposed P²LR significantly improves the UDA ReID accuracy, with 9.8%, 5.7%, 6.1%, and 6.6% mAP improvements on four UDA ReID settings. Compared to MEB-Net (Zhai et al. 2020b) which establishes three networks to perform mutual mean learning, we increase the mAP by 5.0%, 4.7% with a simpler architecture design. Notably, UNRN and GLT leverage source data during target fine-tuning stage and build an external support memory to mine hard pairs. Our P²LR still achieves 3.7% and 3.7% mAP gains to UNRN, 2.5% and 2.2% mAP gains to GLT on the MSMT dataset. In general, our method P²LR achieves the state-of-the-art performance on all datasets, which verifies the effectiveness of P²LR.

In this section, we carry out extensive ablation studies to validate the effectiveness of each component in P²LR.

Effectiveness of progressive label refinery. To alleviate the negative effects of noisy/wrong pseudo labels, we exploit the characteristics of probability distribution among identities to evaluate probabilistic uncertainty of pseudo labels and refine the pseudo labels by alternative optimization. We validate the effectiveness of the proposed progressive label refinery module by comparing the performance of Baseline and Baseline+P²LR. Without P²LR, the achieved mAP and Rank-1 accuracy are 74.5% and 90.3%, respectively. With P²LR, the achieved mAP is 81.0% and Rank-1 accuracy is 92.6%, respectively. The mAP is significantly improved by 6.5% with the sole P²LR on the Duke2Market task. The results show that the proposed method is effective to alleviate the negative effects caused by noisy/wrong pseudo labels and significantly improves UDA person ReID performance.

Different designs of label correctness estimation. A straightforward way to evaluate the uncertainty of pseudo labels is referring to the $l_{2}$ distance to the nearest centroid in feature space. As shown in Table 2, the mAP and Rank-1 accuracy is improved by 3.2% and 1.8% with the probabilistic uncertainty criterion. That is because the probability distribution based uncertainty evaluation considers more global references than $l_{2}$ distance in local feature space. Besides, we find introducing an external classifier with cluster centroid for uncertainty evaluation outperforms internal classifiers in $\emph{M}(\cdot|\mathbf{w})$. It can be attributed to the fact that internal classifiers are more easily misled by noisy labeling during training. External classifiers whose weights are generated by clustering could correct the misleading to some extent.

We compare our label evaluation method to prediction consistency based method UNRN. Our method surpasses UNRN with large margins. The uncertainty (noise level) of pseudo labels should be measured from the intrinsic property of its own probabilistic distribution, especially for UDA ReID. Since noise already exists in teacher models, the consistency-based uncertainty as in UNRN might overfit biased teacher models.

Progressive label refinery vs Sample Reweighting. We compare the label refinery with reweighting method proposed in UNRN (Zheng et al. 2021a). In general, our method filters out wrong labels with the guidance of uncertainty, while the reweighting-based method reduces the negative influence in loss functions. The comparative results are presented in Table 2. The proposed progressive label refinery significantly outperforms reweighting method. It indicates that removing wrong labeled samples in training is more effective for reducing their negative influence.

Parameter analysis. We experiment with different ideal distribution $Q$ by setting different $\epsilon$. We present the mAP/R1/R5/R10 in Table 2 and mAP curves with the number of refinery steps in Figure 6a, respectively. It can be seen $\epsilon$ has important impacts while the mAP curve of $\epsilon$=0.99 grows fastest and highest. Therefore, we set $\epsilon$=0.99 for all other experiments. We then explore the influence of temperature parameter $\alpha$ in the uncertainty measurement while setting $p_{0}=0.2$ in Figure 6b. The achieved mAP and Rank-1 accuracy maintain high when $\alpha$ is set to $20\sim 50$. When $\alpha=20$, the achieved mAP is 80.4% and Rank-1 accuracy is 91.4%. When $\alpha=50$, the achieved mAP is 80.2% and Rank-1 accuracy is 92.0%. Afterwards, we present the influence of $p_{0}$ in progressive label refinery Figure 6c setting $\alpha=20$. The mAP and Rank-1 accuracy reach peak (81.0% and 92.6%) when $p$ is around 0.3. It indicates we preserve about 30% of samples and eliminate 70% ones in the early refinery steps. We progressively exploit more uncertain samples in later refinery steps for strong performance.

Visualization. We present the visualization results to validate the effectiveness of probabilistic uncertainty measurement for selecting samples. The selected certain samples and un-selected uncertain samples of three clusters determined by the proposed criterion in the first refinery step are presented in Figure 5. It can be observed that most selected samples are from the same identity while un-selected samples are hard samples of the identity or from other identities. By combining the selected certain samples with high confidence into target domain fine-tuning, the proposed P²LR can achieve superior UDA person ReID performance.